Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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. #91777 | C2 | semidirect |
| 2. C5×#893 | C2 | semidirect |
| 3. C3×#4043 | C2 | semidirect |
| 4. #91462 | C2 | semidirect |
| 5. #91452 | C2 | semidirect |
| 7. #91370 | C2 | semidirect |
| 8. #91365 | C2 | semidirect |
| 9. #91357 | C2 | semidirect |
| 10. #91341 | C2 | semidirect |
| 11. Dic3×Dic10 | C2 | semidirect |
| 42. #4043 | D3 | semidirect |
| 72. #893 | D5 | semidirect |
| 228. C3×C5 | #542 | semidirect |
| 272. C5 | #5643 | semidirect |
| 289. C3 | #65895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91777 | 2 |
| C5×#893 | 2 |
| C3×#4043 | 2 |
| #91462 | 2 |
| #91452 | 2 |
| #91449 | 2 |
| #91370 | 2 |
| #91365 | 2 |
| #91357 | 2 |
| #91341 | 2 |
| Dic3×Dic10 | 2 |
| #65895 | 3 |
| #5643 | 5 |