Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 5. C2×C5×M32 | C4 | semidirect |
| 12. #64772 | C4 | semidirect |
| 64. C2×M32 | Dic5 | semidirect |
| 200. C5 | #7235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2112 | 2 |
| #10602770 | 2 |
| #10602764 | 2 |
| #7235 | 5 |