Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
292 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 292 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. #92000 | C2 | semidirect |
| 2. C3×#4054 | C2 | semidirect |
| 3. #91368 | C2 | semidirect |
| 4. #91312 | C2 | semidirect |
| 5. #91109 | C2 | semidirect |
| 6. C5×#824 | C2 | semidirect |
| 7. #90976 | C2 | semidirect |
| 30. #4054 | D3 | semidirect |
| 62. #824 | D5 | semidirect |
| 193. C3×C5 | #454 | semidirect |
| 237. C5 | #5201 | semidirect |
| 249. C3 | #65042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92000 | 2 |
| C3×#4054 | 2 |
| #91368 | 2 |
| #91312 | 2 |
| #91109 | 2 |
| C5×#824 | 2 |
| #90976 | 2 |
| #65042 | 3 |
| #5201 | 5 |