Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
543 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×#87853 | C2 | semidirect |
| 3. #11717426 | C2 | semidirect |
| 4. D5⋊#681 | C2 | semidirect |
| 13. #87853 | C22 | semidirect |
| 14. C2×#6032 | C22 | semidirect |
| 15. #87849 | C22 | semidirect |
| 16. D5⋊#168 | C22 | semidirect |
| 112. C52 | #568 | semidirect |
| 172. C5 | #66153 | semidirect |
| 173. C5 | #66256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C2×#87853 | 2 |
| #11717426 | 2 |
| D5⋊#681 | 2 |
| #66256 | 5 |
| #66153 | 5 |