Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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. #10605474 | C2 | semidirect |
| 5. #10598157 | C2 | semidirect |
| 6. #10598156 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 31. C5×C4⋊Q8 | Q8 | semidirect |
| 32. C5×#127 | Q8 | semidirect |
| 184. C4⋊Q8 | Dic10 | semidirect |
| 185. #127 | Dic10 | semidirect |
| 335. C5 | #10378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605474 | 2 |
| C5×#1980 | 2 |
| #10602606 | 2 |
| #10602605 | 2 |
| #10598157 | 2 |
| #10598156 | 2 |
| #10598112 | 2 |
| #10378 | 5 |