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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
1T1 | Trivial | $1$ | $1$ | ✓ | ||
2T1 | $C_2$ | $2$ | $-1$ | ✓ | ||
3T1 | $C_3$ | $3$ | $1$ | ✓ | ||
3T2 | $S_3$ | $6$ | $-1$ | ✓ | 6T2 | |
4T4 | $A_4$ | $12$ | $1$ | ✓ | 6T4, 12T4 | |
4T5 | $S_4$ | $24$ | $-1$ | ✓ | 6T7, 6T8, 8T14, 12T8, 12T9, 24T10 | |
5T1 | $C_5$ | $5$ | $1$ | ✓ | ||
5T2 | $D_{5}$ | $10$ | $1$ | ✓ | 10T2 | |
5T3 | $F_5$ | $20$ | $-1$ | ✓ | 10T4, 20T5 | |
5T4 | $A_5$ | $60$ | $1$ | 6T12, 10T7, 12T33, 15T5, 20T15, 30T9 | ||
5T5 | $S_5$ | $120$ | $-1$ | 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 | ||
6T12 | $\PSL(2,5)$ | $60$ | $1$ | 5T4, 10T7, 12T33, 15T5, 20T15, 30T9 | ||
6T14 | $\PGL(2,5)$ | $120$ | $-1$ | 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 | ||
6T15 | $A_6$ | $360$ | $1$ | 6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 | ||
6T16 | $S_6$ | $720$ | $-1$ | 6T16, 10T32, 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 | ||
7T1 | $C_7$ | $7$ | $1$ | ✓ | ||
7T2 | $D_{7}$ | $14$ | $-1$ | ✓ | 14T2 | |
7T3 | $C_7:C_3$ | $21$ | $1$ | ✓ | 21T2 | |
7T4 | $F_7$ | $42$ | $-1$ | ✓ | 14T4, 21T4, 42T4 | |
7T5 | $\GL(3,2)$ | $168$ | $1$ | 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2 | ||
7T6 | $A_7$ | $2520$ | $1$ | 15T47 x 2, 21T33, 35T28, 42T294, 42T299 | ||
7T7 | $S_7$ | $5040$ | $-1$ | 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418 | ||
8T25 | $C_2^3:C_7$ | $56$ | $1$ | ✓ | 14T6, 28T11 | |
8T36 | $C_2^3:(C_7: C_3)$ | $168$ | $1$ | ✓ | 14T11, 24T283, 28T27, 42T26 | |
8T37 | $\PSL(2,7)$ | $168$ | $1$ | 7T5 x 2, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2 | ||
8T43 | $\PGL(2,7)$ | $336$ | $-1$ | 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83 | ||
8T48 | $C_2^3:\GL(3,2)$ | $1344$ | $1$ | 8T48, 14T34 x 2, 28T153, 28T159 x 2, 42T210 x 2, 42T211 x 2 | ||
8T49 | $A_8$ | $20160$ | $1$ | 15T72 x 2, 28T433, 35T36 | ||
8T50 | $S_8$ | $40320$ | $-1$ | 16T1838, 28T502, 30T1153, 35T44 | ||
9T9 | $C_3^2:C_4$ | $36$ | $1$ | ✓ | 6T10 x 2, 12T17 x 2, 18T10, 36T14 | |
9T14 | $C_3^2:Q_8$ | $72$ | $1$ | ✓ | 12T47, 18T35 x 3, 24T82, 36T55 | |
9T15 | $C_3^2:C_8$ | $72$ | $-1$ | ✓ | 12T46, 18T28, 24T81, 36T49 | |
9T16 | $S_3^2:C_2$ | $72$ | $-1$ | ✓ | 6T13 x 2, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 | |
9T19 | $(C_3^2:C_8):C_2$ | $144$ | $-1$ | ✓ | 12T84, 18T68, 18T71, 18T73, 24T278, 24T279, 24T280, 36T171, 36T172, 36T175 | |
9T23 | $(C_3^2:Q_8):C_3$ | $216$ | $1$ | ✓ | 12T122, 24T562, 24T569, 27T82, 36T287, 36T309 | |
9T26 | $((C_3^2:Q_8):C_3):C_2$ | $432$ | $-1$ | ✓ | 12T157, 18T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709 | |
9T27 | $\PSL(2,8)$ | $504$ | $1$ | 28T70, 36T712 | ||
9T32 | $\mathrm{P}\Gamma\mathrm{L}(2,8)$ | $1512$ | $1$ | 27T391, 28T165, 36T2342 | ||
9T33 | $A_9$ | $181440$ | $1$ | 36T23796 | ||
9T34 | $S_9$ | $362880$ | $-1$ | 18T887, 36T28590 | ||
10T7 | $A_{5}$ | $60$ | $1$ | 5T4, 6T12, 12T33, 15T5, 20T15, 30T9 | ||
10T13 | $S_5$ | $120$ | $-1$ | 5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 | ||
10T26 | $\PSL(2,9)$ | $360$ | $1$ | 6T15 x 2, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 | ||
10T30 | $\PGL(2,9)$ | $720$ | $-1$ | 12T182, 20T146, 30T171, 36T1254, 40T590, 45T110 | ||
10T31 | $M_{10}$ | $720$ | $1$ | 12T181, 20T148, 20T150 x 2, 30T162, 36T1253, 40T591, 45T109 | ||
10T32 | $S_{6}$ | $720$ | $-1$ | 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 | ||
10T35 | $(A_6 : C_2) : C_2$ | $1440$ | $-1$ | 12T220, 20T201, 20T204, 20T208, 24T2960, 30T264, 36T2341, 40T1198, 40T1199, 40T1201, 45T187 | ||
10T44 | $A_{10}$ | $1814400$ | $1$ | 45T1982 | ||
10T45 | $S_{10}$ | $3628800$ | $-1$ | 20T1007, 45T2246 | ||
11T1 | $C_{11}$ | $11$ | $1$ | ✓ |
Results are complete for degrees $\leq 23$.