Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
596 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 123 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×#1767 | C2 | semidirect |
| 3. C2×#64684 | C2 | semidirect |
| 4. #10600182 | C2 | semidirect |
| 49. #3935 | D4 | semidirect |
| 51. #1767 | D5 | semidirect |
| 291. C5 | #9689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605044 | 2 |
| C5×#1767 | 2 |
| C2×#64684 | 2 |
| #10600182 | 2 |
| #9689 | 5 |