Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
507 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 181 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×C22⋊C4×C25 | C2 | semidirect |
| 3. C2×C22⋊Dic25 | C2 | semidirect |
| 4. C4×C22⋊D25 | C2 | semidirect |
| 5. #11716443 | C2 | semidirect |
| 6. C22⋊C4×D25 | C2 | semidirect |
| 7. #11716439 | C2 | semidirect |
| 10. C22×C4×C25 | C22 | semidirect |
| 11. C2×C22⋊D25 | C4 | semidirect |
| 15. C22×Dic25 | C22 | semidirect |
| 16. C2×C4×D25 | C22 | semidirect |
| 18. C22⋊C4×C25 | C22 | semidirect |
| 20. C22⋊Dic25 | C22 | semidirect |
| 21. #87720 | C22 | semidirect |
| 22. #87718 | C22 | semidirect |
| 23. C4×Dic25 | C22 | semidirect |
| 26. C23×C25 | C2×C4 | semidirect |
| 31. C22×D25 | C2×C4 | semidirect |
| 35. C22⋊D25 | C2×C4 | semidirect |
| 36. C22⋊D25 | C2×C4 | semidirect |
| 38. C2×Dic25 | C2×C4 | semidirect |
| 109. C2×C22⋊C4 | D25 | semidirect |
| 110. C25 | #518 | semidirect |
| 133. C22×C4 | C2×D25 | semidirect |
| 139. C22⋊C4 | C2×D25 | semidirect |
| 151. C23 | C4×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C4×C22⋊D25 | 2 |
| #11716443 | 2 |
| C22⋊C4×D25 | 2 |
| #11716439 | 2 |
| #65820 | 5 |