| Label |
Name |
Order |
Exponent |
Nilp. class |
Der. length |
Comp. length |
Rank |
$\card{\mathrm{conj}(G)}$ |
Subgroups |
Subgroup classes |
Normal subgroups |
Center |
Central quotient |
Commutator |
Abelianization |
$\card{\mathrm{Aut}(G)}$ |
$\card{\mathrm{Out}(G)}$ |
Tr. deg |
Perm. deg |
$\C$-irrep deg |
$\R$-irrep deg |
$\Q$-irrep deg |
$\C$-rep deg |
$\R$-rep deg |
$\Q$-rep deg |
Type - length |
| 513.1 |
$C_{19}:C_{27}$ |
$3^{3} \cdot 19$ |
$3^{3} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$81$ |
$26$ |
$8$ |
$7$ |
$C_9$ |
$C_{19}:C_3$ |
$C_{19}$ |
$C_{27}$ |
$2 \cdot 3^{4} \cdot 19$ |
$2 \cdot 3^{3}$ |
$513$ |
$46$ |
$3$ |
$6$ |
$324$ |
$3$ |
$6$ |
$36$ |
Solvable - 2 |
| 513.2 |
$C_{513}$ |
$3^{3} \cdot 19$ |
$3^{3} \cdot 19$ |
$1$ |
$1$ |
$4$ |
$1$ |
$513$ |
$8$ |
$8$ |
$8$ |
$C_{513}$ |
$C_1$ |
$C_1$ |
$C_{513}$ |
$2^{2} \cdot 3^{4}$ |
$2^{2} \cdot 3^{4}$ |
$513$ |
$46$ |
$1$ |
? |
$324$ |
$1$ |
? |
? |
Cyclic |
| 513.3 |
$C_{19}:C_{27}$ |
$3^{3} \cdot 19$ |
$3^{3} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$33$ |
$44$ |
$8$ |
$6$ |
$C_3$ |
$C_{19}:C_9$ |
$C_{19}$ |
$C_{27}$ |
$2 \cdot 3^{3} \cdot 19$ |
$2 \cdot 3$ |
$513$ |
$46$ |
$9$ |
$18$ |
$108$ |
$9$ |
$18$ |
$36$ |
Solvable - 2 |
| 513.4 |
$C_{171}:C_3$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$81$ |
$146$ |
$20$ |
$13$ |
$C_9$ |
$C_{19}:C_3$ |
$C_{19}$ |
$C_{3} \times C_{9}$ |
$2^{2} \cdot 3^{4} \cdot 19$ |
$2^{2} \cdot 3^{3}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Solvable - 2 |
| 513.5 |
$C_{171}:C_3$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$65$ |
$146$ |
$16$ |
$10$ |
$C_3$ |
$C_{57}:C_3$ |
$C_{57}$ |
$C_{3}^{2}$ |
$2^{2} \cdot 3^{4} \cdot 19$ |
$2^{2} \cdot 3^{2}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Solvable - 2 |
| 513.6 |
$C_{171}:C_3$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$65$ |
$146$ |
$16$ |
$10$ |
$C_3$ |
$C_{57}:C_3$ |
$C_{57}$ |
$C_{3}^{2}$ |
$2^{2} \cdot 3^{4} \cdot 19$ |
$2^{2} \cdot 3^{2}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Solvable - 2 |
| 513.7 |
$C_{57}:C_9$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$81$ |
$92$ |
$20$ |
$16$ |
$C_3^2$ |
$C_{19}:C_3$ |
$C_{19}$ |
$C_{3} \times C_{9}$ |
$2^{2} \cdot 3^{5} \cdot 19$ |
$2^{2} \cdot 3^{4}$ |
$513$ |
$31$ |
$-$ |
$-$ |
$-$ |
$4$ |
$8$ |
$26$ |
Solvable - 2 |
| 513.8 |
$C_{57}.C_3^2$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$65$ |
$92$ |
$16$ |
$10$ |
$C_3$ |
$C_{57}:C_3$ |
