| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T33 |
$A_5$ |
$60$ |
$1$ |
|
$-1$ |
$5$ |
$\PSL(2,5)$ |
5T4, 6T12, 10T7, 15T5, 20T15, 30T9 |
| 12T74 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$7$ |
$C_2$, $\PGL(2,5)$ |
5T5, 6T14, 10T12, 10T13, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
| 12T75 |
$C_2\times A_5$ |
$120$ |
$1$ |
|
$-1$ |
$10$ |
$C_2$, $\PSL(2,5)$ |
10T11, 12T76, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61 |
| 12T76 |
$C_2\times A_5$ |
$120$ |
$1$ |
|
$-1$ |
$10$ |
$\PSL(2,5)$ |
10T11, 12T75, 20T31, 20T36, 24T203, 30T29, 30T30, 40T61 |
| 12T123 |
$C_2\times S_5$ |
$240$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $\PGL(2,5)$ |
10T22 x 2, 12T123, 20T62 x 2, 20T65 x 2, 20T70, 24T570, 24T577, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2 |
| 12T124 |
$A_5:C_4$ |
$240$ |
$-1$ |
|
$-1$ |
$14$ |
$\PGL(2,5)$ |
12T124, 20T66, 24T571, 24T578, 40T178, 40T179 |
| 12T179 |
$\PSL(2,11)$ |
$660$ |
$1$ |
|
$-1$ |
$8$ |
|
11T5 x 2 |
| 12T180 |
$C_2\times A_6$ |
$720$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $A_6$ |
12T180, 20T151, 20T152, 30T172 x 2, 30T179 x 2, 40T587, 40T588 |
| 12T181 |
$A_6.C_2$ |
$720$ |
$1$ |
|
$-1$ |
$8$ |
$C_2$ |
10T31, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109 |
| 12T182 |
$\PGL(2,9)$ |
$720$ |
$1$ |
|
$-1$ |
$11$ |
$C_2$ |
10T30, 20T146, 30T171, 36T1254, 40T590, 45T110 |
| 12T183 |
$S_6$ |
$720$ |
$1$ |
|
$-1$ |
$11$ |
$C_2$, $S_6$ |
6T16 x 2, 10T32, 12T183, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 |
| 12T218 |
$\PGL(2,11)$ |
$1320$ |
$-1$ |
|
$-1$ |
$13$ |
|
22T14, 24T2949 |
| 12T219 |
$S_6\times C_2$ |
$1440$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$, $S_6$ |
12T219 x 3, 20T198 x 2, 20T199 x 2, 24T2959 x 2, 30T260 x 4, 30T261 x 4, 40T1177, 40T1178, 40T1189 x 2, 40T1190 x 4 |
| 12T220 |
$S_6:C_2$ |
$1440$ |
$1$ |
|
$-1$ |
$13$ |
$C_2$ |
10T35, 20T201, 20T204, 20T208, 24T2960, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187 |
| 12T230 |
$C_2^5:A_5$ |
$1920$ |
$1$ |
|
$-1$ |
$16$ |
$\PSL(2,5)$ |
12T230, 20T228 x 2, 24T4946, 32T97740 x 4, 40T1580, 40T1651, 40T1653 |
| 12T255 |
$C_2\wr A_5$ |
$3840$ |
$-1$ |
|
$-1$ |
$32$ |
$\PSL(2,5)$ |
12T255 x 3, 20T280 x 4, 24T7251 x 2, 24T7252 x 2, 24T7253 x 2, 40T2725 x 2, 40T2740 x 2, 40T2763 x 2, 40T2840 x 2, 40T2850 x 2 |
| 12T256 |
$C_2^5.S_5$ |
$3840$ |
$-1$ |
|
$-1$ |
$23$ |
$\PGL(2,5)$ |
12T256, 24T7239, 24T7254, 40T2742, 40T2743 |
| 12T257 |
$C_2^5:S_5$ |
$3840$ |
$1$ |
|
$-1$ |
$23$ |
$\PGL(2,5)$ |
