Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×C5×C22⋊C16 | C2 | semidirect |
| 3. #10602764 | C2 | semidirect |
| 4. #10598017 | C2 | semidirect |
| 7. C22×D40 | C4 | semidirect |
| 12. #65404 | C4 | semidirect |
| 16. C2×#3950 | C4 | semidirect |
| 18. C5×C22⋊C16 | C22 | semidirect |
| 19. #64771 | C22 | semidirect |
| 51. C2×C22⋊C16 | D5 | semidirect |
| 107. C22⋊C16 | C2×D5 | semidirect |
| 288. C5 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65404 | 2 |
| C2×C5×C22⋊C16 | 2 |
| #10602764 | 2 |
| #10598017 | 2 |
| #11886 | 5 |