Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 152 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. #91758 | C2 | semidirect |
| 2. C4×C5×Dic6 | C2 | semidirect |
| 4. #91431 | C2 | semidirect |
| 6. D5×C4⋊Dic3 | C2 | semidirect |
| 7. #91381 | C2 | semidirect |
| 8. #91359 | C2 | semidirect |
| 45. C3×D20 | Q8 | semidirect |
| 55. C4×Dic6 | D5 | semidirect |
| 109. D20 | Dic6 | semidirect |
| 165. C3×C5 | #554 | semidirect |
| 198. C5 | #5543 | semidirect |
| 210. C3 | #65913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91758 | 2 |
| C4×C5×Dic6 | 2 |
| C3×C4×D20 | 2 |
| #91431 | 2 |
| Dic3×D20 | 2 |
| D5×C4⋊Dic3 | 2 |
| #91381 | 2 |
| #91359 | 2 |
| #65913 | 3 |
| #5543 | 5 |