Finite Group DatabasebetaFinite Group DatabasebetaOrder 4000.
210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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⋊(Dic25⋊C5) | C2 | semidirect |
| 3. C23×5−1+2 | C4 | semidirect |
| 6. C2×C4×5−1+2 | C4 | semidirect |
| 9. #11716382 | C5 | semidirect |
| 21. C22⋊Dic25 | C2×C5 | semidirect |
| 33. C23×C25 | C4×C5 | semidirect |
| 38. C2×C4×C25 | C4×C5 | semidirect |
| 42. 5−1+2 | #99 | semidirect |
| 92. C25 | C5×#99 | semidirect |
| 117. C23 | Dic25⋊C5 | semidirect |
| 121. C2×C4 | Dic25⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×5−1+2 | 2 |
| C22⋊(Dic25⋊C5) | 2 |
| C5×#3966 | 5 |
| #11716382 | 5 |