Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
514 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×#64908 | C2 | semidirect |
| 4. C4×#3994 | C2 | semidirect |
| 5. D5⋊(C4⋊C16) | C2 | semidirect |
| 13. C5×#495 | C4 | semidirect |
| 14. #65480 | C4 | semidirect |
| 16. #65444 | C4 | semidirect |
| 18. #64985 | C4 | semidirect |
| 132. #495 | AGL(1,𝔽5) | semidirect |
| 340. C5 | #13254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#495 | 2 |
| C2×#64908 | 2 |
| C2×#64904 | 2 |
| C4×#3994 | 2 |
| D5⋊(C4⋊C16) | 2 |
| #13254 | 5 |