$C_{57}$ |
$C_{3}^{2}$ |
$2 \cdot 3^{5} \cdot 19$ |
$2 \cdot 3^{3}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Solvable - 2 |
| 513.9 |
$C_{19}:\He_3$ |
$3^{3} \cdot 19$ |
$3 \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$65$ |
$272$ |
$22$ |
$10$ |
$C_3$ |
$C_{57}:C_3$ |
$C_{57}$ |
$C_{3}^{2}$ |
$2^{2} \cdot 3^{5} \cdot 19$ |
$2^{2} \cdot 3^{3}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Solvable - 2 |
| 513.10 |
$C_3\times C_{171}$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$1$ |
$1$ |
$4$ |
$2$ |
$513$ |
$20$ |
$20$ |
$20$ |
$C_3\times C_{171}$ |
$C_1$ |
$C_1$ |
$C_{3} \times C_{171}$ |
$2^{3} \cdot 3^{5}$ |
$2^{3} \cdot 3^{5}$ |
$513$ |
$31$ |
$-$ |
? |
$-$ |
$2$ |
? |
? |
Abelian - 2 |
| 513.11 |
$C_{19}\times \He_3$ |
$3^{3} \cdot 19$ |
$3 \cdot 19$ |
$2$ |
$2$ |
$4$ |
$2$ |
$209$ |
$38$ |
$22$ |
$14$ |
$C_{57}$ |
$C_3^2$ |
$C_3$ |
$C_{3} \times C_{57}$ |
$2^{5} \cdot 3^{5}$ |
$2^{5} \cdot 3^{3}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Nilpotent - 2 |
| 513.12 |
$C_9:C_{57}$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$2$ |
$2$ |
$4$ |
$2$ |
$209$ |
$20$ |
$16$ |
$14$ |
$C_{57}$ |
$C_3^2$ |
$C_3$ |
$C_{3} \times C_{57}$ |
$2^{2} \cdot 3^{5}$ |
$2^{2} \cdot 3^{3}$ |
$171$ |
$28$ |
$3$ |
$6$ |
$108$ |
$3$ |
$6$ |
$24$ |
Nilpotent - 2 |
| 513.13 |
$C_{57}:C_9$ |
$3^{3} \cdot 19$ |
$3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$33$ |
$164$ |
$20$ |
$12$ |
$C_3$ |
$C_{19}:C_9$ |
$C_{19}$ |
$C_{3} \times C_{9}$ |
$2^{2} \cdot 3^{3} \cdot 19$ |
$2^{2} \cdot 3$ |
$57$ |
$22$ |
$9$ |
$18$ |
$36$ |
$9$ |
$18$ |
$20$ |
Solvable - 2 |
| 513.14 |
$C_{19}:C_3^3$ |
$3^{3} \cdot 19$ |
$3 \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$81$ |
$452$ |
$56$ |
$34$ |
$C_3^2$ |
$C_{19}:C_3$ |
$C_{19}$ |
$C_{3}^{3}$ |
$2^{5} \cdot 3^{5} \cdot 19$ |
$2^{5} \cdot 3^{4}$ |
$171$ |
$25$ |
$-$ |
$-$ |
$-$ |
$4$ |
$8$ |
$22$ |
Solvable - 2 |
| 513.15 |
$C_3^2\times C_{57}$ |
$3^{3} \cdot 19$ |
$3 \cdot 19$ |
$1$ |
$1$ |
$4$ |
$3$ |
$513$ |
$56$ |
$56$ |
$56$ |
$C_3^2\times C_{57}$ |
$C_1$ |
$C_1$ |
$C_{3}^{2} \times C_{57}$ |
$2^{6} \cdot 3^{5} \cdot 13$ |
$2^{6} \cdot 3^{5} \cdot 13$ |
$513$ |
$28$ |
$-$ |
? |
$-$ |
$3$ |
? |
? |
Abelian - 3 |
| 514.1 |
$D_{257}$ |
$2 \cdot 257$ |
$2 \cdot 257$ |
$-1$ |
$2$ |
$2$ |
$2$ |
$130$ |
$260$ |
$4$ |
$3$ |
$C_1$ |
$D_{257}$ |
$C_{257}$ |
$C_{2}$ |
$2^{8} \cdot 257$ |
$2^{7}$ |
$257$ |
$257$ |
$2$ |
$2$ |
$256$ |
$2$ |
$2$ |
