Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 153. C5 | #7413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599431 | 2 |
| #10598694 | 2 |
| #10598687 | 2 |
| #7413 | 5 |