Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 36. C5×#108 | C8 | semidirect |
| 120. #108 | #170 | semidirect |
| 205. C5 | #9608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604738 | 2 |
| C2×#64882 | 2 |
| #10604687 | 2 |
| Dic5×#108 | 2 |
| #10598793 | 2 |
| #9608 | 5 |