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Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
13T1 | $C_{13}$ | $13$ | $1$ | ✓ | ||
13T2 | $D_{13}$ | $26$ | $1$ | ✓ | 26T2 | |
13T3 | $C_{13}:C_3$ | $39$ | $1$ | ✓ | 39T2 | |
13T4 | $C_{13}:C_4$ | $52$ | $-1$ | ✓ | 26T4 | |
13T5 | $C_{13}:C_6$ | $78$ | $1$ | ✓ | 26T6, 39T6 | |
13T6 | $F_{13}$ | $156$ | $-1$ | ✓ | 26T8, 39T11 | |
14T1 | $C_{14}$ | $14$ | $-1$ | ✓ | $C_2$, $C_7$ | |
14T2 | $D_{7}$ | $14$ | $-1$ | ✓ | $C_2$, $D_{7}$ | 7T2 |
14T3 | $D_{14}$ | $28$ | $-1$ | ✓ | $C_2$, $D_{7}$ | 14T3, 28T4 |
14T4 | $F_7$ | $42$ | $-1$ | ✓ | $C_2$, $F_7$ | 7T4, 21T4, 42T4 |
14T5 | $(C_7:C_3) \times C_2$ | $42$ | $-1$ | ✓ | $C_2$, $C_7:C_3$ | 42T2 |
14T6 | $F_8$ | $56$ | $1$ | ✓ | $C_7$ | 8T25, 28T11 |
14T7 | $F_7 \times C_2$ | $84$ | $-1$ | ✓ | $C_2$, $F_7$ | 14T7, 28T15, 42T10 x 2 |
14T8 | $C_7 \wr C_2$ | $98$ | $-1$ | ✓ | $C_2$ | 14T8 x 2 |
14T9 | $C_2\times F_8$ | $112$ | $-1$ | ✓ | $C_7$ | 16T196, 28T19 x 3, 28T20 |
14T11 | $F_8:C_3$ | $168$ | $1$ | ✓ | $C_7:C_3$ | 8T36, 24T283, 28T27, 42T26 |
14T12 | $C_7^2:C_4$ | $196$ | $1$ | ✓ | $C_2$ | 14T12 x 3, 28T35 x 4 |
14T13 | $D_7^2$ | $196$ | $-1$ | ✓ | $C_2$ | 14T13 x 2, 28T36 x 3 |
14T14 | $C_7:F_7$ | $294$ | $-1$ | ✓ | $C_2$ | 14T14 x 2, 42T61 x 3 |
14T15 | $C_7^2:S_3$ | $294$ | $-1$ | ✓ | $C_2$ | 21T17, 21T18, 42T56, 42T57, 42T62 |
14T18 | $F_8:C_6$ | $336$ | $-1$ | ✓ | $C_7:C_3$ | 16T712, 28T44, 42T67 |
14T20 | $D_7 \wr C_2$ | $392$ | $-1$ | ✓ | $C_2$ | 14T20, 28T53 x 2, 28T54 x 2, 28T55 x 2, 28T57 |
14T21 | $C_2^3:F_8$ | $448$ | $1$ | ✓ | $C_7$ | 14T21 x 6, 28T62 x 21, 28T63 x 14, 28T64 x 42, 28T65 x 7, 28T66 x 7 |
14T22 | $C_7^2:C_3:C_4$ | $588$ | $1$ | ✓ | $C_2$ | 28T75, 42T119, 42T125 |
14T23 | $C_7^2:C_{12}$ | $588$ | $1$ | ✓ | $C_2$ | 14T23 x 3, 28T76 x 4, 42T120 x 4 |
14T24 | $D_7:F_7$ | $588$ | $-1$ | ✓ | $C_2$ | 14T24 x 2, 28T77 x 3, 42T121 x 3 |
14T25 | $C_7^2:D_6$ | $588$ | $-1$ | ✓ | $C_2$ | 21T23 x 2, 28T78, 42T110 x 2, 42T111 x 2, 42T112 x 2, 42T122 |
14T26 | $C_7^2:(C_3\times S_3)$ | $882$ | $-1$ | ✓ | $C_2$ | 21T25, 21T26, 42T143, 42T144, 42T152, 42T153, 42T154, 42T155 |
14T27 | $C_2^6:D_7$ | $896$ | $-1$ | ✓ | $D_{7}$ | 14T27 x 6, 14T28 x 7, 16T1078, 28T98, 28T105 x 7, 28T106 x 21, 28T107 x 21, 28T108 x 7, 28T109 x 7 |
