Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
466 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10604848 | C2 | semidirect |
| 3. C2×#64908 | C2 | semidirect |
| 6. C2×#64849 | C2 | semidirect |
| 7. C2×#64844 | C2 | semidirect |
| 18. C2×C5×SD32 | C4 | semidirect |
| 19. C2×#3960 | C4 | semidirect |
| 20. C2×#3959 | C4 | semidirect |
| 23. C2×#3932 | C4 | semidirect |
| 128. C5×C16 | C22⋊C4 | semidirect |
| 129. #672 | C22⋊C4 | semidirect |
| 137. C2×SD32 | AGL(1,𝔽5) | semidirect |
| 305. C16 | C22⋊AGL(1,𝔽5) | semidirect |
| 354. C5 | #13238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×SD32 | 2 |
| #10604848 | 2 |
| C2×#64908 | 2 |
| #10604802 | 2 |
| C2×#64904 | 2 |
| C2×#64849 | 2 |
| C2×#64844 | 2 |
| #13238 | 5 |