Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
242 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. #10598645 | C2 | semidirect |
| 45. #672 | M16 | semidirect |
| 134. C5 | #12022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603818 | 2 |
| C4×D5×C16 | 2 |
| #10598645 | 2 |
| #12022 | 5 |