Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 90 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×C4⋊Q8 | C2 | semidirect |
| 4. C5×#808 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 16. #5084 | C5 | direct (N × H) |
| 17. C5×C4⋊Q8 | D3 | semidirect |
| 30. C5×D12 | Q8 | semidirect |
| 33. C3×C4⋊Q8 | C2×C5 | semidirect |
| 36. #808 | C2×C5 | semidirect |
| 37. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 78. C4⋊Q8 | C5×D3 | semidirect |
| 95. D12 | C5×Q8 | semidirect |
| 117. C3×C5 | #476 | semidirect |
| 147. C5 | #5084 | direct (N × H) |
| 158. C3 | C5×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C4×C5×D12 | 2 |
| C5×#809 | 2 |
| C5×#808 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#476 | 3 |
| #5084 | 5 |