Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10604152 | C2 | semidirect |
| 3. #10604151 | C2 | semidirect |
| 4. #10598579 | C2 | semidirect |
| 18. C4⋊#674 | C22 | semidirect |
| 19. C4×#674 | C22 | semidirect |
| 231. C5 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65123 | 2 |
| #10604152 | 2 |
| #10604151 | 2 |
| #10598579 | 2 |
| #11631 | 5 |