Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
280 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 82 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×#940 | C2 | semidirect |
| 2. C2×C5×#213 | C2 | semidirect |
| 3. C2×C5×D24 | C2 | semidirect |
| 4. C5×#893 | C2 | semidirect |
| 5. C3×C5×#102 | C2 | semidirect |
| 6. C5×Dic3⋊C8 | C2 | semidirect |
| 7. C5×#809 | C2 | semidirect |
| 22. #4786 | C5 | direct (N × H) |
| 29. C5×#102 | D3 | semidirect |
| 44. C5×D12 | D4 | semidirect |
| 48. #940 | C2×C5 | semidirect |
| 49. C2×#213 | C2×C5 | semidirect |
| 50. C2×D24 | C2×C5 | semidirect |
| 51. #893 | C2×C5 | semidirect |
| 52. C3×#102 | C2×C5 | semidirect |
| 53. Dic3⋊C8 | C2×C5 | semidirect |
| 54. #809 | C2×C5 | semidirect |
| 83. C5×Dic3 | D8 | semidirect |
| 121. #102 | C5×D3 | semidirect |
| 142. D12 | C5×D4 | semidirect |
| 174. C3×C5 | #459 | semidirect |
| 189. Dic3 | C5×D8 | semidirect |
| 220. C5 | #4786 | direct (N × H) |
| 236. C3 | C5×#459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#940 | 2 |
| C2×C5×#213 | 2 |
| C2×C5×D24 | 2 |
| C5×#893 | 2 |
| C3×C5×#102 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×#809 | 2 |
| C5×#459 | 3 |
| #4786 | 5 |