Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
438 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 148 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×#322 | C4 | semidirect |
| 16. #64675 | C4 | semidirect |
| 17. #64674 | C4 | semidirect |
| 77. #322 | AGL(1,𝔽5) | semidirect |
| 95. C5×C8 | #107 | semidirect |
| 97. #168 | #107 | semidirect |
| 176. C8 | #3994 | semidirect |
| 177. C5 | #8820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603848 | 2 |
| #10603847 | 2 |
| #10603845 | 2 |
| D5×#322 | 2 |
| #8820 | 5 |