Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 85 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. #91225 | C2 | semidirect |
| 5. #91224 | C2 | semidirect |
| 128. C3×C5 | #430 | semidirect |
| 157. C5 | #5125 | semidirect |
| 166. C3 | #65729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#208 | 2 |
| C2×#6758 | 2 |
| C3×D5×M16 | 2 |
| #91225 | 2 |
| #91224 | 2 |
| #65729 | 3 |
| #5125 | 5 |