Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 6. C22×C5×C16 | C4 | semidirect |
| 7. C22×#672 | C4 | semidirect |
| 8. #64893 | C4 | semidirect |
| 54. C22×C16 | AGL(1,𝔽5) | semidirect |
| 168. C5 | #7230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604723 | 2 |
| C2×#64727 | 2 |
| #7230 | 5 |