Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 131 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. #10602804 | C2 | semidirect |
| 4. #10598184 | C2 | semidirect |
| 5. #10598182 | C2 | semidirect |
| 7. C22×C5×M16 | C4 | semidirect |
| 11. C5×#424 | C4 | semidirect |
| 13. C5×#407 | C4 | semidirect |
| 14. C5×#405 | C4 | semidirect |
| 19. #64759 | C4 | semidirect |
| 20. #64756 | C4 | semidirect |
| 99. C22×M16 | Dic5 | semidirect |
| 103. #424 | Dic5 | semidirect |
| 107. #407 | Dic5 | semidirect |
| 109. #405 | Dic5 | semidirect |
| 263. C5 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2930 | 2 |
| #10602804 | 2 |
| #10602509 | 2 |
| #10598184 | 2 |
| #10598182 | 2 |
| #12624 | 5 |