Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 354 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. C4×#674 | C4 | semidirect |
| 14. C4×C5×C16 | C4 | semidirect |
| 15. #64722 | C4 | semidirect |
| 16. C4×#672 | C4 | semidirect |
| 77. C4×C16 | AGL(1,𝔽5) | semidirect |
| 176. C5 | #12594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3992 | 2 |
| C4×#3990 | 2 |
| C4×#3930 | 2 |
| #10598660 | 2 |
| #12594 | 5 |