Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C42×C5 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #555 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #91758 | C2 | semidirect |
| 2. C4×C5×D12 | C2 | semidirect |
| 3. C3×C4×D20 | C2 | semidirect |
| 4. #91462 | C2 | semidirect |
| 5. #91456 | C2 | semidirect |
| 6. #91449 | C2 | semidirect |
| 7. #91358 | C2 | semidirect |
| 8. #91338 | C2 | semidirect |
| 33. C4×D20 | D3 | semidirect |
| 55. C4×D12 | D5 | semidirect |
| 173. C3×C5 | #555 | semidirect |
| 211. C5 | #5563 | semidirect |
| 225. C3 | #65897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91758 | 2 |
| C4×C5×D12 | 2 |
| C3×C4×D20 | 2 |
| #91462 | 2 |
| #91456 | 2 |
| #91449 | 2 |
| #91358 | 2 |
| #91338 | 2 |
| #65897 | 3 |
| #5563 | 5 |