$256$ |
Solvable - 2 |
| 514.2 |
$C_{514}$ |
$2 \cdot 257$ |
$2 \cdot 257$ |
$1$ |
$1$ |
$2$ |
$1$ |
$514$ |
$4$ |
$4$ |
$4$ |
$C_{514}$ |
$C_1$ |
$C_1$ |
$C_{514}$ |
$2^{8}$ |
$2^{8}$ |
$514$ |
$259$ |
$1$ |
? |
$256$ |
$1$ |
? |
? |
Cyclic |
| 515.1 |
$C_{515}$ |
$5 \cdot 103$ |
$5 \cdot 103$ |
$1$ |
$1$ |
$2$ |
$1$ |
$515$ |
$4$ |
$4$ |
$4$ |
$C_{515}$ |
$C_1$ |
$C_1$ |
$C_{515}$ |
$2^{3} \cdot 3 \cdot 17$ |
$2^{3} \cdot 3 \cdot 17$ |
$515$ |
$108$ |
$1$ |
? |
$408$ |
$1$ |
? |
? |
Cyclic |
| 516.1 |
$C_{43}:C_{12}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2^{2} \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$26$ |
$180$ |
$12$ |
$8$ |
$C_2$ |
$C_{43}:C_6$ |
$C_{43}$ |
$C_{12}$ |
$2^{2} \cdot 3 \cdot 7 \cdot 43$ |
$2 \cdot 7$ |
$172$ |
$47$ |
$6$ |
$12$ |
$84$ |
$6$ |
$8$ |
$44$ |
Solvable - 2 |
| 516.2 |
$C_{172}:C_3$ |
$2^{2} \cdot 3 \cdot 43$ |
$2^{2} \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$68$ |
$138$ |
$12$ |
$9$ |
$C_4$ |
$C_{43}:C_3$ |
$C_{43}$ |
$C_{12}$ |
$2^{2} \cdot 3 \cdot 7 \cdot 43$ |
$2^{2} \cdot 7$ |
$172$ |
$47$ |
$3$ |
$6$ |
$84$ |
$3$ |
$6$ |
$44$ |
Solvable - 2 |
| 516.3 |
$C_3:C_{172}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2^{2} \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$258$ |
$16$ |
$12$ |
$10$ |
$C_{86}$ |
$S_3$ |
$C_3$ |
$C_{172}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$516$ |
$50$ |
$2$ |
$4$ |
$84$ |
$2$ |
$4$ |
$46$ |
Solvable - 2 |
| 516.4 |
$C_{129}:C_4$ |
$2^{2} \cdot 3 \cdot 43$ |
$2^{2} \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$138$ |
$96$ |
$12$ |
$10$ |
$C_6$ |
$D_{43}$ |
$C_{43}$ |
$C_{12}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7$ |
$516$ |
$50$ |
$2$ |
$4$ |
$168$ |
$2$ |
$4$ |
$46$ |
Solvable - 2 |
| 516.5 |
$C_{129}:C_4$ |
$2^{2} \cdot 3 \cdot 43$ |
$2^{2} \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$132$ |
$184$ |
$12$ |
$9$ |
$C_2$ |
$D_{129}$ |
$C_{129}$ |
$C_{4}$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7$ |
$516$ |
$50$ |
$2$ |
$4$ |
$168$ |
$2$ |
$4$ |
$46$ |
Solvable - 2 |
| 516.6 |
$C_{516}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2^{2} \cdot 3 \cdot 43$ |
$1$ |
$1$ |
$4$ |
$1$ |
$516$ |
$12$ |
$12$ |
$12$ |
$C_{516}$ |
$C_1$ |
$C_1$ |
$C_{516}$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$516$ |
$50$ |
$1$ |
? |
$168$ |
$1$ |
? |
? |
Cyclic |
| 516.7 |
$C_{86}:C_6$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$26$ |
$356$ |
$20$ |
