Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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×#489 | C2 | semidirect |
| 3. C3×#65378 | C2 | semidirect |
| 4. C3×#65375 | C2 | semidirect |
| 5. C3×#64760 | C2 | semidirect |
| 6. C3×#64684 | C2 | semidirect |
| 7. C3×#64684 | C2 | semidirect |
| 8. #10602037 | C3 | direct (N × H) |
| 9. C3×C5×C4⋊Q8 | C22 | semidirect |
| 23. C3×C5×#97 | C22 | semidirect |
| 26. C3×#3935 | C22 | semidirect |
| 27. C3×#3935 | C22 | semidirect |
| 30. C5×#489 | C2×C3 | semidirect |
| 31. #65378 | C2×C3 | semidirect |
| 32. #65375 | C2×C3 | semidirect |
| 33. #64760 | C2×C3 | semidirect |
| 34. #64684 | C2×C3 | semidirect |
| 35. #64684 | C2×C3 | semidirect |
| 68. C3×#489 | D5 | semidirect |
| 72. C5×C4⋊Q8 | C22×C3 | semidirect |
| 86. C5×#97 | C22×C3 | semidirect |
| 89. #3935 | C22×C3 | semidirect |
| 90. #3935 | C22×C3 | semidirect |
| 121. C3×C4⋊Q8 | C2×D5 | semidirect |
| 137. C3×#97 | C2×D5 | semidirect |
| 170. #489 | C3×D5 | semidirect |
| 250. C4⋊Q8 | C2×C3×D5 | semidirect |
| 266. #97 | C2×C3×D5 | semidirect |
| 347. C3×C5 | #1659 | semidirect |
| 405. C5 | C3×#1659 | semidirect |
| 424. C3 | #10602037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66017 | 2 |
| C3×C5×#489 | 2 |
| C3×#65378 | 2 |
| C3×#65375 | 2 |
| C3×#64760 | 2 |
| C3×#64684 | 2 |
| #10602037 | 3 |
| C3×#1659 | 5 |