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. #91786 | C2 | semidirect |
| 2. C5×#893 | C2 | semidirect |
| 3. C3×#4034 | C2 | semidirect |
| 5. #91386 | C2 | semidirect |
| 6. #91373 | C2 | semidirect |
| 7. #91369 | C2 | semidirect |
| 8. #91351 | C2 | semidirect |
| 9. #91342 | C2 | semidirect |
| 10. #91340 | C2 | semidirect |
| 11. #91326 | C2 | semidirect |
| 43. #4034 | D3 | semidirect |
| 72. #893 | D5 | semidirect |
| 228. C3×C5 | #542 | semidirect |
| 272. C5 | #5733 | semidirect |
| 289. C3 | #65895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91786 | 2 |
| C5×#893 | 2 |
| C3×#4034 | 2 |
| #91466 | 2 |
| #91386 | 2 |
| #91373 | 2 |
| #91369 | 2 |
| #91351 | 2 |
| #91342 | 2 |
| #91340 | 2 |
| #91326 | 2 |
| #65895 | 3 |
| #5733 | 5 |