| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 24T201 |
$\SL(2,5)$ |
$120$ |
$1$ |
|
$-1$ |
$9$ |
$\PSL(2,5)$, $A_5$ |
40T60 |
| 24T202 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$7$ |
$C_2$, $\PGL(2,5)$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 30T22, 30T25, 30T27, 40T62 |
| 24T203 |
$C_2\times A_5$ |
$120$ |
$1$ |
|
$-1$ |
$10$ |
$C_2$, $\PSL(2,5)$, $A_5$, $C_2\times A_5$, $C_2\times A_5$ |
10T11, 12T75, 12T76, 20T31, 20T36, 30T29, 30T30, 40T61 |
| 24T284 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 28T32, 42T37, 42T38 x 2 |
| 24T570 |
$C_2\times S_5$ |
$240$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $\PGL(2,5)$, $S_5$ |
10T22 x 2, 12T123 x 2, 20T62 x 2, 20T65 x 2, 20T70, 24T577, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2 |
| 24T571 |
$A_5:C_4$ |
$240$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $C_4$, $\PGL(2,5)$, $S_5$ |
12T124 x 2, 20T66, 24T578, 40T178, 40T179 |
| 24T572 |
$C_2^2\times A_5$ |
$240$ |
$1$ |
|
$-1$ |
$20$ |
$C_2$, $\PSL(2,5)$, $C_2\times A_5$, $C_2\times A_5$ x 2 |
20T64, 24T572 x 2, 24T573, 40T176, 40T177 x 3 |
| 24T573 |
$C_2^2\times A_5$ |
$240$ |
$1$ |
|
$-1$ |
$20$ |
$C_2$ x 3, $C_2^2$, $\PSL(2,5)$, $C_2\times A_5$ x 3 |
20T64, 24T572 x 3, 40T176, 40T177 x 3 |
| 24T574 |
$C_4\times A_5$ |
$240$ |
$1$ |
|
$-1$ |
$20$ |
$C_2$, $\PSL(2,5)$, $C_2\times A_5$ |
20T63, 24T575, 40T174, 40T175 |
| 24T575 |
$C_4\times A_5$ |
$240$ |
$1$ |
|
$-1$ |
$20$ |
$C_2$, $C_4$, $\PSL(2,5)$, $C_2\times A_5$ |
20T63, 24T574, 40T174, 40T175 |
| 24T576 |
$\SL(2,5):C_2$ |
$240$ |
$1$ |
|
$-1$ |
$18$ |
$\PSL(2,5)$, $C_2\times A_5$ |
24T576, 40T188 x 2 |
| 24T577 |
$C_2\times S_5$ |
$240$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$ x 3, $C_2^2$, $\PGL(2,5)$, $S_5$, $C_2\times S_5$ x 2 |
10T22 x 2, 12T123 x 2, 20T62 x 2, 20T65 x 2, 20T70, 24T570, 30T58 x 2, 30T60 x 2, 40T173 x 2, 40T180, 40T181, 40T187 x 2 |
| 24T578 |
$A_5:C_4$ |
$240$ |
$1$ |
|
$-1$ |
$14$ |
$C_2$, $\PGL(2,5)$, $S_5$, $A_5:C_4$ x 2 |
12T124 x 2, 20T66, 24T571, 40T178, 40T179 |
| 24T707 |
$\PGL(2,7)$ |
$336$ |
$-1$ |
|
$-1$ |
$9$ |
$\PGL(2,7)$ |
8T43, 14T16, 16T713, 21T20, 28T42, 28T46, 42T81, 42T82, 42T83 |
| 24T1341 |
$C_2^2:S_5$ |
$480$ |
$1$ |
|
$-1$ |
$19$ |
$C_2$, $D_{4}$, $\PGL(2,5)$, $S_5$ |
20T116, 20T118, 24T1342, 24T1349, 24T1350, 40T404, 40T405, 40T410, 40T413, 40T432 |
| 24T1342 |
$C_2^2:S_5$ |
$480$ |
$1$ |
|
$-1$ |
$19$ |
$C_2$, $\PGL(2,5)$, $S_5$ |
