Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
238 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 126 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. #10598486 | C2 | semidirect |
| 5. AGL(1,𝔽5)×C32 | C2 | semidirect |
| 9. #64877 | C4 | semidirect |
| 12. #64842 | C4 | semidirect |
| 14. C2×C5×C32 | C4 | semidirect |
| 15. C2×#3926 | C4 | semidirect |
| 16. D5×C32 | C4 | semidirect |
| 17. D5×C32 | C4 | semidirect |
| 74. C2×C32 | AGL(1,𝔽5) | semidirect |
| 153. C5 | #13549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604098 | 2 |
| D5⋊M64 | 2 |
| C2×D5×C32 | 2 |
| #10598486 | 2 |
| AGL(1,𝔽5)×C32 | 2 |
| #13549 | 5 |