Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 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. #91759 | C2 | semidirect |
| 2. C5×#870 | C2 | semidirect |
| 4. #91430 | C2 | semidirect |
| 5. #91422 | C2 | semidirect |
| 7. #91362 | C2 | semidirect |
| 8. #91361 | C2 | semidirect |
| 9. #91327 | C2 | semidirect |
| 63. #870 | D5 | semidirect |
| 191. C3×C5 | #563 | semidirect |
| 225. C5 | #5672 | semidirect |
| 238. C3 | #66033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91759 | 2 |
| C5×#870 | 2 |
| C3×#4021 | 2 |
| #91430 | 2 |
| #91422 | 2 |
| #91407 | 2 |
| #91362 | 2 |
| #91361 | 2 |
| #91327 | 2 |
| #66033 | 3 |
| #5672 | 5 |