Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 3. D3×C4⋊Dic5 | C2 | semidirect |
| 4. #91100 | C2 | semidirect |
| 5. C3×#3953 | C2 | semidirect |
| 6. #90974 | C2 | semidirect |
| 7. #90965 | C2 | semidirect |
| 16. #6765 | C4 | semidirect |
| 28. #3953 | D3 | semidirect |
| 37. Dic30 | C2×C4 | semidirect |
| 43. C3×D20 | C2×C4 | semidirect |
| 50. C2×ΓL(1,𝔽25) | D5 | semidirect |
| 110. D20 | C4×D3 | semidirect |
| 173. C3×C5 | #417 | semidirect |
| 215. C5 | #4771 | semidirect |
| 229. C3 | #65422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6765 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| D3×C4⋊Dic5 | 2 |
| #91100 | 2 |
| C3×#3953 | 2 |
| #90974 | 2 |
| #90965 | 2 |
| #65422 | 3 |
| #4771 | 5 |