Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
330 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 17. #170⋊C8 | C4 | semidirect |
| 18. #170⋊C8 | C4 | semidirect |
| 19. C5×#322 | C4 | semidirect |
| 20. #64675 | C4 | semidirect |
| 21. #64674 | C4 | semidirect |
| 22. #64674 | C4 | semidirect |
| 99. #322 | AGL(1,𝔽5) | semidirect |
| 220. C5 | #8139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603838 | 2 |
| #10603811 | 2 |
| #10598864 | 2 |
| #10598529 | 2 |
| #10598526 | 2 |
| #8139 | 5 |