Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
574 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 100 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. C4×C5×#41⋊C3 | C2 | semidirect |
| 3. C5×#5424 | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C4×C5×#226 | C2 | semidirect |
| 8. C5×#985 | C4 | direct (N × H) |
| 14. C4×#985 | C5 | direct (N × H) |
| 17. C4×C5×#41 | D3 | semidirect |
| 28. C5×#41⋊C3 | C2×C4 | semidirect |
| 30. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 31. C5×#226 | C2×C4 | semidirect |
| 36. C4×#41⋊C3 | C2×C5 | semidirect |
| 37. #5424 | C2×C5 | semidirect |
| 38. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 39. C4×#226 | C2×C5 | semidirect |
| 78. #985 | C4×C5 | direct (N × H) |
| 87. C5×#41 | C4×D3 | semidirect |
| 121. C4×#41 | C5×D3 | semidirect |
| 139. #41⋊C3 | C2×C4×C5 | semidirect |
| 141. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 142. #226 | C2×C4×C5 | semidirect |
| 221. C4×C5 | #985 | direct (N × H) |
| 225. #41 | C4×C5×D3 | semidirect |
| 297. C5 | C4×#985 | direct (N × H) |
| 309. C4 | C5×#985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#985 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#5424 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C4×C5×#226 | 2 |
| C4×C5×#135 | 3 |
| C42×C5×D3 | 4 |
| C4×#985 | 5 |