Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
182 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #10602289 | C2 | semidirect |
| 5. #10598318 | C2 | semidirect |
| 6. #10598092 | C2 | semidirect |
| 7. #10598091 | C2 | semidirect |
| 12. C5×Q64 | C4 | semidirect |
| 13. C5×SD64 | C4 | semidirect |
| 70. Q64 | Dic5 | semidirect |
| 71. SD64 | Dic5 | semidirect |
| 155. C5 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2264 | 2 |
| #10602305 | 2 |
| #10602289 | 2 |
| #10598319 | 2 |
| #10598318 | 2 |
| #10598092 | 2 |
| #10598091 | 2 |
| #13657 | 5 |