Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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×#942 | C2 | semidirect |
| 2. C2×C5×#215 | C2 | semidirect |
| 4. C5×#907 | C2 | semidirect |
| 5. C3×C5×#101 | C2 | semidirect |
| 6. C5×#823 | C2 | semidirect |
| 7. C5×#822 | C2 | semidirect |
| 24. #4754 | C5 | direct (N × H) |
| 30. C5×#101 | D3 | semidirect |
| 48. #942 | C2×C5 | semidirect |
| 49. C2×#215 | C2×C5 | semidirect |
| 51. #907 | C2×C5 | semidirect |
| 52. C3×#101 | C2×C5 | semidirect |
| 53. #823 | C2×C5 | semidirect |
| 54. #822 | C2×C5 | semidirect |
| 115. #101 | C5×D3 | semidirect |
| 160. C3×C5 | #471 | semidirect |
| 193. C5 | #4754 | 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×#942 | 2 |
| C2×C5×#215 | 2 |
| C5×#908 | 2 |
| C5×#907 | 2 |
| C3×C5×#101 | 2 |
| C5×#823 | 2 |
| C5×#822 | 2 |
| C5×#471 | 3 |
| #4754 | 5 |