Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
724 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11756557 | C2 | semidirect |
| 3. C2×C3×#3965 | C2 | semidirect |
| 4. #11748424 | C2 | semidirect |
| 5. #11745971 | C2 | semidirect |
| 13. C5×#940 | C4 | semidirect |
| 15. C5×#936 | C4 | semidirect |
| 24. C2×#3965 | D3 | semidirect |
| 37. C2×C5×D12 | C2×C4 | semidirect |
| 39. C2×C5×Dic6 | C2×C4 | semidirect |
| 43. C4×Dic15 | D4 | semidirect |
| 47. C4×C5×Dic3 | C2×C4 | semidirect |
| 98. #940 | Dic5 | semidirect |
| 100. #936 | Dic5 | semidirect |
| 162. C2×D12 | C2×Dic5 | semidirect |
| 164. C2×Dic6 | C2×Dic5 | semidirect |
| 175. C4×Dic3 | C2×Dic5 | semidirect |
| 281. C3×C5 | #1911 | semidirect |
| 332. C5 | #70071 | semidirect |
| 348. C3 | #10602646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756557 | 2 |
| C5×#5805 | 2 |
| C2×C3×#3965 | 2 |
| #11748424 | 2 |
| #11745971 | 2 |
| #10602646 | 3 |
| #70071 | 5 |