Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 91 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×#1847 | C2 | semidirect |
| 3. C2×#64685 | C2 | semidirect |
| 5. #10600376 | C2 | semidirect |
| 7. #10598121 | C2 | semidirect |
| 78. #1847 | D5 | semidirect |
| 384. C5 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605986 | 2 |
| C5×#1847 | 2 |
| C2×#64685 | 2 |
| C2×#64684 | 2 |
| #10600376 | 2 |
| #10600374 | 2 |
| #10598121 | 2 |
| #10427 | 5 |