Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1220 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 311 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. #10615850 | C2 | semidirect |
| 3. #10602654 | C2 | semidirect |
| 4. #10602612 | C2 | semidirect |
| 6. C2×C5×H(5,𝔽2) | C4 | semidirect |
| 9. C5×#536 | C4 | semidirect |
| 12. C2×C5×#124 | C4 | semidirect |
| 13. C4×C5×#41 | C4 | semidirect |
| 16. #65529 | C22 | semidirect |
| 17. #64765 | C22 | semidirect |
| 18. #64761 | C22 | semidirect |
| 95. C2×H(5,𝔽2) | Dic5 | semidirect |
| 98. #536 | Dic5 | semidirect |
| 101. C2×#124 | Dic5 | semidirect |
| 103. C4×#41 | Dic5 | semidirect |
| 254. C5 | #33362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3500 | 2 |
| #10615850 | 2 |
| #10602654 | 2 |
| #10602612 | 2 |
| #33362 | 5 |