Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 9. C5×C82 | C4 | semidirect |
| 10. C8×#168 | C4 | semidirect |
| 11. C8×#168 | C4 | semidirect |
| 50. C82 | AGL(1,𝔽5) | semidirect |
| 119. C5 | #8816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603848 | 2 |
| #10603845 | 2 |
| C82×D5 | 2 |
| #8816 | 5 |