Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
630 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10604895 | C2 | semidirect |
| 3. C2×#64918 | C2 | semidirect |
| 4. #10598713 | C2 | semidirect |
| 5. #10598712 | C2 | semidirect |
| 371. C5 | #7678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605730 | 2 |
| #10604895 | 2 |
| C2×#64918 | 2 |
| #10598713 | 2 |
| #10598712 | 2 |
| #7678 | 5 |