Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
210 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 72. #170 | Q32 | semidirect |
| 131. C5 | #12083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604068 | 2 |
| #10600111 | 2 |
| #10598644 | 2 |
| C16×#170 | 2 |
| #10598610 | 2 |
| #12083 | 5 |