Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. C3×C5×#367 | C2 | semidirect |
| 4. C3×#64725 | C2 | semidirect |
| 5. C3×#64709 | C2 | semidirect |
| 6. #10600138 | C3 | direct (N × H) |
| 14. C3×D5×C16 | C4 | semidirect |
| 18. C5×#367 | C2×C3 | semidirect |
| 19. #64725 | C2×C3 | semidirect |
| 20. #64709 | C2×C3 | semidirect |
| 35. C3×#367 | D5 | semidirect |
| 44. D5×C16 | C3×C4 | semidirect |
| 78. #367 | C3×D5 | semidirect |
| 149. C3×C5 | #2158 | semidirect |
| 174. C5 | C3×#2158 | semidirect |
| 183. C3 | #10600138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D5×C16 | 2 |
| C3×#65169 | 2 |
| C3×C5×#367 | 2 |
| C3×#64725 | 2 |
| C3×#64709 | 2 |
| #10600138 | 3 |
| C3×#2158 | 5 |