Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
536 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10608329 | C2 | semidirect |
| 5. C5×#1272 | C2 | semidirect |
| 6. #10597971 | C2 | semidirect |
| 7. #10597968 | C2 | semidirect |
| 71. #1272 | D5 | semidirect |
| 108. C2×Dic10 | SD16 | semidirect |
| 121. C4⋊Dic5 | SD16 | semidirect |
| 398. C5 | #7748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10608329 | 2 |
| #10600481 | 2 |
| #10599469 | 2 |
| #10599422 | 2 |
| C5×#1272 | 2 |
| #10597971 | 2 |
| #10597968 | 2 |
| #7748 | 5 |