Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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. #91790 | C2 | semidirect |
| 2. C2×C3×D40 | C2 | semidirect |
| 3. #91312 | C2 | semidirect |
| 4. C5×#819 | C2 | semidirect |
| 5. #90958 | C2 | semidirect |
| 20. C2×D40 | D3 | semidirect |
| 40. #819 | D5 | semidirect |
| 122. C3×C5 | #472 | semidirect |
| 150. C5 | #5160 | semidirect |
| 158. C3 | #65186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91790 | 2 |
| C2×C3×D40 | 2 |
| #91312 | 2 |
| C5×#819 | 2 |
| #90958 | 2 |
| #65186 | 3 |
| #5160 | 5 |