Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
676 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 676 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 |
|---|---|---|
| 4. #10598715 | C2 | semidirect |
| 85. C2×Dic10 | M16 | semidirect |
| 307. C5 | #7609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65263 | 2 |
| #10604902 | 2 |
| #10604895 | 2 |
| #10598715 | 2 |
| #7609 | 5 |