Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 101 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. #10600068 | C2 | semidirect |
| 3. #10599845 | C2 | semidirect |
| 4. C5×D4⋊C16 | C2 | semidirect |
| 5. D4⋊#672 | C2 | semidirect |
| 6. #10598047 | C2 | semidirect |
| 7. #10597994 | C2 | semidirect |
| 19. C5×C4⋊C16 | C22 | semidirect |
| 20. C4×C5×C16 | C22 | semidirect |
| 25. C4⋊#672 | C22 | semidirect |
| 26. C4×#672 | C22 | semidirect |
| 69. D4⋊C16 | D5 | semidirect |
| 130. C4⋊C16 | C2×D5 | semidirect |
| 135. C4×C16 | C2×D5 | semidirect |
| 321. C5 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×D5 | 2 |
| #10600068 | 2 |
| #10599845 | 2 |
| C5×D4⋊C16 | 2 |
| D4⋊#672 | 2 |
| #10598047 | 2 |
| #10597994 | 2 |
| #11631 | 5 |