Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
318 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 15. C5×#367 | C4 | semidirect |
| 16. #64725 | C4 | semidirect |
| 17. #64710 | C4 | semidirect |
| 68. C5×C16 | C4⋊C4 | semidirect |
| 69. #672 | C4⋊C4 | semidirect |
| 78. #367 | AGL(1,𝔽5) | semidirect |
| 164. C16 | C4⋊AGL(1,𝔽5) | semidirect |
| 193. C5 | #13167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64849 | 2 |
| C2×#64844 | 2 |
| #10604075 | 2 |
| D5×#367 | 2 |
| #10598619 | 2 |
| #13167 | 5 |