Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#64763 | C2 | semidirect |
| 4. #10602753 | C3 | direct (N × H) |
| 11. C5×#564 | C2×C3 | semidirect |
| 13. #64763 | C2×C3 | semidirect |
| 21. C3×#564 | D5 | semidirect |
| 47. #564 | C3×D5 | semidirect |
| 89. C3×C5 | #1658 | semidirect |
| 103. C5 | C3×#1658 | semidirect |
| 108. C3 | #10602753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#564 | 2 |
| C3×#65356 | 2 |
| C3×#64763 | 2 |
| #10602753 | 3 |
| C3×#1658 | 5 |