| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 45T1 |
$C_{45}$ |
$45$ |
$1$ |
✓ |
$1$ |
$45$ |
$C_3$, $C_5$, $C_9$, $C_{15}$ |
|
| 45T2 |
$C_3\times C_{15}$ |
$45$ |
$1$ |
✓ |
$1$ |
$45$ |
$C_3$ x 4, $C_5$, $C_3^2$, $C_{15}$ x 4 |
|
| 45T3 |
$S_3\times C_{15}$ |
$90$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_3$, $S_3$, $C_5$, $S_3\times C_3$, $C_{15}$, $S_3 \times C_5$ |
30T15 |
| 45T4 |
$D_{45}$ |
$90$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$, $D_{5}$, $D_{9}$, $D_{15}$ |
|
| 45T5 |
$C_3\times D_{15}$ |
$90$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_3$, $S_3$, $D_{5}$, $S_3\times C_3$, $D_{15}$, $D_5\times C_3$ |
30T16 |
| 45T6 |
$C_3:D_{15}$ |
$90$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$ x 4, $D_{5}$, $C_3^2:C_2$, $D_{15}$ x 4 |
|
| 45T7 |
$C_9\times D_5$ |
$90$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_3$, $D_{5}$, $C_9$, $D_5\times C_3$ |
|
| 45T8 |
$C_3^2\times D_5$ |
$90$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_3$ x 4, $D_{5}$, $C_3^2$, $D_5\times C_3$ x 4 |
|
| 45T9 |
$C_5\times D_9$ |
$90$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $C_5$, $D_{9}$, $S_3 \times C_5$ |
|
| 45T10 |
$C_{15}:S_3$ |
$90$ |
$1$ |
✓ |
$-1$ |
$30$ |
$S_3$ x 4, $C_5$, $C_3^2:C_2$, $S_3 \times C_5$ x 4 |
|
| 45T11 |
$C_5\times \He_3$ |
$135$ |
$1$ |
✓ |
$2$ |
$55$ |
$C_3$, $C_5$, $C_3^2:C_3$, $C_{15}$ |
45T11 x 3 |
| 45T12 |
$C_9:C_{15}$ |
$135$ |
$1$ |
✓ |
$2$ |
$55$ |
$C_3$, $C_5$, $C_9:C_3$, $C_{15}$ |
|
| 45T13 |
$S_3\times D_{15}$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$S_3$ x 2, $D_{5}$, $S_3^2$, $D_{15}$, $D_5\times S_3$ |
30T42 |
| 45T14 |
$C_{15}:D_6$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_3$, $S_3$, $D_{5}$, $S_3\times C_3$, $D_5\times C_3$, $D_5\times S_3$ |
30T44 |
| 45T15 |
$C_5\times S_3^2$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$S_3$ x 2, $C_5$, $S_3^2$, $S_3 \times C_5$ x 2 |
30T41 |
| 45T16 |
$\GL(2,4)$ |
$180$ |
$1$ |
|
$-1$ |
$15$ |
$C_3$, $A_5$, $A_5$, $\GL(2,4)$ x 2, $\GL(2,4)$ |
15T15 x 2, 15T16, 18T90, 30T45, 36T176 |
| 45T17 |
$C_{45}:C_4$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$S_3$, $F_5$, $D_{9}$, $C_{15} : C_4$ |
|
| 45T18 |
$C_{15}:C_{12}$ |
$180$ |
$1$ |
✓ |
$-1$ |
$27$ |
$C_3$, $S_3$, $F_5$, $S_3\times C_3$, $C_{15} : C_4$, $F_5\times C_3$ |
30T47 |
| 45T19 |
$C_3^2:F_5$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$S_3$ x 4, $F_5$, $C_3^2:C_2$, $C_{15} : C_4$ x 4 |
|
| 45T20 |
$D_5\times D_9$ |
$180$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$, $D_{5}$, $D_{9}$, $D_5\times S_3$ |
|
| 45T21 |
$C_{15}:D_6$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$S_3$ x 2, $D_{5}$, $S_3^2$, $D_5\times S_3$ x 2 |
30T43 |
| 45T22 |
$C_{15}:D_6$ |
$180$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$ x 4, $D_{5}$, $C_3^2:C_2$, $D_5\times S_3$ x 4 |
|
| 45T23 |
$C_9\times F_5$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_3$, $F_5$, $C_9$, $F_5\times C_3$ |
|
| 45T24 |
$C_3^2\times F_5$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_3$ x 4, $F_5$, $C_3^2$, $F_5\times C_3$ x 4 |
|
| 45T25 |
$C_3^2:C_{20}$ |
$180$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_5$, $C_3^2:C_4$ |
