Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
346 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 56. #3956 | C8 | semidirect |
| 289. C5 | #9549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604738 | 2 |
| M16×#170 | 2 |
| #10604271 | 2 |
| C2×#64872 | 2 |
| #10599766 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #9549 | 5 |