Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
544 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×#3966 | C2 | semidirect |
| 3. #10602395 | C2 | semidirect |
| 4. #10598140 | C2 | semidirect |
| 5. #10598136 | C2 | semidirect |
| 7. C2×C4×C5×D4 | C4 | semidirect |
| 9. C5×#397 | C4 | semidirect |
| 11. C5×#392 | C4 | semidirect |
| 15. C5×#382 | C4 | semidirect |
| 115. C2×C4×D4 | Dic5 | semidirect |
| 119. #397 | Dic5 | semidirect |
| 121. #392 | Dic5 | semidirect |
| 125. #382 | Dic5 | semidirect |
| 362. C5 | #11774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2535 | 2 |
| C4×#3966 | 2 |
| #10602395 | 2 |
| #10598140 | 2 |
| #10598136 | 2 |
| #11774 | 5 |