Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
598 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #10598134 | C2 | semidirect |
| 50. C2×C5×Q8 | M16 | semidirect |
| 173. C2×Q8 | #681 | semidirect |
| 242. C5 | #11506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#391 | 2 |
| #10602345 | 2 |
| #10598134 | 2 |
| #11506 | 5 |