Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
314 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 48 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. C5×#568⋊C3 | C2 | semidirect |
| 3. C5×#5424 | C2 | semidirect |
| 6. C5×#986 | C4 | semidirect |
| 8. C5×#984 | C4 | semidirect |
| 13. #73132 | C5 | direct (N × H) |
| 15. C5×#568 | D3 | semidirect |
| 30. #568⋊C3 | C2×C5 | semidirect |
| 31. #5424 | C2×C5 | semidirect |
| 64. #986 | C4×C5 | semidirect |
| 66. #984 | C4×C5 | semidirect |
| 111. #568 | C5×D3 | semidirect |
| 286. C5 | #73132 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5923 | 2 |
| C5×#568⋊C3 | 2 |
| C5×#5424 | 2 |
| C5×#1881 | 3 |
| C5×#825 | 4 |
| #73132 | 5 |