Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
495 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 149 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×Dic50 | C2 | semidirect |
| 3. C2×C22⋊C4×C25 | C2 | semidirect |
| 4. C2×C22⋊Dic25 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. C2×#87720 | C2 | semidirect |
| 7. C2×C4×Dic25 | C2 | semidirect |
| 8. #11716447 | C2 | direct (N × H) |
| 19. C2×Dic50 | C22 | semidirect |
| 20. C22⋊C4×C25 | C22 | semidirect |
| 21. C22⋊Dic25 | C22 | semidirect |
| 22. #87720 | C22 | semidirect |
| 23. #87720 | C22 | semidirect |
| 24. C4×Dic25 | C22 | semidirect |
| 90. C2×C25 | #124 | semidirect |
| 122. C2×C22⋊C4 | D25 | semidirect |
| 124. C25 | C2×#124 | semidirect |
| 156. C22⋊C4 | C2×D25 | semidirect |
| 205. C2 | #11716447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C22×Dic50 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×#87720 | 2 |
| C2×C4×Dic25 | 2 |
| #11716447 | 2 |
| C2×#4031 | 5 |