Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 3. #10600131 | C2 | semidirect |
| 5. #10598096 | C2 | semidirect |
| 6. #10598091 | C2 | semidirect |
| 7. #10598070 | C2 | semidirect |
| 15. #64742 | C4 | semidirect |
| 16. #64740 | C4 | semidirect |
| 155. C5 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602305 | 2 |
| #10602303 | 2 |
| #10600131 | 2 |
| C5×#1418 | 2 |
| #10598096 | 2 |
| #10598091 | 2 |
| #10598070 | 2 |
| #13657 | 5 |