Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
476 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C2×C3×C5×C4⋊C4 | C2 | semidirect |
| 3. C2×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C2×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C5×C3⋊#95 | C2 | semidirect |
| 17. #4991 | C5 | direct (N × H) |
| 19. C2×C5×C4⋊C4 | D3 | semidirect |
| 37. C2×C3×C4×C5 | D4 | semidirect |
| 43. C2×C3×C4⋊C4 | C2×C5 | semidirect |
| 44. C2×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 45. C2×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 46. C3⋊#95 | C2×C5 | semidirect |
| 101. C2×C4×C5 | D12 | semidirect |
| 104. C2×C4⋊C4 | C5×D3 | semidirect |
| 128. C2×C3×C4 | C5×D4 | semidirect |
| 159. C3×C5 | #394 | semidirect |
| 199. C2×C4 | C5×D12 | semidirect |
| 207. C5 | #4991 | direct (N × H) |
| 224. C3 | C5×#394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D12 | 2 |
| C2×C3×C5×C4⋊C4 | 2 |
| C2×C5×(C2×D3)⋊C4 | 2 |
| C5×C3⋊#95 | 2 |
| C5×#394 | 3 |
| #4991 | 5 |