Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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. C5×#897 | C2 | semidirect |
| 3. C2×#6660 | C2 | semidirect |
| 4. C2×#6650 | C2 | semidirect |
| 5. #91093 | C2 | semidirect |
| 6. C3×#3939 | C2 | semidirect |
| 7. #90972 | C2 | semidirect |
| 29. #3939 | D3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 48. #897 | D5 | semidirect |
| 108. #168 | D12 | semidirect |
| 163. C3×C5 | #468 | semidirect |
| 203. C5 | #4886 | semidirect |
| 217. C3 | #65338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#897 | 2 |
| #91460 | 2 |
| C2×#6660 | 2 |
| C2×#6650 | 2 |
| #91093 | 2 |
| C3×#3939 | 2 |
| #90972 | 2 |
| #65338 | 3 |
| #4886 | 5 |