Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
| 2. C2×C5×D3×C8 | C2 | semidirect |
| 4. C3×C5×C4⋊C8 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C5×#803 | C2 | semidirect |
| 22. #4836 | C5 | direct (N × H) |
| 26. C5×C4⋊C8 | D3 | semidirect |
| 45. C5×C3⋊C8 | D4 | semidirect |
| 46. C2×ΓL(1,𝔽25) | C2×C5 | semidirect |
| 47. C2×D3×C8 | C2×C5 | semidirect |
| 49. C3×C4⋊C8 | C2×C5 | semidirect |
| 50. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 51. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 52. #803 | C2×C5 | semidirect |
| 73. C2×C5×D3 | M16 | semidirect |
| 112. C4⋊C8 | C5×D3 | semidirect |
| 136. C3⋊C8 | C5×D4 | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 170. C2×D3 | C5×M16 | semidirect |
| 203. C5 | #4836 | direct (N × H) |
| 217. C3 | C5×#435 | 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 |
| C2×C5×D3×C8 | 2 |
| C4×C5×D12 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#803 | 2 |
| C5×#435 | 3 |
| #4836 | 5 |