Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
246 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 24. C2×#674 | C8 | semidirect |
| 26. C5×M32 | C8 | semidirect |
| 33. #3944 | C8 | semidirect |
| 91. M32 | #170 | semidirect |
| 154. C5 | #7140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64886 | 2 |
| #10604687 | 2 |
| Dic5×M32 | 2 |
| #7140 | 5 |