Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10604795 | C2 | semidirect |
| 2. #10604059 | C2 | semidirect |
| 4. #10598801 | C2 | semidirect |
| 5. #10598644 | C2 | semidirect |
| 6. #170⋊C16 | C2 | semidirect |
| 7. #10598609 | C2 | semidirect |
| 73. D40 | M16 | semidirect |
| 111. #170 | D16 | semidirect |
| 203. C5 | #12069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604795 | 2 |
| #10604059 | 2 |
| #10599967 | 2 |
| #10598801 | 2 |
| #10598644 | 2 |
| #170⋊C16 | 2 |
| #10598609 | 2 |
| #12069 | 5 |