Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #10602831 | C2 | semidirect |
| 3. C2×#64782 | C2 | semidirect |
| 4. C2×#64725 | C2 | semidirect |
| 5. C2×#64722 | C2 | semidirect |
| 9. C2×C5×D16 | C4 | semidirect |
| 77. C5×C16 | C22⋊C4 | semidirect |
| 82. C2×D16 | Dic5 | semidirect |
| 185. C16 | C22⋊Dic5 | semidirect |
| 216. C5 | #13239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D16 | 2 |
| #10602831 | 2 |
| C2×#64782 | 2 |
| C2×#64725 | 2 |
| C2×#64722 | 2 |
| #13239 | 5 |