Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. #10604752 | C2 | semidirect |
| 3. #10604737 | C2 | semidirect |
| 4. #10598624 | C2 | semidirect |
| 5. #10598623 | C2 | semidirect |
| 18. #64889 | C22 | semidirect |
| 20. #64879 | C22 | semidirect |
| 21. C8×#170 | C22 | semidirect |
| 80. Dic20 | M16 | semidirect |
| 82. D40 | M16 | semidirect |
| 233. C5 | #11669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610989 | 2 |
| #10604752 | 2 |
| #10604737 | 2 |
| #10598624 | 2 |
| #10598623 | 2 |
| #11669 | 5 |