Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 14. #64886 | C4 | semidirect |
| 15. C4×#674 | C4 | semidirect |
| 17. C5×C4⋊C16 | C4 | semidirect |
| 18. #64721 | C4 | semidirect |
| 19. C4⋊#672 | C4 | semidirect |
| 76. #674 | C4⋊C4 | semidirect |
| 88. C4⋊C16 | AGL(1,𝔽5) | semidirect |
| 148. C4×C5 | #347 | semidirect |
| 211. C5 | #12666 | semidirect |
| 223. C4 | #64846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64846 | 2 |
| #10603842 | 2 |
| C4×#3990 | 2 |
| #10600077 | 2 |
| #10598660 | 2 |
| #12666 | 5 |