Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #10600837 | C2 | semidirect |
| 5. #10600794 | C2 | semidirect |
| 6. C5×#1395 | C2 | semidirect |
| 7. #10598191 | C2 | semidirect |
| 78. #1395 | D5 | semidirect |
| 351. C5 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610397 | 2 |
| #10600929 | 2 |
| #10600849 | 2 |
| #10600837 | 2 |
| #10600794 | 2 |
| C5×#1395 | 2 |
| #10598191 | 2 |
| #12963 | 5 |