Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
824 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 156 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×C3×#4007 | C2 | semidirect |
| 3. C3×#65689 | C2 | semidirect |
| 4. C3×#65676 | C2 | semidirect |
| 5. #10604617 | C3 | direct (N × H) |
| 10. C3×C5×#127 | C4 | semidirect |
| 12. C3×#4086 | C4 | semidirect |
| 13. C3×#4020 | C4 | semidirect |
| 20. C2×#4007 | C2×C3 | semidirect |
| 21. #65689 | C2×C3 | semidirect |
| 22. #65676 | C2×C3 | semidirect |
| 39. C3×D5⋊C8 | D4 | semidirect |
| 51. C5×#127 | C3×C4 | semidirect |
| 53. #4086 | C3×C4 | semidirect |
| 54. #4020 | C3×C4 | semidirect |
| 88. C3×#127 | AGL(1,𝔽5) | semidirect |
| 110. D5⋊C8 | C3×D4 | semidirect |
| 181. #127 | C3×AGL(1,𝔽5) | semidirect |
| 250. C3×C5 | #1961 | semidirect |
| 300. C5 | C3×#1961 | semidirect |
| 316. C3 | #10604617 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×#127 | 2 |
| C2×C3×#4007 | 2 |
| C3×#65689 | 2 |
| C3×#65676 | 2 |
| #10604617 | 3 |
| C3×#1961 | 5 |