Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×D120 | C2 | semidirect |
| 2. C5×#901 | C2 | semidirect |
| 3. #91305 | C2 | semidirect |
| 4. C3×#3951 | C2 | semidirect |
| 5. #90960 | C2 | semidirect |
| 23. #3951 | D3 | semidirect |
| 38. #901 | D5 | semidirect |
| 122. C3×C5 | #472 | semidirect |
| 150. C5 | #4897 | semidirect |
| 158. C3 | #65431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D120 | 2 |
| C5×#901 | 2 |
| #91305 | 2 |
| C3×#3951 | 2 |
| #90960 | 2 |
| #65431 | 3 |
| #4897 | 5 |