Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
622 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 134 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×H(3,ℤ/4) | C4 | semidirect |
| 17. #64777 | C4 | semidirect |
| 18. #64751 | C4 | semidirect |
| 116. H(3,ℤ/4) | AGL(1,𝔽5) | semidirect |
| 293. C5 | #11286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#430 | 2 |
| #10604753 | 2 |
| #10604386 | 2 |
| #10604372 | 2 |
| D5×H(3,ℤ/4) | 2 |
| #11286 | 5 |