Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
280 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C5×D24 | C2 | semidirect |
| 2. #91463 | C2 | semidirect |
| 3. #91435 | C2 | semidirect |
| 4. C2×#6652 | C2 | semidirect |
| 5. #91098 | C2 | semidirect |
| 6. C3×#3953 | C2 | semidirect |
| 7. #90966 | C2 | semidirect |
| 28. #3953 | D3 | semidirect |
| 39. C5×D12 | D4 | semidirect |
| 50. C2×D24 | D5 | semidirect |
| 82. Dic15 | D8 | semidirect |
| 142. D12 | C22⋊D5 | semidirect |
| 174. C3×C5 | #459 | semidirect |
| 220. C5 | #4786 | semidirect |
| 236. C3 | #65439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D24 | 2 |
| #91463 | 2 |
| #91435 | 2 |
| C2×#6652 | 2 |
| #91098 | 2 |
| C3×#3953 | 2 |
| #90966 | 2 |
| #65439 | 3 |
| #4786 | 5 |