Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10604979 | C2 | semidirect |
| 3. #10604956 | C2 | semidirect |
| 6. #10604732 | C2 | semidirect |
| 7. #10604719 | C2 | semidirect |
| 8. C22×C5×SD16 | C4 | semidirect |
| 18. C2×#3967 | C4 | semidirect |
| 19. C2×#3964 | C4 | semidirect |
| 24. C2×#3949 | C4 | semidirect |
| 145. C22×SD16 | AGL(1,𝔽5) | semidirect |
| 399. C5 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65460 | 2 |
| #10604979 | 2 |
| #10604956 | 2 |
| #10604937 | 2 |
| #10604911 | 2 |
| #10604732 | 2 |
| #10604719 | 2 |
| #9816 | 5 |