Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. C5×#3037 | C2 | semidirect |
| 3. #10614207 | C2 | semidirect |
| 4. #10602604 | C2 | semidirect |
| 5. #10602414 | C2 | semidirect |
| 6. #10601295 | C2 | semidirect |
| 7. #10598206 | C2 | semidirect |
| 81. #3037 | D5 | semidirect |
| 98. C2×C5×Q8 | D8 | semidirect |
| 309. C2×Q8 | #686 | semidirect |
| 420. C5 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3037 | 2 |
| #10615033 | 2 |
| #10614207 | 2 |
| #10602604 | 2 |
| #10602414 | 2 |
| #10601295 | 2 |
| #10598206 | 2 |
| #10242 | 5 |