Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
639 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 213 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. C23×Dic25 | C2 | semidirect |
| 3. C22×C4×D25 | C2 | semidirect |
| 4. C2×C22⋊C4×C25 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. C2×#87718 | C2 | semidirect |
| 7. C2×C4×Dic25 | C2 | semidirect |
| 8. #11716443 | C2 | direct (N × H) |
| 13. C2×C22⋊D25 | C4 | semidirect |
| 19. C22×Dic25 | C22 | semidirect |
| 21. C2×C4×D25 | C22 | semidirect |
| 22. C22⋊C4×C25 | C22 | semidirect |
| 23. #87720 | C22 | semidirect |
| 24. #87718 | C22 | semidirect |
| 25. C4×Dic25 | C22 | semidirect |
| 29. C23×C25 | C2×C4 | semidirect |
| 34. C22×D25 | C2×C4 | semidirect |
| 40. C22⋊D25 | C2×C4 | semidirect |
| 43. C2×Dic25 | C2×C4 | semidirect |
| 44. C2×Dic25 | D4 | semidirect |
| 61. C22×C25 | C22×C4 | semidirect |
| 68. C2×D25 | C22×C4 | semidirect |
| 72. Dic25 | C22×C4 | semidirect |
| 73. Dic25 | C2×D4 | semidirect |
| 93. C2×C25 | C4×D4 | semidirect |
| 126. C2×C22⋊C4 | D25 | semidirect |
| 128. C25 | C2×C4×D4 | semidirect |
| 161. C22⋊C4 | C2×D25 | semidirect |
| 175. C23 | C4×D25 | semidirect |
| 200. C22 | C2×C4×D25 | semidirect |
| 211. C2 | #11716443 | 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 |
| C23×Dic25 | 2 |
| C22×C4×D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×#87720 | 2 |
| C2×#87718 | 2 |
| C2×C4×Dic25 | 2 |
| #11716443 | 2 |
| C2×#4027 | 5 |