20T116, 20T118, 24T1341, 24T1349, 24T1350, 40T404, 40T405, 40T410, 40T413, 40T432 |
| 24T1343 |
$D_4\times A_5$ |
$480$ |
$1$ |
|
$-1$ |
$25$ |
$C_2$, $D_{4}$, $\PSL(2,5)$, $C_2\times A_5$ |
20T119 x 2, 24T1343, 24T1344 x 2, 40T402 x 2, 40T403 x 2, 40T419 |
| 24T1344 |
$D_4\times A_5$ |
$480$ |
$1$ |
|
$-1$ |
$25$ |
$C_2$, $\PSL(2,5)$, $C_2\times A_5$ |
20T119 x 2, 24T1343 x 2, 24T1344, 40T402 x 2, 40T403 x 2, 40T419 |
| 24T1345 |
$C_2^2\times S_5$ |
$480$ |
$1$ |
|
$-1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $\PGL(2,5)$, $C_2\times S_5$ x 3 |
20T117 x 4, 24T1345 x 3, 40T414 x 4, 40T415 x 12, 40T433 |
| 24T1346 |
$C_2^2.S_5$ |
$480$ |
$1$ |
|
$-1$ |
$28$ |
$C_2$, $\PGL(2,5)$, $C_2\times S_5$, $A_5:C_4$ x 2 |
24T1346 x 3, 40T423 |
| 24T1347 |
$C_4\times S_5$ |
$480$ |
$1$ |
|
$-1$ |
$28$ |
$C_2$, $C_4$, $\PGL(2,5)$, $C_2\times S_5$ |
20T123 x 2, 24T1347, 24T1348 x 2, 40T408 x 2, 40T409 x 2, 40T430 |
| 24T1348 |
$C_4\times S_5$ |
$480$ |
$1$ |
|
$-1$ |
$28$ |
$C_2$, $\PGL(2,5)$, $C_2\times S_5$ |
20T123 x 2, 24T1347 x 2, 24T1348, 40T408 x 2, 40T409 x 2, 40T430 |
| 24T1349 |
$C_2^2:S_5$ |
$480$ |
$1$ |
|
$-1$ |
$19$ |
$C_2$, $\PGL(2,5)$, $C_2\times S_5$ |
20T116, 20T118, 24T1341, 24T1342, 24T1350, 40T404, 40T405, 40T410, 40T413, 40T432 |
| 24T1350 |
$C_2^2:S_5$ |
$480$ |
$1$ |
|
$-1$ |
$19$ |
$C_2$, $D_{4}$, $\PGL(2,5)$, $C_2\times S_5$ |
20T116, 20T118, 24T1341, 24T1342, 24T1349, 40T404, 40T405, 40T410, 40T413, 40T432 |
| 24T1351 |
$A_5:Q_8$ |
$480$ |
$1$ |
|
$-1$ |
$19$ |
$C_2$, $\PGL(2,5)$, $C_2\times S_5$ |
24T1351, 40T429 |
| 24T1352 |
$C_4:S_5$ |
$480$ |
$1$ |
|
$-1$ |
$19$ |
$C_2$, $D_{4}$, $\PGL(2,5)$, $C_2\times S_5$ |
20T120 x 2, 24T1352, 40T411 x 2, 40T412 x 2, 40T431 |
| 24T1353 |
$\GL(2,5)$ |
$480$ |
$-1$ |
|
$-1$ |
$24$ |
$\PGL(2,5)$, $A_5:C_4$ |
24T1353 x 3 |
| 24T1355 |
$C_3\times \GL(3,2)$ |
$504$ |
$1$ |
|
$-1$ |
$18$ |
$\PSL(2,7)$ |
21T22 x 2, 24T1355, 24T1356, 42T96 x 2, 42T103 x 2 |
| 24T1356 |
$C_3\times \GL(3,2)$ |
$504$ |
$1$ |
|
$-1$ |
$18$ |
$C_3$, $\PSL(2,7)$ |
21T22 x 2, 24T1355 x 2, 42T96 x 2, 42T103 x 2 |
| 24T1546 |
$A_4\times A_5$ |
$720$ |
$1$ |
|
$-1$ |
$20$ |
$A_4$, $\PSL(2,5)$ |
20T147, 30T163, 36T1241, 36T1242, 40T593 |
| 24T2665 |
$D_4\times S_5$ |
$960$ |
$1$ |
|
$-1$ |
$35$ |
$C_2$, $D_{4}$, $\PGL(2,5)$, $C_2\times S_5$ |
20T174 x 4, 24T2665 x 3, 40T896 x 4, 40T897 x 4, 40T905 x 2, 40T917 x 2, 40T918 x 2 |
| 24T2666 |
$D_4:S_5$ |
$960$ |
$1$ |
|
$-1$ |
$35$ |
$C_2$, $\PGL(2,5)$, $C_2\times S_5$ |
