Refine search
Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
---|---|---|---|---|---|---|
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 |
15T5 | $A_5$ | $60$ | $1$ | $A_5$ | 5T4, 6T12, 10T7, 12T33, 20T15, 30T9 | |
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 |
15T10 | $S_5$ | $120$ | $1$ | $S_5$ | 5T5, 6T14, 10T12, 10T13, 12T74, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 | |
15T11 | $F_5 \times S_3$ | $120$ | $-1$ | ✓ | $S_3$, $F_5$ | 30T23, 30T24, 30T32 |
15T12 | $(C_5^2 : C_3):C_2$ | $150$ | $1$ | ✓ | $C_3$ | 15T12, 25T15, 30T35 x 2 |
15T13 | $(C_5^2 : C_3):C_2$ | $150$ | $-1$ | ✓ | $S_3$ | 15T14, 25T16, 30T37, 30T38 |
15T14 | $(C_5^2 : C_3):C_2$ | $150$ | $-1$ | ✓ | $S_3$ | 15T13, 25T16, 30T37, 30T38 |
15T15 | $\GL(2,4)$ | $180$ | $1$ | $A_5$ | 15T15, 15T16, 18T90, 30T45, 36T176, 45T16 | |
15T16 | $\GL(2,4)$ | $180$ | $1$ | $C_3$, $A_5$ | 15T15 x 2, 18T90, 30T45, 36T176, 45T16 | |
15T17 | $(C_5^2 : C_3):C_4$ | $300$ | $1$ | ✓ | $S_3$ | 15T17, 25T28, 30T71 x 2 |
15T18 | $((C_5^2 : C_3):C_2):C_2$ | $300$ | $-1$ | ✓ | $S_3$ | 15T18, 25T27, 30T66 x 2, 30T72 x 2, 30T80 x 2 |
15T19 | $(C_5^2 : C_4):C_3$ | $300$ | $-1$ | ✓ | $C_3$ | 15T19, 25T26, 30T78 x 2 |
15T20 | $A_6$ | $360$ | $1$ | 6T15 x 2, 10T26, 15T20, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 | ||
15T21 | $\GL(2,4):C_2$ | $360$ | $1$ | $S_5$ | 15T21, 15T22, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45 | |
15T22 | $\GL(2,4):C_2$ | $360$ | $1$ | $S_3$, $S_5$ | 15T21 x 2, 18T146, 30T89, 30T93 x 2, 30T101, 36T554, 45T45 | |
15T23 | $A_5 \times S_3$ | $360$ | $-1$ | $S_3$, $A_5$ | 18T145, 30T85, 30T94, 30T102, 36T551, 36T552, 36T553, 45T40 | |
15T24 | $S_5 \times C_3$ | $360$ | $-1$ | $C_3$, $S_5$ | 18T144, 30T90, 30T98, 30T103, 36T550, 45T44 | |
15T25 | $C_5\wr C_3$ | $375$ | $1$ | ✓ | $C_3$ | 15T25 x 7 |
15T26 | $C_3^4:C_5$ | $405$ | $1$ | ✓ | $C_5$ | 15T26 x 7, 45T61 x 2, 45T62 x 16, 45T63 x 8 |
15T27 | $C_5^2:(C_4\times S_3)$ | $600$ | $-1$ | ✓ | $S_3$ | 15T27, 25T43, 30T150 x 2, 30T153 x 2, 30T155 x 2 |
15T28 | $S_6$ | $720$ | $1$ | 6T16 x 2, 10T32, 12T183 x 2, 15T28, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 | ||
15T29 | $S_5 \times S_3$ | $720$ | $-1$ | $S_3$, $S_5$ | 18T227, 30T165, 30T167, 30T170, 30T174, 30T178, 36T1249, 36T1250, 36T1251, 45T94 | |
15T30 | $C_5^3:C_6$ | $750$ | $1$ | ✓ | $C_3$ | 15T30 x 7, 30T188 x 8 |