$12$ |
$C_2$ |
$C_{43}:C_6$ |
$C_{43}$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3 \cdot 7 \cdot 43$ |
$2 \cdot 7$ |
$86$ |
$45$ |
$6$ |
$6$ |
$42$ |
$6$ |
$6$ |
$42$ |
Solvable - 2 |
| 516.8 |
$S_3\times D_{43}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$69$ |
$452$ |
$20$ |
$10$ |
$C_1$ |
$S_3\times D_{43}$ |
$C_{129}$ |
$C_{2}^{2}$ |
$2^{2} \cdot 3^{2} \cdot 7 \cdot 43$ |
$3 \cdot 7$ |
$129$ |
$46$ |
$4$ |
$4$ |
$84$ |
$4$ |
$4$ |
$44$ |
Solvable - 2 |
| 516.9 |
$C_{86}:C_6$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$68$ |
$230$ |
$20$ |
$15$ |
$C_2^2$ |
$C_{43}:C_3$ |
$C_{43}$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7$ |
$172$ |
$47$ |
$-$ |
$-$ |
$-$ |
$4$ |
$7$ |
$43$ |
Solvable - 2 |
| 516.10 |
$A_4\times C_{43}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$172$ |
$20$ |
$10$ |
$6$ |
$C_{43}$ |
$A_4$ |
$C_2^2$ |
$C_{129}$ |
$2^{4} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$172$ |
$47$ |
$3$ |
$6$ |
$126$ |
$3$ |
$5$ |
$45$ |
Solvable - 2 |
| 516.11 |
$C_{43}:A_4$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$60$ |
$230$ |
$10$ |
$5$ |
$C_1$ |
$C_{43}:A_4$ |
$C_2\times C_{86}$ |
$C_{3}$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 43$ |
$2 \cdot 3 \cdot 7$ |
$172$ |
$47$ |
$3$ |
$6$ |
$126$ |
$3$ |
$6$ |
$45$ |
Solvable - 2 |
| 516.12 |
$C_3\times D_{86}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$138$ |
$272$ |
$20$ |
$14$ |
$C_6$ |
$D_{43}$ |
$C_{43}$ |
$C_{2} \times C_{6}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7$ |
$258$ |
$48$ |
$2$ |
$4$ |
$84$ |
$2$ |
$4$ |
$44$ |
Solvable - 2 |
| 516.13 |
$S_3\times C_{86}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$258$ |
$32$ |
$20$ |
$14$ |
$C_{86}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{86}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$258$ |
$48$ |
$2$ |
$4$ |
$84$ |
$2$ |
$4$ |
$44$ |
Solvable - 2 |
| 516.14 |
$D_{258}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$132$ |
$536$ |
$20$ |
$11$ |
$C_2$ |
$D_{129}$ |
$C_{129}$ |
$C_{2}^{2}$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7$ |
$258$ |
$48$ |
$2$ |
$2$ |
$84$ |
$2$ |
$2$ |
$44$ |
Solvable - 2 |
| 516.15 |
$C_2\times C_{258}$ |
$2^{2} \cdot 3 \cdot 43$ |
$2 \cdot 3 \cdot 43$ |
$1$ |
$1$ |
$4$ |
$2$ |
$516$ |
$20$ |
$20$ |
$20$ |
$C_2\times C_{258}$ |
$C_1$ |
$C_1$ |
$C_{2} \times C_{258}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$516$ |
$50$ |
$-$ |
? |
$-$ |
$2$ |
? |