24T2666 x 3, 40T904 x 2, 40T911 |
| 24T2667 |
$C_3:\PGL(2,7)$ |
$1008$ |
$-1$ |
|
$-1$ |
$15$ |
$S_3$, $\PGL(2,7)$ |
42T174 |
| 24T2668 |
$C_3\times \PGL(2,7)$ |
$1008$ |
$-1$ |
|
$-1$ |
$27$ |
$\PGL(2,7)$ |
24T2668, 24T2669, 42T173 |
| 24T2669 |
$C_3\times \PGL(2,7)$ |
$1008$ |
$-1$ |
|
$-1$ |
$27$ |
$C_3$, $\PGL(2,7)$ |
24T2668 x 2, 42T173 |
| 24T2671 |
$S_3\times \GL(3,2)$ |
$1008$ |
$1$ |
|
$-1$ |
$18$ |
$S_3$, $\PSL(2,7)$ |
21T27 x 2, 42T169 x 2, 42T170 x 2, 42T171 x 2, 42T175 x 2 |
| 24T2947 |
$\SL(2,11)$ |
$1320$ |
$1$ |
|
$-1$ |
$15$ |
$\PSL(2,11)$ |
|
| 24T2948 |
$C_2\times \PSL(2,11)$ |
$1320$ |
$1$ |
|
$-1$ |
$16$ |
$C_2$, $\PSL(2,11)$ |
22T13 x 2 |
| 24T2949 |
$\PGL(2,11)$ |
$1320$ |
$1$ |
|
$-1$ |
$13$ |
$C_2$, $\PGL(2,11)$ |
12T218, 22T14 |
| 24T2952 |
$C_2^2\times A_6$ |
$1440$ |
$1$ |
|
$-1$ |
$28$ |
$C_2$ x 3, $C_2^2$, $A_6$, $C_2\times A_6$ x 3 |
24T2952, 40T1195 x 3, 40T1196 |
| 24T2953 |
$C_4\times A_6$ |
$1440$ |
$1$ |
|
$-1$ |
$28$ |
$C_2$, $C_4$, $A_6$, $C_2\times A_6$ |
24T2953, 40T1193, 40T1194, 40T1197 x 2 |
| 24T2954 |
$A_6.C_2^2$ |
$1440$ |
$1$ |
|
$-1$ |
$16$ |
$C_2$ x 3, $C_2^2$, $A_6.C_2$ |
20T197 x 2, 20T202 x 2, 40T1187, 40T1188, 40T1192 x 4 |
| 24T2955 |
$A_6:C_4$ |
$1440$ |
$1$ |
|
$-1$ |
$16$ |
$C_2$, $C_4$, $A_6.C_2$ |
40T1185, 40T1186, 40T1191 x 2 |
| 24T2956 |
$C_2\times \PGL(2,9)$ |
$1440$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$ x 3, $C_2^2$, $\PGL(2,9)$ |
20T205 x 2, 40T1179, 40T1182 |
| 24T2957 |
$A_6:C_4$ |
$1440$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$, $C_4$, $\PGL(2,9)$ |
20T200 x 2, 40T1180, 40T1181 |
| 24T2958 |
$A_6:C_4$ |
$1440$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$, $C_4$, $S_6$, $S_6$ |
24T2958, 40T1175, 40T1176 |
| 24T2959 |
$C_2\times S_6$ |
$1440$ |
$1$ |
|
$-1$ |
$22$ |
$C_2$ x 3, $C_2^2$, $S_6$, $S_6$, $S_6\times C_2$ x 2 |
12T219 x 4, 20T198 x 2, 20T199 x 2, 24T2959, 30T260 x 4, 30T261 x 4, 40T1177, 40T1178, 40T1189 x 2, 40T1190 x 4 |
| 24T2960 |
$S_6:C_2$ |
$1440$ |
$1$ |
|
$-1$ |
$13$ |
$C_2$ x 3, $C_2^2$, $S_6:C_2$ |
10T35, 12T220, 20T201, 20T204, 20T208, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187 |
| 24T2961 |
$A_4\times S_5$ |
$1440$ |
$1$ |
|
$-1$ |
$28$ |
$A_4$, $\PGL(2,5)$ |
20T206, 30T259, 30T266, 36T2331, 36T2332, 40T1202, 40T1207 |
| 24T2962 |
$A_4:S_5$ |
$1440$ |
$1$ |
|
$-1$ |
$19$ |
$S_4$, $\PGL(2,5)$ |
20T207, 30T265, 30T267, 36T2337, 36T2338, 40T1203, 40T1208 |
Results are complete for degrees $\leq 23$.
