Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #10617080 | C2 | semidirect |
| 5. #10604287 | C2 | semidirect |
| 6. #10598767 | C2 | semidirect |
| 7. #10598766 | C2 | semidirect |
| 19. C2×C5×#102 | C4 | semidirect |
| 20. C2×#3964 | C4 | semidirect |
| 22. C2×#3949 | C4 | semidirect |
| 23. C2×#3939 | C4 | semidirect |
| 159. C2×#102 | AGL(1,𝔽5) | semidirect |
| 409. C5 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617080 | 2 |
| C2×#65068 | 2 |
| #10604937 | 2 |
| #10604911 | 2 |
| #10604287 | 2 |
| #10598767 | 2 |
| #10598766 | 2 |
| #9242 | 5 |