Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×C5×#131⋊C3 | C2 | semidirect |
| 3. C2×#4094⋊C3 | C2 | semidirect |
| 4. #66084⋊C3 | C2 | direct (N × H) |
| 5. C2×#66084 | C3 | semidirect |
| 12. C5×#131⋊C3 | C22 | semidirect |
| 13. #4094⋊C3 | C22 | semidirect |
| 16. C2×C5×#131 | C2×C3 | semidirect |
| 17. C2×#4094 | C2×C3 | semidirect |
| 19. #66084 | C2×C3 | semidirect |
| 36. C2×#131⋊C3 | D5 | semidirect |
| 49. C5×#131 | C22×C3 | semidirect |
| 53. #4094 | C22×C3 | semidirect |
| 85. #131⋊C3 | C2×D5 | semidirect |
| 143. C2×#131 | C3×D5 | semidirect |
| 218. #131 | C2×C3×D5 | semidirect |
| 319. C2×C5 | #568⋊C3 | semidirect |
| 365. C5 | C2×#568⋊C3 | semidirect |
| 387. C2 | #66084⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41⋊C3 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C2×#4094⋊C3 | 2 |
| #66084⋊C3 | 2 |
| C2×#66084 | 3 |
| C2×C3×#676 | 4 |
| C2×#568⋊C3 | 5 |