Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. #91098 | C2 | semidirect |
| 5. C3×#3946 | C2 | semidirect |
| 6. #90983 | C2 | semidirect |
| 7. #90982 | C2 | semidirect |
| 29. #3946 | D3 | semidirect |
| 73. Dic15 | M16 | semidirect |
| 75. C3×Dic5 | M16 | semidirect |
| 141. Dic5 | ΓL(1,𝔽25) | semidirect |
| 155. C3×C5 | #423 | semidirect |
| 190. C5 | #4837 | semidirect |
| 202. C3 | #65407 | 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×D3×Dic5 | 2 |
| C2×#6650 | 2 |
| #91098 | 2 |
| C3×#3946 | 2 |
| #90983 | 2 |
| #90982 | 2 |
| #65407 | 3 |
| #4837 | 5 |