Finite Group DatabasebetaFinite Group DatabasebetaOrder 4000.
192 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 192 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. #87716⋊C5 | C2 | semidirect |
| 8. #11716380 | C5 | semidirect |
| 17. #87716 | C2×C5 | semidirect |
| 34. 5−1+2 | #100 | semidirect |
| 71. C25 | C5×#100 | 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 |
| #87716⋊C5 | 2 |
| C5×#3965 | 5 |
| #11716380 | 5 |