Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 10. #64883 | C4 | semidirect |
| 11. C4×C5×C16 | C4 | semidirect |
| 14. C4×#672 | C4 | semidirect |
| 59. C4×C16 | AGL(1,𝔽5) | semidirect |
| 152. C5 | #7218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603846 | 2 |
| #10603821 | 2 |
| #10599845 | 2 |
| #7218 | 5 |