| 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 |
| 60.1 |
$C_3:C_{20}$ |
$2^{2} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$16$ |
$12$ |
$10$ |
$C_{10}$ |
$S_3$ |
$C_3$ |
$C_{20}$ |
$2^{4} \cdot 3$ |
$2^{3}$ |
$60$ |
$12$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 60.2 |
$C_5:C_{12}$ |
$2^{2} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$24$ |
$20$ |
$12$ |
$10$ |
$C_6$ |
$D_5$ |
$C_5$ |
$C_{12}$ |
$2^{4} \cdot 5$ |
$2^{3}$ |
$60$ |
$12$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 60.3 |
$C_{15}:C_4$ |
$2^{2} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$18$ |
$32$ |
$12$ |
$9$ |
$C_2$ |
$D_{15}$ |
$C_{15}$ |
$C_{4}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{3}$ |
$60$ |
$12$ |
$2$ |
$4$ |
$16$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 60.5 |
$A_5$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$5$ |
$59$ |
$9$ |
$2$ |
$C_1$ |
$A_5$ |
$A_5$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$5$ |
$5$ |
$3$ |
$3$ |
$4$ |
$3$ |
$3$ |
$4$ |
Simple |
| 60.6 |
$C_3\times F_5$ |
$2^{2} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$15$ |
$28$ |
$12$ |
$8$ |
$C_3$ |
$F_5$ |
$C_5$ |
$C_{12}$ |
$2^{3} \cdot 5$ |
$2$ |
$15$ |
$8$ |
$4$ |
$8$ |
$8$ |
$4$ |
$6$ |
$6$ |
Solvable - 2 |
| 60.7 |
$C_{15}:C_4$ |
$2^{2} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$9$ |
$40$ |
$12$ |
$7$ |
$C_1$ |
$C_{15}:C_4$ |
$C_{15}$ |
$C_{4}$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$15$ |
$8$ |
$4$ |
$8$ |
$8$ |
$4$ |
$6$ |
$6$ |
Solvable - 2 |
| 60.8 |
$S_3\times D_5$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$12$ |
$72$ |
$20$ |
$10$ |
$C_1$ |
$S_3\times D_5$ |
$C_{15}$ |
$C_{2}^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$15$ |
$8$ |
$4$ |
$4$ |
$8$ |
$4$ |
$4$ |
$6$ |
Solvable - 2 |
| 60.9 |
$C_5\times A_4$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$20$ |
$20$ |
$10$ |
$6$ |
$C_5$ |
$A_4$ |
$C_2^2$ |
$C_{15}$ |
$2^{5} \cdot 3$ |
$2^{3}$ |
$20$ |
$9$ |
$3$ |
$6$ |
$12$ |
$3$ |
$5$ |
$7$ |
Solvable - 2 |
| 60.10 |
$C_3\times D_{10}$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$24$ |
$44$ |
$20$ |
$14$ |
$C_6$ |
$D_5$ |
$C_5$ |
$C_{2} \times C_{6}$ |
$2^{4} \cdot 5$ |
$2^{3}$ |
$30$ |
$10$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$6$ |
Solvable - 2 |
| 60.11 |
$S_3\times C_{10}$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$32$ |
$20$ |
$14$ |
$C_{10}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{10}$ |
$2^{4} \cdot 3$ |
$2^{3}$ |
$30$ |
$10$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$6$ |
Solvable - 2 |
| 60.12 |
$D_{30}$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$18$ |
$80$ |
$20$ |
$11$ |
$C_2$ |
$D_{15}$ |
$C_{15}$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{3}$ |
$30$ |
$10$ |
$2$ |
$2$ |
$8$ |
$2$ |
$2$ |
$6$ |
Solvable - 2 |
| 84.1 |
$C_7:C_{12}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$14$ |
$36$ |
$12$ |
$8$ |
$C_2$ |
$F_7$ |
$C_7$ |
$C_{12}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2$ |
$28$ |
$11$ |
$6$ |
$12$ |
$12$ |
$6$ |
$8$ |
$8$ |
Solvable - 2 |
| 84.2 |
$C_7:C_{12}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$20$ |
$30$ |
$12$ |
$9$ |
$C_4$ |
$C_7:C_3$ |
$C_7$ |
$C_{12}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2^{2}$ |
$28$ |
$11$ |
$3$ |
$6$ |
$12$ |
$3$ |
$6$ |
$8$ |
Solvable - 2 |
