Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1062 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 244 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 |
|---|---|---|
| 22. C5×#494 | C4 | semidirect |
| 23. #65470 | C4 | semidirect |
| 24. #65381 | C4 | semidirect |
| 25. #64988 | C4 | semidirect |
| 106. #494 | AGL(1,𝔽5) | semidirect |
| 182. C4×C5 | #441 | semidirect |
| 185. Dic5 | #441 | semidirect |
| 249. C5 | #21691 | semidirect |
| 261. C4 | #65739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65739 | 2 |
| AGL(1,𝔽5)×C4⋊Q8 | 2 |
| D5×#494 | 2 |
| #10604849 | 2 |
| #10604672 | 2 |
| #10603847 | 2 |
| C4×#3992 | 2 |
| #21691 | 5 |