12T257, 20T281 x 2, 20T291 x 2, 24T7238, 24T7255, 32T206828 x 4, 40T2727 x 2, 40T2744, 40T2745, 40T2755 x 2, 40T2837 x 2, 40T2844 x 2 |
| 12T269 |
$\SOPlus(4,4)$ |
$7200$ |
$1$ |
|
$-1$ |
$20$ |
$C_2$ |
10T40, 20T363, 24T9631, 25T88, 30T652, 36T7075, 40T5410 |
| 12T270 |
$C_2\wr S_5$ |
$7680$ |
$-1$ |
|
$-1$ |
$37$ |
$\PGL(2,5)$ |
12T270 x 3, 24T9634 x 2, 24T9678 x 2, 24T9679 x 2, 24T9680 x 2, 40T5431, 40T5432, 40T5458, 40T5465 |
| 12T272 |
$M_{11}$ |
$7920$ |
$1$ |
|
$-1$ |
$10$ |
|
11T6, 22T22 |
| 12T277 |
$C_2^5:A_6$ |
$11520$ |
$1$ |
|
$-1$ |
$23$ |
$A_6$ |
20T452 x 2, 32T720334 x 2, 40T10389, 40T10390 |
| 12T278 |
$A_5^2:C_4$ |
$14400$ |
$-1$ |
|
$-1$ |
$22$ |
$C_2$ |
10T42, 20T457, 20T461, 24T12116, 25T100, 30T817, 36T9861, 40T10509, 40T10510, 40T10511 |
| 12T279 |
$\PGOPlus(4,5)$ |
$14400$ |
$1$ |
|
$-1$ |
$25$ |
$C_2$ |
10T41, 20T456, 20T459, 24T12117, 25T101, 30T819, 36T9862, 40T10506, 40T10507, 40T10508 |
| 12T285 |
$C_2^5:S_6$ |
$23040$ |
$1$ |
|
$-1$ |
$37$ |
$S_6$ |
12T285, 20T531 x 4, 24T12618, 32T1120025 x 4, 40T14226 x 2, 40T14229, 40T14232 x 2, 40T14235, 40T14236 x 2 |
| 12T286 |
$C_2\wr A_6$ |
$23040$ |
$-1$ |
|
$-1$ |
$40$ |
$A_6$ |
12T286, 24T12619, 40T14221, 40T14222, 40T14238, 40T14242 |
| 12T287 |
$C_2^5.S_6$ |
$23040$ |
$-1$ |
|
$-1$ |
$37$ |
$S_6$ |
12T287, 24T12620, 40T14224, 40T14233, 40T14234 x 2 |
| 12T288 |
$S_5\wr C_2$ |
$28800$ |
$-1$ |
|
$-1$ |
$35$ |
$C_2$ |
10T43, 20T539, 20T540, 20T542, 20T544, 24T13996, 24T13997, 24T13998, 25T106, 30T1011, 36T13308, 40T14374, 40T14375, 40T14376, 40T14377, 40T14378, 40T14379, 40T14380, 40T14381 |
| 12T293 |
$C_2^6.S_6$ |
$46080$ |
$-1$ |
|
$-1$ |
$65$ |
$S_6$ |
12T293 x 3, 24T14632 x 2, 24T14633 x 2, 24T14634 x 2, 40T18563 x 2, 40T18564 x 2, 40T18573 x 2, 40T18579 x 2 |
| 12T295 |
$M_{12}$ |
$95040$ |
$1$ |
|
$-1$ |
$15$ |
|
12T295 |
| 12T296 |
$A_6\wr C_2$ |
$259200$ |
$1$ |
|
$-1$ |
$35$ |
$C_2$ |
12T296, 20T888, 30T1681 x 2, 36T25180 x 2, 40T107011 |
| 12T297 |
$A_6^2:C_2^2$ |
$518400$ |
$1$ |
|
$-1$ |
$49$ |
$C_2$ |
12T297, 20T934, 24T20411 x 2, 30T1851 x 2, 36T30378 x 2, 40T139782 x 2, 40T139783 |
| 12T298 |
$A_6^2:C_4$ |
$518400$ |
$-1$ |
|
$-1$ |
$46$ |
$C_2$ |
12T298, 20T937, 24T20412 x 2, 30T1854 x 2, 36T30377 x 2, 40T139787, 40T139788 x 2 |
| 12T299 |
$S_6\wr C_2$ |
$1036800$ |
$-1$ |
|
$-1$ |
$77$ |
$C_2$ |
12T299, 20T973, 24T21434 x 2, 24T21435 x 2, 24T21436 x 2, 30T2029 x 2, 36T36499 x 2, 40T148363 x 2, 40T148364, 40T148365 x 2, 40T148366, 40T148367 |
| 12T300 |
$A_{12}$ |
$239500800$ |
$1$ |
|
$-1$ |
$43$ |
|
|
| 12T301 |
$S_{12}$ |
$479001600$ |
$-1$ |
|
$-1$ |
$77$ |
|
24T24748 |
Results are complete for degrees $\leq 23$.