| 84.3 |
$C_3:C_{28}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$42$ |
$16$ |
$12$ |
$10$ |
$C_{14}$ |
$S_3$ |
$C_3$ |
$C_{28}$ |
$2^{3} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$84$ |
$14$ |
$2$ |
$4$ |
$12$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 84.4 |
$C_7:C_{12}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$24$ |
$12$ |
$10$ |
$C_6$ |
$D_7$ |
$C_7$ |
$C_{12}$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3$ |
$84$ |
$14$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 84.5 |
$C_{21}:C_4$ |
$2^{2} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$24$ |
$40$ |
$12$ |
$9$ |
$C_2$ |
$D_{21}$ |
$C_{21}$ |
$C_{4}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$84$ |
$14$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 84.7 |
$C_2\times F_7$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$14$ |
$68$ |
$20$ |
$12$ |
$C_2$ |
$F_7$ |
$C_7$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2$ |
$14$ |
$9$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 2 |
| 84.8 |
$S_3\times D_7$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$15$ |
$92$ |
$20$ |
$10$ |
$C_1$ |
$S_3\times D_7$ |
$C_{21}$ |
$C_{2}^{2}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$3$ |
$21$ |
$10$ |
$4$ |
$4$ |
$12$ |
$4$ |
$4$ |
$8$ |
Solvable - 2 |
| 84.9 |
$C_{14}:C_6$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$20$ |
$50$ |
$20$ |
$15$ |
$C_2^2$ |
$C_7:C_3$ |
$C_7$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$28$ |
$11$ |
$-$ |
$-$ |
$-$ |
$4$ |
$7$ |
$7$ |
Solvable - 2 |
| 84.10 |
$C_7\times A_4$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$28$ |
$20$ |
$10$ |
$6$ |
$C_7$ |
$A_4$ |
$C_2^2$ |
$C_{21}$ |
$2^{4} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$28$ |
$11$ |
$3$ |
$6$ |
$18$ |
$3$ |
$5$ |
$9$ |
Solvable - 2 |
| 84.11 |
$C_7:A_4$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$12$ |
$50$ |
$10$ |
$5$ |
$C_1$ |
$C_7:A_4$ |
$C_2\times C_{14}$ |
$C_{3}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3$ |
$28$ |
$11$ |
$3$ |
$6$ |
$18$ |
$3$ |
$6$ |
$9$ |
Solvable - 2 |
| 84.12 |
$C_3\times D_{14}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$56$ |
$20$ |
$14$ |
$C_6$ |
$D_7$ |
$C_7$ |
$C_{2} \times C_{6}$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3$ |
$42$ |
$12$ |
$2$ |
$4$ |
$12$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 84.13 |
$S_3\times C_{14}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$42$ |
$32$ |
$20$ |
$14$ |
$C_{14}$ |
$S_3$ |
$C_3$ |
$C_{2} \times C_{14}$ |
$2^{3} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$42$ |
$12$ |
$2$ |
$4$ |
$12$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 84.14 |
$D_{42}$ |
$2^{2} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$24$ |
$104$ |
$20$ |
$11$ |
$C_2$ |
$D_{21}$ |
$C_{21}$ |
$C_{2}^{2}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$42$ |
$12$ |
$2$ |
$2$ |
$12$ |
$2$ |
$2$ |
$8$ |
Solvable - 2 |
| 90.1 |
$C_5\times D_9$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$32$ |
$12$ |
$8$ |
$C_5$ |
$D_9$ |
$C_9$ |
$C_{10}$ |
$2^{3} \cdot 3^{3}$ |
$2^{2} \cdot 3$ |
$45$ |
$14$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 90.2 |
$C_9\times D_5$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$36$ |
$24$ |
$12$ |
$9$ |
$C_9$ |
$D_5$ |
$C_5$ |
$C_{18}$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3$ |
