Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 74 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×C3×C5×SD16 | C2 | semidirect |
| 2. C5×#942 | C2 | semidirect |
| 4. C5×#901 | C2 | semidirect |
| 5. C5×#836 | C2 | semidirect |
| 6. C5×#833 | C2 | semidirect |
| 7. C5×#819 | C2 | semidirect |
| 24. #5177 | C5 | direct (N × H) |
| 27. C2×C5×SD16 | D3 | semidirect |
| 48. C2×C3×SD16 | C2×C5 | semidirect |
| 49. #942 | C2×C5 | semidirect |
| 51. #901 | C2×C5 | semidirect |
| 52. #836 | C2×C5 | semidirect |
| 53. #833 | C2×C5 | semidirect |
| 54. #819 | C2×C5 | semidirect |
| 112. C2×SD16 | C5×D3 | semidirect |
| 160. C3×C5 | #471 | semidirect |
| 193. C5 | #5177 | direct (N × H) |
| 202. C3 | C5×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD16 | 2 |
| C5×#942 | 2 |
| C5×#932 | 2 |
| C5×#901 | 2 |
| C5×#836 | 2 |
| C5×#833 | 2 |
| C5×#819 | 2 |
| C5×#471 | 3 |
| #5177 | 5 |