? |
Abelian - 2 |
| 517.1 |
$C_{517}$ |
$11 \cdot 47$ |
$11 \cdot 47$ |
$1$ |
$1$ |
$2$ |
$1$ |
$517$ |
$4$ |
$4$ |
$4$ |
$C_{517}$ |
$C_1$ |
$C_1$ |
$C_{517}$ |
$2^{2} \cdot 5 \cdot 23$ |
$2^{2} \cdot 5 \cdot 23$ |
$517$ |
$58$ |
$1$ |
? |
$460$ |
$1$ |
? |
? |
Cyclic |
| 518.1 |
$D_7\times C_{37}$ |
$2 \cdot 7 \cdot 37$ |
$2 \cdot 7 \cdot 37$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$185$ |
$20$ |
$8$ |
$6$ |
$C_{37}$ |
$D_7$ |
$C_7$ |
$C_{74}$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$2^{2} \cdot 3^{3}$ |
$259$ |
$44$ |
$2$ |
$4$ |
$216$ |
$2$ |
$4$ |
$42$ |
Solvable - 2 |
| 518.2 |
$C_7\times D_{37}$ |
$2 \cdot 7 \cdot 37$ |
$2 \cdot 7 \cdot 37$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$140$ |
$80$ |
$8$ |
$6$ |
$C_7$ |
$D_{37}$ |
$C_{37}$ |
$C_{14}$ |
$2^{3} \cdot 3^{3} \cdot 37$ |
$2^{2} \cdot 3^{3}$ |
$259$ |
$44$ |
$2$ |
$4$ |
$216$ |
$2$ |
$4$ |
$42$ |
Solvable - 2 |
| 518.3 |
$D_{259}$ |
$2 \cdot 7 \cdot 37$ |
$2 \cdot 7 \cdot 37$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$131$ |
$308$ |
$8$ |
$5$ |
$C_1$ |
$D_{259}$ |
$C_{259}$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 7 \cdot 37$ |
$2^{2} \cdot 3^{3}$ |
$259$ |
$44$ |
$2$ |
$2$ |
$216$ |
$2$ |
$2$ |
$42$ |
Solvable - 2 |
| 518.4 |
$C_{518}$ |
$2 \cdot 7 \cdot 37$ |
$2 \cdot 7 \cdot 37$ |
$1$ |
$1$ |
$3$ |
$1$ |
$518$ |
$8$ |
$8$ |
$8$ |
$C_{518}$ |
$C_1$ |
$C_1$ |
$C_{518}$ |
$2^{3} \cdot 3^{3}$ |
$2^{3} \cdot 3^{3}$ |
$518$ |
$46$ |
$1$ |
? |
$216$ |
$1$ |
? |
? |
Cyclic |
| 519.1 |
$C_{519}$ |
$3 \cdot 173$ |
$3 \cdot 173$ |
$1$ |
$1$ |
$2$ |
$1$ |
$519$ |
$4$ |
$4$ |
$4$ |
$C_{519}$ |
$C_1$ |
$C_1$ |
$C_{519}$ |
$2^{3} \cdot 43$ |
$2^{3} \cdot 43$ |
$519$ |
$176$ |
$1$ |
? |
$344$ |
$1$ |
? |
? |
Cyclic |
| 520.1 |
$C_5:C_{104}$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$208$ |
$24$ |
$16$ |
$14$ |
$C_{52}$ |
$D_5$ |
$C_5$ |
$C_{104}$ |
$2^{6} \cdot 3 \cdot 5$ |
$2^{5} \cdot 3$ |
$520$ |
$26$ |
$2$ |
$4$ |
$96$ |
$2$ |
$4$ |
$20$ |
Solvable - 2 |
| 520.2 |
$C_{13}:C_{40}$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$160$ |
$40$ |
$16$ |
$14$ |
$C_{20}$ |
$D_{13}$ |
$C_{13}$ |
$C_{40}$ |
$2^{6} \cdot 3 \cdot 13$ |
$2^{5} \cdot 3$ |
$520$ |
$26$ |
$2$ |
$4$ |
$96$ |
$2$ |
$4$ |
$20$ |
Solvable - 2 |
| 520.3 |
$C_{65}:C_8$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$136$ |
$96$ |
$16$ |
$13$ |
$C_4$ |
$D_{65}$ |
$C_{65}$ |
$C_{8}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 13$ |
