Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
752 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#65526 | C2 | semidirect |
| 3. #10602930 | C2 | semidirect |
| 4. C2×#64762 | C2 | semidirect |
| 5. #10598135 | C2 | semidirect |
| 68. #3968 | D4 | semidirect |
| 467. C5 | #13093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2431 | 2 |
| C2×#65526 | 2 |
| #10602930 | 2 |
| C2×#64762 | 2 |
| #10598135 | 2 |
| #13093 | 5 |