Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
156 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 62 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×#368 | C2 | semidirect |
| 3. C3×#64719 | C2 | semidirect |
| 4. #10598074 | C3 | direct (N × H) |
| 13. C5×#368 | C2×C3 | semidirect |
| 14. #64719 | C2×C3 | semidirect |
| 24. C3×#368 | D5 | semidirect |
| 54. #368 | C3×D5 | semidirect |
| 102. C3×C5 | #1419 | semidirect |
| 121. C5 | C3×#1419 | semidirect |
| 127. C3 | #10598074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D80 | 2 |
| C3×C5×#368 | 2 |
| C3×#64719 | 2 |
| #10598074 | 3 |
| C3×#1419 | 5 |