Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 12. #64886 | C4 | semidirect |
| 13. #64859 | C4 | semidirect |
| 14. C4×C5×C16 | C4 | semidirect |
| 15. C16×Dic5 | C4 | semidirect |
| 16. C4×#672 | C4 | semidirect |
| 71. C4×C16 | AGL(1,𝔽5) | semidirect |
| 152. C5 | #12592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603838 | 2 |
| #10603823 | 2 |
| C4×D5×C16 | 2 |
| (C2×AGL(1,𝔽5))⋊C16 | 2 |
| #12592 | 5 |