Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C3×C4×Dic10 | C2 | semidirect |
| 4. C4×C3⋊#168 | C2 | semidirect |
| 5. #90986 | C2 | semidirect |
| 6. #90970 | C2 | semidirect |
| 20. #6656 | C4 | direct (N × H) |
| 24. C4×Dic10 | D3 | semidirect |
| 40. C3×Dic10 | C2×C4 | semidirect |
| 42. C3⋊#168 | C2×C4 | semidirect |
| 68. C3×C4×C5 | SD16 | semidirect |
| 97. Dic10 | C4×D3 | semidirect |
| 131. C4×C5 | #215 | semidirect |
| 148. C3×C5 | C4×SD16 | semidirect |
| 156. C3×C4 | #687 | semidirect |
| 182. C5 | C4×#215 | semidirect |
| 191. C4 | #6656 | direct (N × H) |
| 194. C3 | C4×#687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D12 | 2 |
| C3×C4×Dic10 | 2 |
| C2×#6656 | 2 |
| C4×C3⋊#168 | 2 |
| #90986 | 2 |
| #90970 | 2 |
| #90966 | 2 |
| C4×#687 | 3 |
| C4×#215 | 5 |