Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 1. #10605952 | C2 | semidirect |
| 5. #10598229 | C2 | semidirect |
| 6. #10598227 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 26. C5×C4⋊Q8 | Q8 | semidirect |
| 27. C5×#127 | Q8 | semidirect |
| 171. C4⋊Q8 | Dic10 | semidirect |
| 172. #127 | Dic10 | semidirect |
| 313. C5 | #10362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605952 | 2 |
| C5×#1517 | 2 |
| #10602608 | 2 |
| #10602607 | 2 |
| #10598229 | 2 |
| #10598227 | 2 |
| #10598122 | 2 |
| #10362 | 5 |