| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 9T28 |
$S_3 \wr C_3 $ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$C_3$ |
12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
| 9T29 |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$17$ |
$S_3$ |
12T175, 18T219, 18T220, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
| 9T30 |
$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
$648$ |
$1$ |
✓ |
$-1$ |
$14$ |
$S_3$ |
12T177 x 2, 12T178, 18T217, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
| 10T29 |
$((C_2^4 : C_5):C_4)\times C_2$ |
$640$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$F_5$ |
10T29, 20T129, 20T131 x 2, 20T132, 20T133, 20T134, 20T135, 20T137 x 2, 20T140, 32T34608 x 2, 40T460, 40T462, 40T473, 40T474, 40T475, 40T476, 40T487, 40T488, 40T489, 40T490, 40T557, 40T558 x 2, 40T561, 40T562, 40T563, 40T564, 40T565, 40T566, 40T567 x 2, 40T576, 40T577, 40T578, 40T579, 40T586 |
| 10T30 |
$\PGL(2,9)$ |
$720$ |
$-1$ |
|
$-1$ |
$11$ |
|
12T182, 20T146, 30T171, 36T1254, 40T590, 45T110 |
| 10T31 |
$M_{10}$ |
$720$ |
$1$ |
|
$-1$ |
$8$ |
|
12T181, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109 |
| 10T32 |
$S_{6}$ |
$720$ |
$-1$ |
|
$-1$ |
$11$ |
|
6T16 x 2, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 |
| 10T33 |
$F_5 \wr C_2$ |
$800$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$C_2$ |
20T155, 20T161, 20T167, 20T169, 25T50, 40T874, 40T875, 40T876, 40T877, 40T878, 40T879, 40T880, 40T881, 40T882, 40T883 |
| 10T34 |
$C_2^4 : A_5$ |
$960$ |
$1$ |
|
$-1$ |
$12$ |
$A_5$ |
16T1081, 20T172, 20T177, 30T214, 30T217, 40T888, 40T889, 40T932, 40T942, 40T944, 40T945 |
| 11T5 |
$\PSL(2,11)$ |
$660$ |
$1$ |
|
$-1$ |
$8$ |
|
11T5, 12T179 |
Results are complete for degrees $\leq 23$.
