Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 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. #64879 | C4 | semidirect |
| 18. C8×#170 | C4 | semidirect |
| 19. C5×#322 | C4 | semidirect |
| 20. #64675 | C4 | semidirect |
| 21. #64674 | C4 | semidirect |
| 22. #64674 | C4 | semidirect |
| 96. #322 | AGL(1,𝔽5) | semidirect |
| 216. C5 | #8142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603840 | 2 |
| #10603809 | 2 |
| #10598864 | 2 |
| #10598529 | 2 |
| #10598526 | 2 |
| #8142 | 5 |