Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 68 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×#2888 | C3 | semidirect |
| 9. #2888⋊C3 | C5 | direct (N × H) |
| 21. #568⋊C3 | C2×C5 | semidirect |
| 37. #2888 | C3×C5 | semidirect |
| 197. C5 | #2888⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#994 | 2 |
| C5×#568⋊C3 | 2 |
| C5×#2888 | 3 |
| C3×C5×#101 | 4 |
| #2888⋊C3 | 5 |