Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×C5×#365 | C2 | semidirect |
| 4. #10601498 | C2 | semidirect |
| 6. #10598302 | C2 | semidirect |
| 7. #10598212 | C2 | semidirect |
| 22. #64729 | C4 | semidirect |
| 44. C2×C5×C16 | C2×C4 | semidirect |
| 49. #3950 | C2×C4 | semidirect |
| 59. C2×#365 | D5 | semidirect |
| 169. C2×C16 | C4×D5 | semidirect |
| 267. C5 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65158 | 2 |
| C2×C5×#365 | 2 |
| #10602233 | 2 |
| #10601498 | 2 |
| C2×#64715 | 2 |
| #10598302 | 2 |
| #10598212 | 2 |
| #12956 | 5 |