Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
810 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. #10602653 | C2 | semidirect |
| 3. C2×#64765 | C2 | semidirect |
| 4. #10602446 | C2 | semidirect |
| 9. C5×#535 | C4 | semidirect |
| 11. C5×#533 | C4 | semidirect |
| 14. C5×#518 | C4 | semidirect |
| 16. C4×C5×#41 | C4 | semidirect |
| 127. #535 | Dic5 | semidirect |
| 129. #533 | Dic5 | semidirect |
| 132. #518 | Dic5 | semidirect |
| 134. C4×#41 | Dic5 | semidirect |
| 334. C5 | #12727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3508 | 2 |
| #10602653 | 2 |
| C2×#64765 | 2 |
| #10602446 | 2 |
| #12727 | 5 |