Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C5×#131 | C2 | semidirect |
| 2. C5×#949 | C2 | semidirect |
| 3. C2×C5×D24 | C2 | semidirect |
| 4. C5×#823 | C2 | semidirect |
| 5. C5×#819 | C2 | semidirect |
| 18. #5142 | C5 | direct (N × H) |
| 21. C5×#131 | D3 | semidirect |
| 36. C3×#131 | C2×C5 | semidirect |
| 37. #949 | C2×C5 | semidirect |
| 38. C2×D24 | C2×C5 | semidirect |
| 39. #823 | C2×C5 | semidirect |
| 40. #819 | C2×C5 | semidirect |
| 85. #131 | C5×D3 | semidirect |
| 122. C3×C5 | #472 | semidirect |
| 150. C5 | #5142 | 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 |
|---|---|
| C3×C5×#131 | 2 |
| C5×#949 | 2 |
| C2×C5×D24 | 2 |
| C5×#823 | 2 |
| C5×#819 | 2 |
| C5×#472 | 3 |
| #5142 | 5 |