Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
524 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #10610237 | C2 | semidirect |
| 5. #10600282 | C2 | semidirect |
| 6. #10600264 | C2 | semidirect |
| 7. #10598159 | C2 | semidirect |
| 103. C5×M16 | SD16 | semidirect |
| 279. M16 | #687 | semidirect |
| 350. C5 | #10197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615051 | 2 |
| #10615048 | 2 |
| #10610237 | 2 |
| C5×#1980 | 2 |
| #10600282 | 2 |
| #10600264 | 2 |
| #10598159 | 2 |
| #10197 | 5 |