Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 104 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. #65739 | C4 | semidirect |
| 20. #64910 | C4 | semidirect |
| 23. C5×#358 | C4 | semidirect |
| 24. #64784 | C4 | semidirect |
| 25. #64723 | C4 | semidirect |
| 26. #64712 | C4 | semidirect |
| 130. #358 | AGL(1,𝔽5) | semidirect |
| 294. C5 | #12648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65739 | 2 |
| C2×#64910 | 2 |
| C2×#64845 | 2 |
| #10604078 | 2 |
| #10600015 | 2 |
| #10598663 | 2 |
| #10598621 | 2 |
| #12648 | 5 |