Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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. C5×#1744 | C2 | semidirect |
| 4. #10600184 | C2 | semidirect |
| 5. #10598146 | C2 | semidirect |
| 19. #64679 | C4 | semidirect |
| 49. #1744 | D5 | semidirect |
| 253. C5 | #8179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605030 | 2 |
| C5×#1744 | 2 |
| C2×#64679 | 2 |
| #10600184 | 2 |
| #10598146 | 2 |
| #8179 | 5 |