Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 4. #10598646 | C2 | semidirect |
| 5. #10598644 | C2 | semidirect |
| 58. C5×C16 | M16 | semidirect |
| 138. C16 | #700 | semidirect |
| 162. C5 | #12025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603820 | 2 |
| #10603818 | 2 |
| #10599864 | 2 |
| #10598646 | 2 |
| #10598644 | 2 |
| #12025 | 5 |