Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 196 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 |
|---|---|---|
| 5. #10603878 | C3 | direct (N × H) |
| 11. C3×#4002 | C4 | semidirect |
| 12. C3×C5×#97 | C4 | semidirect |
| 13. C3×#3947 | C4 | semidirect |
| 14. C3×#3935 | C4 | semidirect |
| 42. #4002 | C3×C4 | semidirect |
| 43. C5×#97 | C3×C4 | semidirect |
| 44. #3947 | C3×C4 | semidirect |
| 45. #3935 | C3×C4 | semidirect |
| 68. C3×#97 | AGL(1,𝔽5) | semidirect |
| 128. #97 | C3×AGL(1,𝔽5) | semidirect |
| 166. C3×C5 | #1745 | semidirect |
| 194. C5 | C3×#1745 | semidirect |
| 203. C3 | #10603878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C42×AGL(1,𝔽5) | 2 |
| C3×#65676 | 2 |
| C3×D5×#97 | 2 |
| C3×(C2×AGL(1,𝔽5))⋊C8 | 2 |
| #10603878 | 3 |
| C3×#1745 | 5 |