| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 30T1 |
$C_{30}$ |
$30$ |
$-1$ |
✓ |
$1$ |
$30$ |
$C_2$, $C_3$, $C_5$, $C_6$, $C_{10}$, $C_{15}$ |
|
| 30T2 |
$C_5\times S_3$ |
$30$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $C_5$, $S_3$, $C_{10}$, $S_3 \times C_5$ |
15T4 |
| 30T3 |
$D_{15}$ |
$30$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$, $D_{5}$, $S_3$, $D_5$, $D_{15}$ |
15T2 |
| 30T4 |
$C_3\times D_5$ |
$30$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $C_3$, $D_{5}$, $C_6$, $D_5$, $D_5\times C_3$ |
15T3 |
| 30T5 |
$C_3\times D_{10}$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $C_3$, $D_{5}$, $C_6$, $D_{10}$, $D_5\times C_3$ |
30T5 |
| 30T6 |
$C_{15}:C_4$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$9$ |
$C_2$, $S_3$, $F_5$, $S_3$, $F_5$, $C_{15} : C_4$ |
15T6 |
| 30T7 |
$C_3\times F_5$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $C_3$, $F_5$, $C_6$, $F_5$, $F_5\times C_3$ |
15T8 |
| 30T8 |
$S_3\times D_5$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{5}$, $S_3$, $D_{10}$, $D_5\times S_3$ |
15T7, 30T10, 30T13 |
| 30T9 |
$A_5$ |
$60$ |
$1$ |
|
$-1$ |
$5$ |
$A_5$, $\PSL(2,5)$, $A_{5}$, $A_5$ |
5T4, 6T12, 10T7, 12T33, 15T5, 20T15 |
| 30T10 |
$S_3\times D_5$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_5$, $D_5\times S_3$ |
15T7, 30T8, 30T13 |
| 30T11 |
$C_5\times A_4$ |
$60$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_3$, $C_5$, $A_4$, $C_{15}$ |
20T14 |
| 30T12 |
$S_3\times C_{10}$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $C_5$, $D_{6}$, $C_{10}$, $S_3 \times C_5$ |
30T12 |
| 30T13 |
$S_3\times D_5$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$12$ |
$C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_{10}$, $D_5\times S_3$ |
15T7, 30T8, 30T10 |
| 30T14 |
$D_{30}$ |
$60$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_{10}$, $D_{15}$ |
30T14 |
| 30T15 |
$S_3\times C_{15}$ |
$90$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $C_5$, $S_3\times C_3$, $C_{10}$ |
45T3 |
| 30T16 |
$C_3\times D_{15}$ |
$90$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $D_{5}$, $S_3\times C_3$, $D_5$ |
45T5 |
| 30T17 |
$C_{30}:C_4$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $F_5$, $D_{6}$, $F_{5}\times C_2$, $C_{15} : C_4$ |
30T17 |
| 30T18 |
$C_{10}\times A_4$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$40$ |
$C_3$, $C_5$, $A_4\times C_2$, $C_{15}$ |
40T59 |
| 30T19 |
$C_5:S_4$ |
$120$ |
$1$ |
✓ |
$-1$ |
$13$ |
$S_3$, $D_{5}$, $S_4$, $D_{15}$ |
20T33, 30T31, 40T63 |
| 30T20 |
$D_5\times A_4$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $D_{5}$, $A_4\times C_2$, $D_5\times C_3$ |
20T37, 30T28, 40T65 |
| 30T21 |
$S_3\times D_{10}$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$24$ |
$C_2$, $S_3$, $D_{5}$, $D_{6}$, $D_{10}$, $D_5\times S_3$ |
30T21 x 3 |
| 30T22 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$7$ |
$S_5$, $\PGL(2,5)$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T25, 30T27, 40T62 |
| 30T23 |
$S_3\times F_5$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $F_5$, $D_{6}$, $F_{5}\times C_2$, $F_5 \times S_3$ |
15T11, 30T24, 30T32 |
| 30T24 |
$S_3\times F_5$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $F_5$, $D_{6}$, $F_5$, $F_5 \times S_3$ |
15T11, 30T23, 30T32 |
