Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 422 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. #10604852 | C2 | semidirect |
| 3. D5⋊#362 | C2 | semidirect |
| 6. D5⋊#368 | C2 | semidirect |
| 7. #10604098 | C2 | semidirect |
| 18. C2×C5×SD32 | C4 | semidirect |
| 19. C2×#3960 | C4 | semidirect |
| 20. C2×#3959 | C4 | semidirect |
| 25. C2×#3932 | C4 | semidirect |
| 150. C2×SD32 | AGL(1,𝔽5) | semidirect |
| 361. C5 | #13246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×SD32 | 2 |
| #10604852 | 2 |
| D5⋊#362 | 2 |
| #10604806 | 2 |
| D5⋊#361 | 2 |
| D5⋊#368 | 2 |
| #10604098 | 2 |
| #13246 | 5 |