Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×#6662 | C2 | semidirect |
| 5. #91100 | C2 | semidirect |
| 6. C3×#3948 | C2 | semidirect |
| 7. #90987 | C2 | semidirect |
| 29. #3948 | D3 | semidirect |
| 155. C3×C5 | #470 | semidirect |
| 190. C5 | #4816 | semidirect |
| 202. C3 | #65426 | 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 |
| #91369 | 2 |
| #91365 | 2 |
| C2×#6662 | 2 |
| #91100 | 2 |
| C3×#3948 | 2 |
| #90987 | 2 |
| #65426 | 3 |
| #4816 | 5 |