$45$ |
$14$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 90.3 |
$D_{45}$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$24$ |
$84$ |
$12$ |
$7$ |
$C_1$ |
$D_{45}$ |
$C_{45}$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3$ |
$45$ |
$14$ |
$2$ |
$2$ |
$24$ |
$2$ |
$2$ |
$10$ |
Solvable - 2 |
| 90.5 |
$C_3^2\times D_5$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$36$ |
$48$ |
$24$ |
$18$ |
$C_3^2$ |
$D_5$ |
$C_5$ |
$C_{3} \times C_{6}$ |
$2^{6} \cdot 3 \cdot 5$ |
$2^{5} \cdot 3$ |
$45$ |
$11$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$8$ |
Solvable - 2 |
| 90.6 |
$S_3\times C_{15}$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$45$ |
$28$ |
$18$ |
$12$ |
$C_{15}$ |
$S_3$ |
$C_3$ |
$C_{30}$ |
$2^{4} \cdot 3$ |
$2^{3}$ |
$30$ |
$11$ |
$2$ |
$4$ |
$16$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 90.7 |
$C_3\times D_{15}$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$27$ |
$60$ |
$18$ |
$10$ |
$C_3$ |
$D_{15}$ |
$C_{15}$ |
$C_{6}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{3}$ |
$30$ |
$11$ |
$2$ |
$4$ |
$16$ |
$2$ |
$4$ |
$8$ |
Solvable - 2 |
| 90.8 |
$C_{15}:S_3$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$30$ |
$56$ |
$24$ |
$14$ |
$C_5$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{10}$ |
$2^{6} \cdot 3^{3}$ |
$2^{5} \cdot 3$ |
$45$ |
$11$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$8$ |
Solvable - 2 |
| 90.9 |
$C_3:D_{15}$ |
$2 \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$24$ |
$144$ |
$24$ |
$13$ |
$C_1$ |
$C_3:D_{15}$ |
$C_3\times C_{15}$ |
$C_{2}$ |
$2^{6} \cdot 3^{3} \cdot 5$ |
$2^{5} \cdot 3$ |
$45$ |
$11$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$8$ |
Solvable - 2 |
| 126.1 |
$C_7:C_{18}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$21$ |
$36$ |
$12$ |
$8$ |
$C_3$ |
$F_7$ |
$C_7$ |
$C_{18}$ |
$2 \cdot 3^{2} \cdot 7$ |
$3$ |
$63$ |
$16$ |
$6$ |
$12$ |
$36$ |
$6$ |
$8$ |
$12$ |
Solvable - 2 |
| 126.2 |
$C_7:C_{18}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$24$ |
$12$ |
$10$ |
$C_6$ |
$C_7:C_3$ |
$C_7$ |
$C_{18}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3$ |
$126$ |
$18$ |
$3$ |
$6$ |
$36$ |
$3$ |
$6$ |
$12$ |
Solvable - 2 |
| 126.3 |
$C_7\times D_9$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$42$ |
$32$ |
$12$ |
$8$ |
$C_7$ |
$D_9$ |
$C_9$ |
$C_{14}$ |
$2^{2} \cdot 3^{4}$ |
$2 \cdot 3^{2}$ |
$63$ |
$16$ |
$2$ |
$4$ |
$36$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 126.4 |
$C_9\times D_7$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$45$ |
$30$ |
$12$ |
$9$ |
$C_9$ |
$D_7$ |
$C_7$ |
$C_{18}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2}$ |
$63$ |
$16$ |
$2$ |
$4$ |
$36$ |
$2$ |
$4$ |
$12$ |
Solvable - 2 |
| 126.5 |
$D_{63}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$33$ |
$110$ |
$12$ |
$7$ |
$C_1$ |
$D_{63}$ |
$C_{63}$ |
$C_{2}$ |
$2^{2} \cdot 3^{4} \cdot 7$ |
$2 \cdot 3^{2}$ |
$63$ |
$16$ |
$2$ |
$2$ |
$36$ |
$2$ |
$2$ |
$12$ |
Solvable - 2 |
| 126.7 |
$C_3\times F_7$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$21$ |
$84$ |
$24$ |
$14$ |
$C_3$ |
$F_7$ |
$C_7$ |
$C_{3} \times C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3$ |
$21$ |
$10$ |
$6$ |
$12$ |
$12$ |
$6$ |
$8$ |
$8$ |
Solvable - 2 |
| 126.8 |
$C_{21}:C_6$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$15$ |
$76$ |
$18$ |
