Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×C4×Dic10 | C2 | semidirect |
| 3. C2×#6656 | C2 | semidirect |
| 4. C4⋊(C3⋊#168) | C2 | semidirect |
| 5. #90966 | C2 | semidirect |
| 20. C4×Dic10 | D3 | semidirect |
| 34. C3×Dic10 | D4 | semidirect |
| 57. C3×C4×C5 | SD16 | semidirect |
| 83. Dic10 | D12 | semidirect |
| 112. C4×C5 | #215 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 135. C3×C4 | #687 | semidirect |
| 159. C5 | #5027 | semidirect |
| 167. C4 | #6656 | semidirect |
| 170. C3 | #65364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#874 | 2 |
| C3×C4×Dic10 | 2 |
| C2×#6656 | 2 |
| C4⋊(C3⋊#168) | 2 |
| #90966 | 2 |
| #65364 | 3 |
| #5027 | 5 |