Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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. #10605128 | C2 | semidirect |
| 4. #10598206 | C2 | semidirect |
| 5. #10598105 | C2 | semidirect |
| 23. C5×C4⋊Q8 | Q8 | semidirect |
| 24. C5×#127 | Q8 | semidirect |
| 140. C4⋊Q8 | Dic10 | semidirect |
| 141. #127 | Dic10 | semidirect |
| 258. C5 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605128 | 2 |
| C5×#1963 | 2 |
| #10602604 | 2 |
| #10598206 | 2 |
| #10598105 | 2 |
| #10370 | 5 |