Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #10600926 | C2 | semidirect |
| 5. #10598192 | C2 | semidirect |
| 7. C2×#4094 | C4 | semidirect |
| 11. #65523 | C4 | semidirect |
| 16. #65213 | C4 | semidirect |
| 17. C2×C4×#168 | C4 | semidirect |
| 18. C5×#356 | C4 | semidirect |
| 19. C5×#355 | C4 | semidirect |
| 118. #356 | Dic5 | semidirect |
| 119. #355 | Dic5 | semidirect |
| 282. C5 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615006 | 2 |
| C5×#2132 | 2 |
| #10602612 | 2 |
| #10600926 | 2 |
| #10598192 | 2 |
| #12633 | 5 |