$2^{5} \cdot 3$ |
$520$ |
$26$ |
$2$ |
$4$ |
$96$ |
$2$ |
$4$ |
$20$ |
Solvable - 2 |
| 520.4 |
$C_{520}$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$1$ |
$1$ |
$5$ |
$1$ |
$520$ |
$16$ |
$16$ |
$16$ |
$C_{520}$ |
$C_1$ |
$C_1$ |
$C_{520}$ |
$2^{6} \cdot 3$ |
$2^{6} \cdot 3$ |
$520$ |
$26$ |
$1$ |
? |
$192$ |
$1$ |
? |
? |
Cyclic |
| 520.5 |
$C_{13}:C_{40}$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$70$ |
$64$ |
$16$ |
$12$ |
$C_{10}$ |
$C_{13}:C_4$ |
$C_{13}$ |
$C_{40}$ |
$2^{5} \cdot 3 \cdot 13$ |
$2^{3} \cdot 3$ |
$520$ |
$26$ |
$4$ |
$8$ |
$48$ |
$4$ |
$6$ |
$20$ |
Solvable - 2 |
| 520.6 |
$C_{65}:C_8$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$46$ |
$120$ |
$16$ |
$11$ |
$C_2$ |
$C_{65}:C_4$ |
$C_{65}$ |
$C_{8}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13$ |
$2^{3} \cdot 3$ |
$520$ |
$26$ |
$4$ |
$8$ |
$48$ |
$4$ |
$8$ |
$20$ |
Solvable - 2 |
| 520.7 |
$C_5:C_{104}$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$130$ |
$32$ |
$16$ |
$12$ |
$C_{26}$ |
$F_5$ |
$C_5$ |
$C_{104}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3$ |
$520$ |
$26$ |
$4$ |
$8$ |
$48$ |
$4$ |
$6$ |
$20$ |
Solvable - 2 |
| 520.8 |
$C_{65}:C_8$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$58$ |
$104$ |
$16$ |
$11$ |
$C_2$ |
$C_{65}:C_4$ |
$C_{65}$ |
$C_{8}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13$ |
$2^{3} \cdot 3$ |
$520$ |
$26$ |
$4$ |
$8$ |
$48$ |
$4$ |
$8$ |
$20$ |
Solvable - 2 |
| 520.9 |
$C_{65}:C_8$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$40$ |
$176$ |
$16$ |
$10$ |
$C_2$ |
$C_{65}:C_4$ |
$C_{65}$ |
$C_{8}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13$ |
$2^{3} \cdot 3$ |
$520$ |
$26$ |
$4$ |
$8$ |
$96$ |
$4$ |
$6$ |
$20$ |
Solvable - 2 |
| 520.10 |
$C_{65}:C_8$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{3} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$40$ |
$176$ |
$16$ |
$10$ |
$C_2$ |
$C_{65}:C_4$ |
$C_{65}$ |
$C_{8}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13$ |
$2^{3} \cdot 3$ |
$520$ |
$26$ |
$4$ |
$8$ |
$96$ |
$4$ |
$6$ |
$20$ |
Solvable - 2 |
| 520.11 |
$C_{10}.D_{26}$ |
$2^{3} \cdot 5 \cdot 13$ |
$2^{2} \cdot 5 \cdot 13$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$64$ |
$272$ |
$32$ |
$18$ |
$C_2$ |
$D_5\times D_{13}$ |
$C_{65}$ |
$C_{2} \times C_{4}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 13$ |
$2^{4} \cdot 3$ |
$260$ |
$22$ |
$4$ |
$8$ |
$96$ |
$4$ |
$6$ |
$18$ |
Solvable - 2 |
