Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 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. #91758 | C2 | semidirect |
| 3. C3×C4×Dic10 | C2 | semidirect |
| 4. #91432 | C2 | semidirect |
| 5. D3×C4⋊Dic5 | C2 | semidirect |
| 7. #91388 | C2 | semidirect |
| 8. #91369 | C2 | semidirect |
| 34. C4×Dic10 | D3 | semidirect |
| 42. C5×D12 | Q8 | semidirect |
| 134. D12 | Dic10 | semidirect |
| 165. C3×C5 | #554 | semidirect |
| 198. C5 | #5579 | semidirect |
| 210. C3 | #65877 | 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×Dic10 | 2 |
| #91432 | 2 |
| D3×C4⋊Dic5 | 2 |
| Dic5×D12 | 2 |
| #91388 | 2 |
| #91369 | 2 |
| #65877 | 3 |
| #5579 | 5 |