Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 128 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. #91824 | C2 | semidirect |
| 3. C3×#4081 | C2 | semidirect |
| 4. #67⋊Dic5 | C2 | semidirect |
| 5. Dic5×#67 | C2 | semidirect |
| 6. #91525 | C2 | semidirect |
| 7. #91525 | C2 | semidirect |
| 8. #91423 | C2 | semidirect |
| 9. #91324 | C2 | semidirect |
| 38. #4081 | D3 | semidirect |
| 208. C3×C5 | #559 | semidirect |
| 250. C5 | #5664 | semidirect |
| 265. C3 | #66047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91824 | 2 |
| C5×#940 | 2 |
| C3×#4081 | 2 |
| #67⋊Dic5 | 2 |
| Dic5×#67 | 2 |
| #91525 | 2 |
| #91423 | 2 |
| #91324 | 2 |
| #66047 | 3 |
| #5664 | 5 |