Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1011 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 245 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. C22×C4×D25 | C2 | semidirect |
| 3. C2×C22⋊C4×C25 | C2 | semidirect |
| 4. C2×C22⋊Dic25 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. C22⋊C4×D25 | C2 | direct (N × H) |
| 9. C23×D25 | C4 | semidirect |
| 13. C22×C4×C25 | C22 | semidirect |
| 14. C22×Dic25 | C22 | semidirect |
| 16. C2×C4×D25 | C22 | semidirect |
| 17. C22⋊C4×C25 | C22 | semidirect |
| 18. C22⋊Dic25 | C22 | semidirect |
| 19. #87720 | C22 | semidirect |
| 22. C23×C25 | C2×C4 | semidirect |
| 29. C22×D25 | C2×C4 | semidirect |
| 30. C22×D25 | C2×C4 | semidirect |
| 35. C2×C4×C25 | C23 | semidirect |
| 37. C2×Dic25 | C23 | semidirect |
| 48. C22×C25 | C22×C4 | semidirect |
| 54. C2×D25 | C22⋊C4 | direct (N × H) |
| 56. C2×D25 | C22×C4 | semidirect |
| 75. C2×C25 | C2×C22⋊C4 | semidirect |
| 79. D25 | C2×C22⋊C4 | direct (N × H) |
| 103. C2×C22⋊C4 | D25 | direct (N × H) |
| 104. C25 | C22×C22⋊C4 | semidirect |
| 129. C22×C4 | C2×D25 | semidirect |
| 132. C22⋊C4 | C2×D25 | direct (N × H) |
| 149. C23 | C4×D25 | semidirect |
| 156. C2×C4 | C22×D25 | semidirect |
| 168. C22 | C2×C4×D25 | semidirect |
| 176. C2 | C22⋊C4×D25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D25 | 2 |
| C22×C4×D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87720 | 2 |
| C22⋊C4×D25 | 2 |
| C2×D5×C22⋊C4 | 5 |