Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10604060 | C2 | semidirect |
| 5. #10598644 | C2 | semidirect |
| 6. #170⋊C16 | C2 | semidirect |
| 7. #10598610 | C2 | semidirect |
| 72. Dic20 | M16 | semidirect |
| 194. C5 | #12075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604795 | 2 |
| #10604060 | 2 |
| #10599968 | 2 |
| #10598801 | 2 |
| #10598644 | 2 |
| #170⋊C16 | 2 |
| #10598610 | 2 |
| #12075 | 5 |