Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
226 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10598643 | C2 | semidirect |
| 54. #672 | M16 | semidirect |
| 149. C5 | #12019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10603820 | 2 |
| #10603816 | 2 |
| D5×#346 | 2 |
| #10598643 | 2 |
| #12019 | 5 |