Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
226 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 72 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×#335 | C4 | semidirect |
| 14. #64678 | C4 | semidirect |
| 68. #335 | AGL(1,𝔽5) | semidirect |
| 174. C5 | #7217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603845 | 2 |
| #10603829 | 2 |
| #10599362 | 2 |
| #7217 | 5 |