Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
590 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 147 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×#64706 | C2 | semidirect |
| 5. #10600185 | C2 | semidirect |
| 48. #1767 | D5 | semidirect |
| 248. C5 | #9710 | 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×#64706 | 2 |
| C2×#64705 | 2 |
| #10600185 | 2 |
| #9710 | 5 |