Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10604849 | C2 | semidirect |
| 4. C2×#64910 | C2 | semidirect |
| 6. C2×#64847 | C2 | semidirect |
| 7. C2×#64846 | C2 | semidirect |
| 18. C2×C5×Q32 | C4 | semidirect |
| 19. C2×#3961 | C4 | semidirect |
| 20. C2×#3960 | C4 | semidirect |
| 23. C2×#3932 | C4 | semidirect |
| 134. C2×Q32 | AGL(1,𝔽5) | semidirect |
| 336. C5 | #13250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65207 | 2 |
| #10604849 | 2 |
| #10604844 | 2 |
| C2×#64910 | 2 |
| C2×#64907 | 2 |
| C2×#64847 | 2 |
| C2×#64846 | 2 |
| #13250 | 5 |