Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
200 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×C5×C4⋊C16 | C2 | semidirect |
| 3. C5×#4461 | C2 | semidirect |
| 12. #67557 | C5 | direct (N × H) |
| 14. C5×C4⋊C16 | D3 | semidirect |
| 29. C3×C4⋊C16 | C2×C5 | semidirect |
| 30. #4461 | C2×C5 | semidirect |
| 71. C4⋊C16 | C5×D3 | semidirect |
| 150. C3×C5 | #1330 | semidirect |
| 180. C5 | #67557 | direct (N × H) |
| 190. C3 | C5×#1330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4688 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C5×#4461 | 2 |
| C5×#1330 | 3 |
| #67557 | 5 |