Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
186 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10604774 | C2 | semidirect |
| 2. #10604111 | C2 | semidirect |
| 4. #10598798 | C2 | semidirect |
| 5. #10598669 | C2 | semidirect |
| 6. #10598658 | C2 | semidirect |
| 7. #10598652 | C2 | semidirect |
| 170. C5 | #13647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604774 | 2 |
| #10604111 | 2 |
| #10599915 | 2 |
| #10598798 | 2 |
| #10598669 | 2 |
| #10598658 | 2 |
| #10598652 | 2 |
| #13647 | 5 |