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. #64885 | C4 | semidirect |
| 12. C5×#334 | C4 | semidirect |
| 14. #64677 | C4 | semidirect |
| 63. #334 | AGL(1,𝔽5) | semidirect |
| 154. C5 | #7218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603846 | 2 |
| #10603829 | 2 |
| #10599323 | 2 |
| #7218 | 5 |