Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
826 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 151 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. C5×#1393 | C2 | semidirect |
| 4. #10598186 | C2 | semidirect |
| 5. #10598132 | C2 | semidirect |
| 7. C2×D5×C4⋊C4 | C4 | semidirect |
| 9. C2×#4018 | C4 | semidirect |
| 14. #65263 | C4 | semidirect |
| 18. #65218 | C4 | semidirect |
| 20. #65029 | C4 | semidirect |
| 51. C5×#99 | C2×C4 | semidirect |
| 53. #3966 | C2×C4 | semidirect |
| 61. #1393 | D5 | semidirect |
| 215. #99 | C4×D5 | semidirect |
| 359. C5 | #12583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65029 | 2 |
| #10608025 | 2 |
| C5×#1393 | 2 |
| #10598186 | 2 |
| #10598132 | 2 |
| #12583 | 5 |