Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10602470 | C2 | semidirect |
| 3. C2×#64757 | C2 | semidirect |
| 4. #10600208 | C2 | semidirect |
| 5. #10598104 | C2 | semidirect |
| 52. #3963 | D4 | semidirect |
| 403. C5 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2656 | 2 |
| #10602470 | 2 |
| C2×#64757 | 2 |
| #10600208 | 2 |
| #10598104 | 2 |
| #10403 | 5 |