Finite Group DatabasebetaFinite Group DatabasebetaOrder 5024.
42 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D157⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4⋊#10597845 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q8×D157 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#10597845 | — | 2 | 1 | no | — |
| 5 | #11929441 | — | 2 | 1 | no | — |
| 6 | Dic314 | — | 2 | 1 | no | — |
| 7 | Dic314 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C4×D157 | — | 2 | 1 | no | — |
| 9 | C4×D157 | C22 | 1 | 1 | yes | characteristic |
| 10 | Q8×C157 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×D157 | D4 | 1 | 1 | yes | characteristic |
| 12 | #10597845 | — | 4 | 1 | no | — |
| 13 | C4×C157 | — | 2 | 1 | no | — |
| 14 | C4×C157 | C2×C4 | 1 | 1 | yes | characteristic |
| 15 | Dic157 | — | 2 | 1 | no | — |
| 16 | Dic157 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×C157 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 18 | D157 | SD16 | 1 | 1 | yes | characteristic |
| 19 | D157 | Q16 | 1 | 1 | yes | characteristic |
| 20 | C157 | #103 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | #103 | — | 157 | 1 | no | maximal, Sylow |
| 22 | C2×Q8 | — | 157 | 1 | no | — |
| 23 | C2×C8 | — | 157 | 1 | no | — |
| 24 | C4⋊C4 | — | 157 | 1 | no | — |
| 25 | Q8 | — | 314 | 1 | no | — |
| 26 | Q8 | — | 157 | 1 | no | — |
| 27 | Q8 | #10597845 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×C4 | — | 314 | 1 | no | — |
| 29 | C2×C4 | — | 314 | 1 | no | — |
| 30 | C2×C4 | — | 157 | 1 | no | — |
| 31 | C8 | — | 314 | 1 | no | — |
| 32 | C22 | — | 157 | 1 | no | — |
| 33 | C4 | — | 2 | 1 | no | — |
| 34 | C4 | — | 314 | 1 | no | — |
| 35 | C4 | — | 628 | 1 | no | — |
| 36 | C4 | — | 157 | 1 | no | — |
| 37 | C4 | C2×#10597845 | 1 | 1 | yes | characteristic |
| 38 | C2 | — | 157 | 1 | no | — |
| 39 | C2 | — | 157 | 1 | no | — |
| 40 | C2 | C22⋊#10597845 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. Dic314 | C4 | semidirect |
| 10. Q8×C157 | C4 | semidirect |
| 20. C157 | #103 | semidirect |
| 27. Q8 | #10597845 | semidirect |