30T49 x 2 |
| 45T26 |
$(C_3\times C_{15}):C_4$ |
$180$ |
$1$ |
✓ |
$-1$ |
$18$ |
$D_{5}$, $C_3^2:C_4$ |
30T48 x 2 |
| 45T27 |
$C_3^2:F_5$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$F_5$, $C_3^2:C_4$ |
30T46 x 2 |
| 45T28 |
$C_5^2:C_3^2$ |
$225$ |
$1$ |
✓ |
$-1$ |
$33$ |
$C_3$ x 4, $C_3^2$, $C_5^2 : C_3$ |
45T28 |
| 45T29 |
$C_5^2:C_9$ |
$225$ |
$1$ |
✓ |
$-1$ |
$33$ |
$C_3$, $C_9$, $C_5^2 : C_3$ |
45T29 |
| 45T30 |
$C_3^2:C_{30}$ |
$270$ |
$-1$ |
✓ |
$-1$ |
$50$ |
$C_3$, $C_5$, $C_3^2 : S_3 $, $C_{15}$ |
45T37 |
| 45T31 |
$C_3^2:D_{15}$ |
$270$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$S_3$, $D_{5}$, $(C_3^2:C_3):C_2$, $D_{15}$ |
45T31 x 3 |
| 45T32 |
$C_3^2:D_{15}$ |
$270$ |
$1$ |
✓ |
$-1$ |
$32$ |
$S_3$, $D_{5}$, $C_3^2 : C_6$, $D_{15}$ |
45T34 |
| 45T33 |
$C_{45}:C_6$ |
$270$ |
$1$ |
✓ |
$-1$ |
$32$ |
$S_3$, $D_{5}$, $(C_9:C_3):C_2$, $D_{15}$ |
|
| 45T34 |
$C_3^2:D_{15}$ |
$270$ |
$-1$ |
✓ |
$-1$ |
$32$ |
$C_3$, $D_{5}$, $C_3^2 : S_3 $, $D_5\times C_3$ |
45T32 |
| 45T35 |
$D_5\times \He_3$ |
$270$ |
$1$ |
✓ |
$-1$ |
$44$ |
$C_3$, $D_{5}$, $C_3^2:C_3$, $D_5\times C_3$ |
45T35 x 3 |
| 45T36 |
$C_{45}:C_6$ |
$270$ |
$1$ |
✓ |
$-1$ |
$44$ |
$C_3$, $D_{5}$, $C_9:C_3$, $D_5\times C_3$ |
|
| 45T37 |
$C_3^2:C_{30}$ |
$270$ |
$1$ |
✓ |
$-1$ |
$50$ |
$S_3$, $C_5$, $C_3^2 : C_6$, $S_3 \times C_5$ |
45T30 |
| 45T38 |
$C_9:C_{30}$ |
$270$ |
$1$ |
✓ |
$-1$ |
$50$ |
$S_3$, $C_5$, $(C_9:C_3):C_2$, $S_3 \times C_5$ |
|
| 45T39 |
$\He_3:C_{10}$ |
$270$ |
$-1$ |
✓ |
$-1$ |
$50$ |
$S_3$, $C_5$, $(C_3^2:C_3):C_2$, $S_3 \times C_5$ |
45T39 x 3 |
| 45T40 |
$S_3\times A_5$ |
$360$ |
$-1$ |
|
$-1$ |
$15$ |
$S_3$, $A_5$, $A_5$, $A_5 \times S_3$ |
15T23, 18T145, 30T85, 30T94, 30T102, 36T551, 36T552, 36T553 |
| 45T41 |
$D_5.S_3^2$ |
$360$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$S_3$ x 2, $F_5$, $S_3^2$, $C_{15} : C_4$, $F_5 \times S_3$ |
30T83 |
| 45T42 |
$D_5\times S_3^2$ |
$360$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$S_3$ x 2, $D_{5}$, $S_3^2$, $D_5\times S_3$ x 2 |
30T84 |
| 45T43 |
$D_{15}:C_{12}$ |
$360$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_3$, $S_3$, $F_5$, $S_3\times C_3$, $F_5\times C_3$, $F_5 \times S_3$ |
30T91 |
| 45T44 |
$C_3\times S_5$ |
$360$ |
$1$ |
|
$-1$ |
$21$ |
$C_3$, $S_5$, $S_5$, $S_5 \times C_3$ |
15T24, 18T144, 30T90, 30T98, 30T103, 36T550 |
| 45T45 |
$C_3:S_5$ |
$360$ |
$-1$ |
|
$-1$ |
$12$ |
$S_3$, $S_5$, $S_5$, $\GL(2,4):C_2$ x 2, $\GL(2,4):C_2$ |
15T21 x 2, 15T22, 18T146, 30T89, 30T93 x 2, 30T101, 36T554 |
| 45T46 |
$D_9\times F_5$ |
$360$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$S_3$, $F_5$, $D_{9}$, $F_5 \times S_3$ |
|
| 45T47 |
$D_5.S_3^2$ |
$360$ |
$1$ |
✓ |
$-1$ |
$24$ |
$S_3$ x 2, $F_5$, $S_3^2$, $F_5 \times S_3$ x 2 |
30T86 |
| 45T48 |
$C_3:S_3\times F_5$ |
$360$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$S_3$ x 4, $F_5$, $C_3^2:C_2$, $F_5 \times S_3$ x 4 |
|
| 45T49 |
$A_6$ |
$360$ |
$1$ |
|
$-1$ |
$7$ |
$A_6$ x 2 |
6T15 x 2, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304 |
| 45T50 |
$C_3^2:C_4\times D_5$ |
$360$ |
$1$ |
✓ |
$-1$ |
$24$ |
$D_{5}$, $C_3^2:C_4$ |
30T99 x 2 |
Results are complete for degrees $\leq 23$.
