Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #10605400 | C2 | semidirect |
| 5. #10598237 | C2 | semidirect |
| 6. #10598228 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 30. C5×C4⋊Q8 | Q8 | semidirect |
| 31. C5×#127 | Q8 | semidirect |
| 196. C4⋊Q8 | Dic10 | semidirect |
| 197. #127 | Dic10 | semidirect |
| 361. C5 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605400 | 2 |
| C5×#1502 | 2 |
| #10602609 | 2 |
| #10602604 | 2 |
| #10598237 | 2 |
| #10598228 | 2 |
| #10598111 | 2 |
| #10370 | 5 |