Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
168 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 26 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. C2×C5×#1044 | C2 | semidirect |
| 3. C5×#6036 | C2 | semidirect |
| 7. C5×D52 | C4 | semidirect |
| 10. #87835 | C5 | direct (N × H) |
| 17. C2×#1044 | C2×C5 | semidirect |
| 20. #6036 | C2×C5 | semidirect |
| 21. C53 | C22⋊C4 | semidirect |
| 33. D52 | C4×C5 | semidirect |
| 72. C52 | C5×C22⋊C4 | semidirect |
| 120. C5 | #87835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D52 | 2 |
| C2×C5×#1044 | 2 |
| C5×#6036 | 2 |
| #87835 | 5 |
| C5×C22⋊C4 | 25 |