Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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. D5⋊(C22⋊C16) | C2 | semidirect |
| 3. #10604151 | C2 | semidirect |
| 4. #10604021 | C2 | semidirect |
| 7. C2×D5⋊C16 | C22 | semidirect |
| 14. #64887 | C22 | semidirect |
| 15. C4⋊#674 | C22 | semidirect |
| 16. C4×#674 | C22 | semidirect |
| 46. C2×D20 | C16 | semidirect |
| 81. C22×D5 | C2×C16 | semidirect |
| 86. C2×C4×C5 | C2×C16 | semidirect |
| 93. D20 | C2×C16 | semidirect |
| 178. C2×C4 | D5⋊C16 | semidirect |
| 187. C5 | #33486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65123 | 2 |
| D5⋊(C22⋊C16) | 2 |
| #10604151 | 2 |
| #10604021 | 2 |
| #33486 | 5 |