Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 7. C5×#500 | C4 | semidirect |
| 8. C5×#494 | C4 | semidirect |
| 9. C5×#487 | C4 | semidirect |
| 93. #500 | Dic5 | semidirect |
| 94. #494 | Dic5 | semidirect |
| 95. #487 | Dic5 | semidirect |
| 240. C5 | #9765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3170 | 2 |
| #10602629 | 2 |
| #10602615 | 2 |
| #10600544 | 2 |
| #10600525 | 2 |
| #9765 | 5 |