Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
248 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. #10598640 | C2 | semidirect |
| 5. #10598640 | C2 | semidirect |
| 6. #10598639 | C2 | semidirect |
| 7. #10598638 | C2 | semidirect |
| 75. #674 | M16 | semidirect |
| 199. C5 | #11414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604702 | 2 |
| #10604688 | 2 |
| #10599886 | 2 |
| #10598640 | 2 |
| #10598639 | 2 |
| #10598638 | 2 |
| #11414 | 5 |