Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
702 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×#3968 | C2 | semidirect |
| 3. #10602926 | C2 | semidirect |
| 4. C2×#64762 | C2 | semidirect |
| 5. #10598135 | C2 | semidirect |
| 70. #3968 | D4 | semidirect |
| 282. C22×C5 | #355 | semidirect |
| 428. C5 | #13092 | semidirect |
| 443. C22 | #64762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2436 | 2 |
| C22×#3968 | 2 |
| #10602926 | 2 |
| C2×#64762 | 2 |
| #10598135 | 2 |
| #13092 | 5 |