Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
310 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 16. C5×C4⋊C16 | C4 | semidirect |
| 17. #64721 | C4 | semidirect |
| 18. C4⋊#672 | C4 | semidirect |
| 91. C4⋊C16 | AGL(1,𝔽5) | semidirect |
| 149. C4×C5 | #365 | semidirect |
| 153. Dic5 | #365 | semidirect |
| 215. C5 | #13183 | semidirect |
| 227. C4 | #64847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64847 | 2 |
| C4×#3995 | 2 |
| #10603847 | 2 |
| #10600077 | 2 |
| #10598663 | 2 |
| #13183 | 5 |