Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
846 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 216 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 | direct (N × H) |
| 3. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 4. C2×C4×C5×#41 | C3 | semidirect |
| 5. C2×C5×#41⋊C3 | C4 | direct (N × H) |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. C2×C4×#41⋊C3 | C5 | direct (N × H) |
| 13. C4×C5×#41 | C2×C3 | semidirect |
| 20. C5×#41⋊C3 | C2×C4 | direct (N × H) |
| 21. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 25. C4×#41⋊C3 | C2×C5 | direct (N × H) |
| 26. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 29. C2×C5×#41 | C3×C4 | semidirect |
| 48. C2×C4×#41 | C3×C5 | semidirect |
| 54. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 55. C2×#41⋊C3 | C4×C5 | direct (N × H) |
| 59. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 64. C5×#41 | C2×C3×C4 | semidirect |
| 92. C4×#41 | C2×C3×C5 | semidirect |
| 104. #41⋊C3 | C2×C4×C5 | direct (N × H) |
| 105. C2×SL(2,𝔽3) | C2×C4×C5 | semidirect |
| 130. C2×C4×C5 | #41⋊C3 | direct (N × H) |
| 135. C2×#41 | C3×C4×C5 | semidirect |
| 162. SL(2,𝔽3) | C22×C4×C5 | semidirect |
| 174. C4×C5 | C2×#41⋊C3 | direct (N × H) |
| 179. #41 | C2×C3×C4×C5 | semidirect |
| 212. C2×C5 | C4×#41⋊C3 | direct (N × H) |
| 237. C2×C4 | C5×#41⋊C3 | direct (N × H) |
| 243. C5 | C2×C4×#41⋊C3 | direct (N × H) |
| 255. C4 | C2×C5×#41⋊C3 | direct (N × H) |
| 258. C2 | C4×C5×#41⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C2×C4×C5×#41 | 3 |
| C2×C3×C42×C5 | 4 |
| C2×C4×#41⋊C3 | 5 |