Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 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. #10600077 | C2 | semidirect |
| 3. #10599845 | C2 | semidirect |
| 4. C5×D4⋊C16 | C2 | semidirect |
| 5. D4⋊#672 | C2 | semidirect |
| 6. #10598049 | C2 | semidirect |
| 7. #10597997 | C2 | semidirect |
| 68. D4⋊C16 | D5 | semidirect |
| 132. C5×D4 | M32 | semidirect |
| 153. Dic10 | M32 | semidirect |
| 265. D4 | #3930 | semidirect |
| 291. C5 | #11623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#711 | 2 |
| #10600077 | 2 |
| #10599845 | 2 |
| C5×D4⋊C16 | 2 |
| D4⋊#672 | 2 |
| #10598049 | 2 |
| #10597997 | 2 |
| #11623 | 5 |