Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
586 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #10598140 | C2 | semidirect |
| 5. #10598137 | C2 | semidirect |
| 6. C2×C5×C22⋊Q8 | C4 | semidirect |
| 9. C5×#397 | C4 | semidirect |
| 11. C5×#393 | C4 | semidirect |
| 17. C4×C5×C22⋊C4 | C4 | semidirect |
| 25. C22×C5×Q8 | C2×C4 | semidirect |
| 32. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 55. C5×#95 | C2×C4 | semidirect |
| 56. C5×#95 | C2×C4 | semidirect |
| 114. C2×C22⋊Q8 | Dic5 | semidirect |
| 118. #397 | Dic5 | semidirect |
| 120. #393 | Dic5 | semidirect |
| 126. C4×C22⋊C4 | Dic5 | semidirect |
| 191. C22×Q8 | C2×Dic5 | semidirect |
| 199. C2×C4⋊C4 | C2×Dic5 | semidirect |
| 223. #95 | C2×Dic5 | semidirect |
| 224. #95 | C2×Dic5 | semidirect |
| 382. C5 | #11759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2561 | 2 |
| C2×#64746 | 2 |
| #10602332 | 2 |
| #10598140 | 2 |
| #10598137 | 2 |
| #11759 | 5 |