Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 216 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×#908 | C2 | semidirect |
| 2. C2×C5×D24 | C2 | semidirect |
| 3. C5×#901 | C2 | semidirect |
| 4. C3×C5×#108 | C2 | semidirect |
| 5. C5×#823 | C2 | semidirect |
| 18. #4897 | C5 | direct (N × H) |
| 22. C5×#108 | D3 | semidirect |
| 36. #908 | C2×C5 | semidirect |
| 37. C2×D24 | C2×C5 | semidirect |
| 38. #901 | C2×C5 | semidirect |
| 39. C3×#108 | C2×C5 | semidirect |
| 40. #823 | C2×C5 | semidirect |
| 86. #108 | C5×D3 | semidirect |
| 122. C3×C5 | #472 | semidirect |
| 150. C5 | #4897 | direct (N × H) |
| 158. C3 | C5×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#908 | 2 |
| C2×C5×D24 | 2 |
| C5×#901 | 2 |
| C3×C5×#108 | 2 |
| C5×#823 | 2 |
| C5×#472 | 3 |
| #4897 | 5 |