Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1792 conjugacy classes of subgroups; only the 918 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 918 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 |
|---|---|---|
| 1. C3×C5×#564 | C2 | semidirect |
| 3. C5×C3⋊#564 | C2 | semidirect |
| 11. D3×#564 | C5 | direct (N × H) |
| 13. C5×#564 | D3 | direct (N × H) |
| 21. C3×#564 | C2×C5 | semidirect |
| 23. C3⋊#564 | C2×C5 | semidirect |
| 48. #564 | C5×D3 | direct (N × H) |
| 71. C5×D3 | #564 | direct (N × H) |
| 86. C3×C5 | C2×#564 | semidirect |
| 98. D3 | C5×#564 | direct (N × H) |
| 99. C5 | D3×#564 | direct (N × H) |
| 104. C3 | C2×C5×#564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#564 | 2 |
| C5×D3×#125 | 2 |
| C5×C3⋊#564 | 2 |
| C2×C5×#564 | 3 |
| D3×#564 | 5 |