15T31 | $C_5^2:D_{15}$ | $750$ | $-1$ | ✓ | $S_3$ | 15T31 x 3, 30T186 x 4, 30T187 x 2 |
15T32 | $C_5\wr S_3$ | $750$ | $-1$ | ✓ | $S_3$ | 15T32 x 3, 30T184 x 4, 30T185 x 2 |
15T33 | $C_3^4:C_{10}$ | $810$ | $-1$ | ✓ | $C_5$ | 15T33 x 7, 30T190 x 8, 45T118 x 2, 45T119 x 16, 45T120 x 8 |
15T34 | $C_3^4:D_5$ | $810$ | $1$ | ✓ | $D_{5}$ | 15T34 x 3, 15T35 x 4, 30T191 x 4, 30T192 x 4, 45T121 x 8, 45T122 x 8, 45T123, 45T124 |
15T35 | $C_3^4:D_5$ | $810$ | $-1$ | ✓ | $D_{5}$ | 15T34 x 4, 15T35 x 3, 30T191 x 4, 30T192 x 4, 45T121 x 8, 45T122 x 8, 45T123, 45T124 |
15T36 | $C_3\wr C_5$ | $1215$ | $1$ | ✓ | $C_5$ | 15T36 x 15, 45T164 x 8, 45T165 x 16, 45T166 x 32, 45T167 x 32, 45T168 x 64, 45T169 x 64 |
15T37 | $C_5\wr C_3:C_4$ | $1500$ | $1$ | ✓ | $S_3$ | 15T37 x 3, 30T282 x 2, 30T288 x 4 |
15T38 | $C_5^3:C_{12}$ | $1500$ | $-1$ | ✓ | $C_3$ | 15T38 x 7, 30T287 x 8 |
15T39 | $C_5^3:A_4$ | $1500$ | $1$ | ✓ | $C_3$ | 20T209, 30T271 x 2, 30T277, 30T279, 30T281 |
15T40 | $C_5^3:D_6$ | $1500$ | $-1$ | ✓ | $S_3$ | 15T40 x 3, 30T273 x 4, 30T275 x 4, 30T280 x 2, 30T284 x 4 |
15T41 | $C_3^4:F_5$ | $1620$ | $-1$ | ✓ | $F_5$ | 15T42, 30T295, 30T296, 30T298, 30T299, 30T302, 45T204, 45T210 |
15T42 | $C_3^4:F_5$ | $1620$ | $1$ | ✓ | $F_5$ | 15T41, 30T295, 30T296, 30T298, 30T299, 30T302, 45T204, 45T210 |
15T43 | $C_3^4:D_{10}$ | $1620$ | $-1$ | ✓ | $D_{5}$ | 15T43 x 7, 30T290 x 8, 30T291 x 8, 30T297 x 8, 45T205 x 16, 45T206 x 2 |
15T44 | $C_7^3:C_6$ | $2430$ | $-1$ | ✓ | $C_5$ | 15T44 x 15, 30T394 x 16, 45T253 x 8, 45T254 x 16, 45T255 x 32, 45T256 x 32, 45T257 x 64, 45T258 x 64 |
15T45 | $C_3^4:D_{15}$ | $2430$ | $-1$ | ✓ | $D_{5}$ | 15T45 x 7, 30T389 x 8, 30T392 x 4, 45T248 x 4, 45T249 x 4, 45T259 x 16, 45T260 x 16, 45T264 x 8 |
15T46 | $C_3\wr D_5$ | $2430$ | $1$ | ✓ | $D_{5}$ | 15T46 x 7, 30T388 x 4, 30T391 x 8, 45T250 x 4, 45T251 x 4, 45T261 x 8, 45T262 x 16, 45T263 x 16 |
15T47 | $A_7$ | $2520$ | $1$ | 7T6, 15T47, 21T33, 35T28, 42T294, 42T299 | ||
15T48 | $C_5^3:S_4$ | $3000$ | $-1$ | ✓ | $S_3$ | 20T270, 30T413, 30T424, 30T431, 30T432, 30T440, 40T2385 |
15T49 | $C_9^2\times C_{54}$ | $3000$ | $-1$ | ✓ | $S_3$ | 15T49 x 3, 30T433 x 4, 30T435 x 2, 30T438 x 4, 30T442 x 4 |
15T50 | $D_5\wr C_3$ | $3000$ | $1$ | ✓ | $C_3$ | 20T269, 30T408, 30T418, 30T419 x 2, 30T420 x 2, 30T421, 30T425, 30T426, 40T2384 |
Results are complete for degrees $\leq 23$.