Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
194 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 4. #10598490 | C2 | semidirect |
| 5. #10598489 | C2 | semidirect |
| 14. C5×M64 | C4 | semidirect |
| 15. #64719 | C4 | semidirect |
| 16. #64667 | C4 | semidirect |
| 33. C5×C32 | C2×C4 | semidirect |
| 34. #3926 | C2×C4 | semidirect |
| 63. M64 | AGL(1,𝔽5) | semidirect |
| 100. C32 | C2×AGL(1,𝔽5) | semidirect |
| 151. C5 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604107 | 2 |
| C2×#64849 | 2 |
| D5×M64 | 2 |
| #10598490 | 2 |
| #10598489 | 2 |
| #13634 | 5 |