Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 110 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×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C3×C4×C5×C8 | C2 | semidirect |
| 4. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 16. #4688 | C5 | direct (N × H) |
| 21. C4×C5×C8 | D3 | semidirect |
| 31. C3×C5×C8 | D4 | semidirect |
| 33. C2×ΓL(1,𝔽25) | C2×C5 | semidirect |
| 35. C3×C4×C8 | C2×C5 | semidirect |
| 36. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 37. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 53. C3×C4×C5 | M16 | semidirect |
| 76. C5×C8 | D12 | semidirect |
| 81. C4×C8 | C5×D3 | semidirect |
| 95. C3×C8 | C5×D4 | semidirect |
| 103. C4×C5 | ΓL(1,𝔽25) | semidirect |
| 115. C3×C5 | #436 | semidirect |
| 121. C3×C4 | C5×M16 | semidirect |
| 139. C8 | C5×D12 | semidirect |
| 144. C5 | #4688 | direct (N × H) |
| 151. C4 | C5×ΓL(1,𝔽25) | semidirect |
| 154. C3 | C5×#436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×ΓL(1,𝔽25) | 2 |
| C4×C5×D12 | 2 |
| C3×C4×C5×C8 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#436 | 3 |
| #4688 | 5 |