Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
483 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 483 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
| 5. C2×C4⋊Dic25 | C2 | semidirect |
| 6. C2×#87718 | C2 | semidirect |
| 7. C2×#87718 | C2 | semidirect |
| 8. #11716440 | C2 | direct (N × H) |
| 19. C2×Dic50 | C22 | semidirect |
| 22. C4⋊Dic25 | C22 | semidirect |
| 23. #87718 | C22 | semidirect |
| 24. #87718 | C22 | semidirect |
| 28. C23×C25 | Q8 | semidirect |
| 58. C22×C25 | C2×Q8 | semidirect |
| 85. C2×C25 | C22⋊Q8 | semidirect |
| 116. C25 | C2×C22⋊Q8 | semidirect |
| 154. C23 | Dic50 | semidirect |
| 176. C22 | C2×Dic50 | semidirect |
| 187. C2 | #11716440 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic25 | 2 |
| C22×Dic50 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| C2×C4⋊Dic25 | 2 |
| C2×#87718 | 2 |
| #11716440 | 2 |
| C2×#4024 | 5 |