$9$ |
$C_1$ |
$C_{21}:C_6$ |
$C_{21}$ |
$C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2$ |
$21$ |
$10$ |
$6$ |
$12$ |
$12$ |
$5$ |
$8$ |
$8$ |
Solvable - 2 |
| 126.9 |
$C_{21}:C_6$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$12$ |
$100$ |
$18$ |
$8$ |
$C_1$ |
$C_{21}:C_6$ |
$C_{21}$ |
$C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2$ |
$21$ |
$10$ |
$6$ |
$6$ |
$12$ |
$6$ |
$6$ |
$8$ |
Solvable - 2 |
| 126.10 |
$C_{21}:C_6$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$30$ |
$72$ |
$24$ |
$16$ |
$C_6$ |
$C_7:C_3$ |
$C_7$ |
$C_{3} \times C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$42$ |
$12$ |
$3$ |
$6$ |
$12$ |
$3$ |
$6$ |
$8$ |
Solvable - 2 |
| 126.11 |
$C_3^2\times D_7$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$45$ |
$60$ |
$24$ |
$18$ |
$C_3^2$ |
$D_7$ |
$C_7$ |
$C_{3} \times C_{6}$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$2^{4} \cdot 3^{2}$ |
$63$ |
$13$ |
$-$ |
$-$ |
$-$ |
$3$ |
$6$ |
$10$ |
Solvable - 2 |
| 126.12 |
$S_3\times C_{21}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$63$ |
$28$ |
$18$ |
$12$ |
$C_{21}$ |
$S_3$ |
$C_3$ |
$C_{42}$ |
$2^{3} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$42$ |
$13$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 126.13 |
$C_3\times D_{21}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$36$ |
$76$ |
$18$ |
$10$ |
$C_3$ |
$D_{21}$ |
$C_{21}$ |
$C_{6}$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3$ |
$42$ |
$13$ |
$2$ |
$4$ |
$24$ |
$2$ |
$4$ |
$10$ |
Solvable - 2 |
| 126.14 |
$C_{21}:S_3$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$42$ |
$56$ |
$24$ |
$14$ |
$C_7$ |
$C_3:S_3$ |
$C_3^2$ |
$C_{14}$ |
$2^{5} \cdot 3^{4}$ |
$2^{4} \cdot 3^{2}$ |
$63$ |
$13$ |
$-$ |
$-$ |
$-$ |
$4$ |
$6$ |
$10$ |
Solvable - 2 |
| 126.15 |
$C_3:D_{21}$ |
$2 \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$3$ |
$33$ |
$188$ |
$24$ |
$13$ |
$C_1$ |
$C_3:D_{21}$ |
$C_3\times C_{21}$ |
$C_{2}$ |
$2^{5} \cdot 3^{4} \cdot 7$ |
$2^{4} \cdot 3^{2}$ |
$63$ |
$13$ |
$-$ |
$-$ |
$-$ |
$4$ |
$4$ |
$10$ |
Solvable - 2 |
| 132.1 |
$C_3:C_{44}$ |
$2^{2} \cdot 3 \cdot 11$ |
$2^{2} \cdot 3 \cdot 11$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$66$ |
$16$ |
$12$ |
$10$ |
$C_{22}$ |
$S_3$ |
$C_3$ |
$C_{44}$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 5$ |
$132$ |
$18$ |
$2$ |
$4$ |
$40$ |
$2$ |
$4$ |
$14$ |
Solvable - 2 |
| 132.2 |
$C_{11}:C_{12}$ |
$2^{2} \cdot 3 \cdot 11$ |
$2^{2} \cdot 3 \cdot 11$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$42$ |
$32$ |
$12$ |
$10$ |
$C_6$ |
$D_{11}$ |
$C_{11}$ |
$C_{12}$ |
$2^{3} \cdot 5 \cdot 11$ |
$2^{2} \cdot 5$ |
$132$ |
$18$ |
$2$ |
$4$ |
$20$ |
$2$ |
$4$ |
$14$ |
Solvable - 2 |
| 132.3 |
$C_{33}:C_4$ |
$2^{2} \cdot 3 \cdot 11$ |
$2^{2} \cdot 3 \cdot 11$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$36$ |
$56$ |
$12$ |
$9$ |
$C_2$ |
$D_{33}$ |
$C_{33}$ |
$C_{4}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 5$ |
$132$ |
$18$ |
$2$ |
$4$ |
$40$ |
$2$ |
$4$ |
$14$ |
Solvable - 2 |
| 132.5 |
$S_3\times D_{11}$ |
$2^{2} \cdot 3 \cdot 11$ |
$2 \cdot 3 \cdot 11$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$21$ |
$132$ |
$20$ |
$10$ |
$C_1$ |
$S_3\times D_{11}$ |
$C_{33}$ |
$C_{2}^{2}$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$5$ |
$33$ |
$14$ |
$4$ |
$4$ |
$20$ |
$4$ |
$4$ |
$12$ |
Solvable - 2 |
