Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
730 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 135 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. #66161⋊C3 | C2 | semidirect |
| 3. Dic5×#41⋊C3 | C2 | semidirect |
| 4. #66146⋊C3 | C2 | semidirect |
| 5. #10619161 | C3 | semidirect |
| 6. C2×C5×#41⋊C3 | C4 | semidirect |
| 11. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 15. #66161 | C2×C3 | semidirect |
| 17. #41×Dic5 | C2×C3 | semidirect |
| 23. C5×#41⋊C3 | C2×C4 | semidirect |
| 24. C5×#41⋊C3 | C2×C4 | semidirect |
| 25. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 37. C2×C5×#41 | C3×C4 | semidirect |
| 69. C2×#41⋊C3 | Dic5 | semidirect |
| 131. #41⋊C3 | C2×Dic5 | semidirect |
| 132. #41⋊C3 | C2×Dic5 | semidirect |
| 133. C2×SL(2,𝔽3) | C2×Dic5 | semidirect |
| 172. C2×#41 | C3×Dic5 | semidirect |
| 307. C5 | #3428⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| #66161⋊C3 | 2 |
| Dic5×#41⋊C3 | 2 |
| #66146⋊C3 | 2 |
| #10619161 | 3 |
| C3×#4072 | 4 |
| #3428⋊C3 | 5 |