Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
476 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 87 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. #10602412 | C2 | semidirect |
| 3. #10602395 | C2 | semidirect |
| 4. #10598137 | C2 | semidirect |
| 5. #10598136 | C2 | semidirect |
| 6. C2×C5×#124 | C4 | semidirect |
| 9. C5×#393 | C4 | semidirect |
| 12. C5×#392 | C4 | semidirect |
| 16. C5×#383 | C4 | semidirect |
| 113. C2×#124 | Dic5 | semidirect |
| 118. #393 | Dic5 | semidirect |
| 121. #392 | Dic5 | semidirect |
| 125. #383 | Dic5 | semidirect |
| 367. C5 | #11825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2631 | 2 |
| #10602412 | 2 |
| #10602395 | 2 |
| #10598137 | 2 |
| #10598136 | 2 |
| #11825 | 5 |