Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 61 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×#2188 | C2 | semidirect |
| 3. #10602861 | C2 | semidirect |
| 5. #10598267 | C2 | semidirect |
| 7. #10598015 | C2 | semidirect |
| 66. #2188 | D5 | semidirect |
| 310. C5 | #12163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612479 | 2 |
| C5×#2188 | 2 |
| #10602861 | 2 |
| #10602856 | 2 |
| #10598267 | 2 |
| #10598017 | 2 |
| #10598015 | 2 |
| #12163 | 5 |