Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10602799 | C2 | semidirect |
| 3. C2×#64773 | C2 | semidirect |
| 4. #10600678 | C2 | semidirect |
| 5. #10600677 | C2 | semidirect |
| 50. #3944 | D4 | semidirect |
| 256. C5 | #13201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2930 | 2 |
| #10602799 | 2 |
| C2×#64773 | 2 |
| #10600678 | 2 |
| #10600677 | 2 |
| #13201 | 5 |