Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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. C5×#1833 | C2 | semidirect |
| 5. #10600678 | C2 | semidirect |
| 6. #10598226 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 17. #65000 | C4 | semidirect |
| 60. #1833 | D5 | semidirect |
| 254. C5 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610292 | 2 |
| C5×#1833 | 2 |
| C2×#64715 | 2 |
| #10601445 | 2 |
| #10600678 | 2 |
| #10598226 | 2 |
| #10598216 | 2 |
| #12826 | 5 |