Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×C5×Q16 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 5. C5×#818 | C2 | semidirect |
| 16. #5188 | C5 | direct (N × H) |
| 17. C2×C5×Q16 | D3 | semidirect |
| 33. C2×C3×Q16 | C2×C5 | semidirect |
| 36. #835 | C2×C5 | semidirect |
| 37. #818 | C2×C5 | semidirect |
| 51. C2×C5×D3 | Q16 | semidirect |
| 77. C2×Q16 | C5×D3 | semidirect |
| 115. C3×C5 | #467 | semidirect |
| 119. C2×D3 | C5×Q16 | semidirect |
| 144. C5 | #5188 | direct (N × H) |
| 154. C3 | C5×#467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C5×#946 | 2 |
| C2×C5×D3×C8 | 2 |
| C5×#835 | 2 |
| C5×#818 | 2 |
| C5×#467 | 3 |
| #5188 | 5 |