Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
430 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 137. #170 | #101 | semidirect |
| 251. C5 | #8165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65703 | 2 |
| #10604335 | 2 |
| #10603893 | 2 |
| #10598918 | 2 |
| #10598562 | 2 |
| #8165 | 5 |