| 30T25 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$7$ |
$C_2$, $S_5$, $S_5$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T27, 40T62 |
| 30T26 |
$C_6\times F_5$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_3$, $F_5$, $C_6$, $F_{5}\times C_2$, $F_5\times C_3$ |
30T26 |
| 30T27 |
$S_5$ |
$120$ |
$1$ |
|
$-1$ |
$7$ |
$S_5$, $S_5$, $S_5$ |
5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 40T62 |
| 30T28 |
$D_5\times A_4$ |
$120$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $D_{5}$, $A_4$, $D_5\times C_3$ |
20T37, 30T20, 40T65 |
| 30T29 |
$C_2\times A_5$ |
$120$ |
$-1$ |
|
$-1$ |
$10$ |
$A_5$, $A_5$ |
10T11, 12T75, 12T76, 20T31, 20T36, 24T203, 30T30, 40T61 |
| 30T30 |
$C_2\times A_5$ |
$120$ |
$-1$ |
|
$-1$ |
$10$ |
$C_2$, $A_5$, $A_5\times C_2$, $A_5$ |
10T11, 12T75, 12T76, 20T31, 20T36, 24T203, 30T29, 40T61 |
| 30T31 |
$C_5:S_4$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$S_3$, $D_{5}$, $S_4$, $D_{15}$ |
20T33, 30T19, 40T63 |
| 30T32 |
$S_3\times F_5$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $S_3$, $F_5$, $S_3$, $F_{5}\times C_2$, $F_5 \times S_3$ |
15T11, 30T23, 30T24 |
| 30T33 |
$C_5\times S_4$ |
$120$ |
$1$ |
✓ |
$-1$ |
$25$ |
$S_3$, $C_5$, $S_4$, $S_3 \times C_5$ |
20T34, 30T34, 40T64 |
| 30T34 |
$C_5\times S_4$ |
$120$ |
$-1$ |
✓ |
$-1$ |
$25$ |
$S_3$, $C_5$, $S_4$, $S_3 \times C_5$ |
20T34, 30T33, 40T64 |
| 30T35 |
$C_5^2:C_6$ |
$150$ |
$-1$ |
✓ |
$-1$ |
$10$ |
$C_2$, $C_3$, $C_6$, $(C_5^2 : C_3):C_2$ |
15T12 x 2, 25T15, 30T35 |
| 30T36 |
$C_5\times D_{15}$ |
$150$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3$, $S_3$, $D_5\times C_5$ |
30T36 |
| 30T37 |
$C_5^2:S_3$ |
$150$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $S_3$, $S_3$, $(C_5^2 : C_3):C_2$ |
15T13, 15T14, 25T16, 30T38 |
| 30T38 |
$C_5^2:S_3$ |
$150$ |
$-1$ |
✓ |
$-1$ |
$13$ |
$C_2$, $S_3$, $S_3$, $(C_5^2 : C_3):C_2$ |
15T13, 15T14, 25T16, 30T37 |
| 30T39 |
$D_5\times C_{15}$ |
$150$ |
$-1$ |
✓ |
$-1$ |
$60$ |
$C_2$, $C_3$, $C_6$, $D_5\times C_5$ |
30T39 |
| 30T40 |
$C_5^2:C_6$ |
$150$ |
$-1$ |
✓ |
$-1$ |
$22$ |
$C_2$, $C_3$, $C_6$, $C_5^2 : C_3$ |
30T40 |
| 30T41 |
$C_5\times S_3^2$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $C_5$, $S_3^2$, $C_{10}$ |
45T15 |
| 30T42 |
$S_3\times D_{15}$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $D_{5}$, $S_3^2$, $D_{10}$ |
45T13 |
| 30T43 |
$C_{15}:D_6$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$21$ |
$C_2$, $D_{5}$, $S_3^2$, $D_5$ |
45T21 |
| 30T44 |
$C_{15}:D_6$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $D_{5}$, $S_3\times C_3$, $D_{10}$ |
45T14 |
| 30T45 |
$\GL(2,4)$ |
$180$ |
$1$ |
|
$-1$ |
$15$ |
$C_3$, $A_{5}$ |
15T15 x 2, 15T16, 18T90, 36T176, 45T16 |
| 30T46 |
$C_3^2:F_5$ |
$180$ |
$1$ |
✓ |
$-1$ |
$15$ |
$C_2$, $F_5$, $C_3^2:C_4$, $F_5$ |
30T46, 45T27 |
| 30T47 |
$C_{15}:C_{12}$ |
$180$ |
$-1$ |
✓ |
$-1$ |
$27$ |
$C_2$, $F_5$, $S_3\times C_3$, $F_5$ |
45T18 |
| 30T48 |
$(C_3\times C_{15}):C_4$ |
$180$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $D_{5}$, $C_3^2:C_4$, $D_5$ |
30T48, 45T26 |
| 30T49 |
$C_3^2:C_{20}$ |
$180$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $C_5$, $C_3^2:C_4$, $C_{10}$ |
30T49, 45T25 |
| 30T50 |
$F_{16}$ |
$240$ |
$1$ |
✓ |
$-1$ |
$16$ |
$C_3$, $C_5$, $C_{15}$ |
16T447, 20T67 |
Results are complete for degrees $\leq 23$.
