Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
730 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 730 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. C5×#519⋊C3 | C2 | semidirect |
| 3. #66146⋊C3 | C2 | semidirect |
| 4. #65908⋊C3 | C2 | semidirect |
| 5. C4×C5⋊(#41⋊C3) | C2 | semidirect |
| 6. #10617773 | C3 | semidirect |
| 8. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 13. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 19. #65908 | C2×C3 | semidirect |
| 21. C4×#713 | C2×C3 | semidirect |
| 27. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 29. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 30. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 38. #519⋊C3 | D5 | semidirect |
| 44. C2×#713 | C3×C4 | semidirect |
| 90. C4×SL(2,𝔽3) | C2×D5 | semidirect |
| 160. C2×SL(2,𝔽3) | C4×D5 | semidirect |
| 361. 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 |
| C5×#519⋊C3 | 2 |
| #66146⋊C3 | 2 |
| #65908⋊C3 | 2 |
| C4×C5⋊(#41⋊C3) | 2 |
| #10617773 | 3 |
| C3×#4023 | 4 |
| #3428⋊C3 | 5 |