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. C5×#909 | C2 | semidirect |
| 3. C2×C5×#204 | C2 | semidirect |
| 4. C5×#901 | C2 | semidirect |
| 5. C3×C5×#108 | C2 | semidirect |
| 6. C5×#824 | C2 | semidirect |
| 7. C5×#823 | C2 | semidirect |
| 24. #4898 | C5 | direct (N × H) |
| 29. C5×#108 | D3 | semidirect |
| 48. #909 | C2×C5 | semidirect |
| 50. C2×#204 | C2×C5 | semidirect |
| 51. #901 | C2×C5 | semidirect |
| 52. C3×#108 | C2×C5 | semidirect |
| 53. #824 | C2×C5 | semidirect |
| 54. #823 | C2×C5 | semidirect |
| 114. #108 | C5×D3 | semidirect |
| 160. C3×C5 | #471 | semidirect |
| 193. C5 | #4898 | 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 |
|---|---|
| C5×#909 | 2 |
| C5×#908 | 2 |
| C2×C5×#204 | 2 |
| C5×#901 | 2 |
| C3×C5×#108 | 2 |
| C5×#824 | 2 |
| C5×#823 | 2 |
| C5×#471 | 3 |
| #4898 | 5 |