14T28 | $C_2^6:D_7$ | $896$ | $1$ | ✓ | $D_{7}$ | 14T27 x 7, 14T28 x 6, 16T1078, 28T98, 28T105 x 7, 28T106 x 21, 28T107 x 21, 28T108 x 7, 28T109 x 7 |
14T29 | $C_2 \wr C_7$ | $896$ | $-1$ | ✓ | $C_7$ | 14T29 x 6, 28T104 x 7, 28T110 x 21, 28T111 x 42, 28T112 x 42, 28T113 x 21, 28T114 x 42, 28T115 x 42, 28T116 x 14, 28T117 x 42, 28T118 x 7 |
14T31 | $D_7^2:S_3$ | $1176$ | $-1$ | ✓ | $C_2$ | 28T133, 28T134, 28T135, 42T194, 42T196 |
14T32 | $D_7^2:C_6$ | $1176$ | $-1$ | ✓ | $C_2$ | 14T32, 28T136 x 2, 28T137 x 2, 28T138 x 2, 28T143, 42T195 x 2 |
14T35 | $C_2^3:F_8:C_3$ | $1344$ | $1$ | ✓ | $C_7:C_3$ | 28T154, 28T155 x 2, 28T157, 42T202, 42T204, 42T205 |
14T36 | $C_7^2:C_3:C_{12}$ | $1764$ | $1$ | ✓ | $C_2$ | 28T169, 42T248, 42T249, 42T250, 42T251, 42T257 |
14T37 | $C_7^2:(C_6\times S_3)$ | $1764$ | $-1$ | ✓ | $C_2$ | 21T29 x 2, 28T170, 42T223 x 2, 42T224 x 2, 42T225 x 2, 42T252, 42T253, 42T254, 42T255 |
14T38 | $C_2\wr D_7$ | $1792$ | $-1$ | ✓ | $D_{7}$ | 14T38 x 13, 28T175, 28T185 x 21, 28T186 x 7, 28T193 x 7, 28T194 x 42, 28T195 x 42, 28T196 x 14, 28T197 x 14, 32T97728 |
14T40 | $C_2^6:F_7$ | $2688$ | $-1$ | ✓ | $F_7$ | 14T41, 16T1502, 28T215, 28T227, 28T228, 28T237, 42T314, 42T315, 42T316, 42T317, 42T318, 42T319 |
14T41 | $C_2^6:F_7$ | $2688$ | $1$ | ✓ | $F_7$ | 14T40, 16T1502, 28T215, 28T227, 28T228, 28T237, 42T314, 42T315, 42T316, 42T317, 42T318, 42T319 |
14T44 | $C_2\wr C_7:C_3$ | $2688$ | $-1$ | ✓ | $C_7:C_3$ | 28T226, 28T235 x 2, 28T236, 42T309, 42T310, 42T311 |
14T45 | $F_7\wr C_2$ | $3528$ | $-1$ | ✓ | $C_2$ | 28T251, 28T252, 28T253, 42T368, 42T369, 42T370, 42T371, 42T372 |
14T48 | $C_2\wr F_7$ | $5376$ | $-1$ | ✓ | $F_7$ | 14T48, 28T287, 28T308, 28T315, 28T316 x 2, 28T317 x 2, 32T397084, 42T448 x 2, 42T449 x 2, 42T450 x 2 |
15T1 | $C_{15}$ | $15$ | $1$ | ✓ | $C_3$, $C_5$ | |
15T2 | $D_{15}$ | $30$ | $-1$ | ✓ | $S_3$, $D_{5}$ | 30T3 |
15T3 | $D_5\times C_3$ | $30$ | $1$ | ✓ | $C_3$, $D_{5}$ | 30T4 |
15T4 | $S_3 \times C_5$ | $30$ | $-1$ | ✓ | $S_3$, $C_5$ | 30T2 |
15T6 | $C_{15} : C_4$ | $60$ | $1$ | ✓ | $S_3$, $F_5$ | 30T6 |
15T7 | $D_5\times S_3$ | $60$ | $-1$ | ✓ | $S_3$, $D_{5}$ | 30T8, 30T10, 30T13 |
15T8 | $F_5\times C_3$ | $60$ | $-1$ | ✓ | $C_3$, $F_5$ | 30T7 |
15T9 | $C_5^2 : C_3$ | $75$ | $1$ | ✓ | $C_3$ | 15T9, 25T6 |
Results are complete for degrees $\leq 23$.