Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
556 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×C5×D16 | C2 | semidirect |
| 2. C2×#65449 | C2 | semidirect |
| 3. C2×#64783 | C2 | semidirect |
| 4. #10602202 | C2 | semidirect |
| 5. #10598299 | C2 | semidirect |
| 47. C22×D16 | D5 | semidirect |
| 228. C5 | #13313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D16 | 2 |
| C2×#65449 | 2 |
| C2×#64783 | 2 |
| #10602202 | 2 |
| #10598299 | 2 |
| #13313 | 5 |