Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #10598143 | C2 | semidirect |
| 249. C5 | #11818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2628 | 2 |
| #10602382 | 2 |
| #10602365 | 2 |
| #10598143 | 2 |
| #11818 | 5 |