Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
322 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 16. C22×C5×C8 | C8 | semidirect |
| 26. C2×#681 | C8 | semidirect |
| 111. C22×C8 | #170 | semidirect |
| 209. C5 | #7188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604877 | 2 |
| #10602758 | 2 |
| #7188 | 5 |