Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
608 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5426 | C2 | semidirect |
| 4. C5×#5394 | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 8. C5×#986 | C4 | direct (N × H) |
| 11. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 13. C5×#859 | C22 | semidirect |
| 14. C4×#986 | C5 | direct (N × H) |
| 16. C4×C5×#41 | D3 | semidirect |
| 28. C5×#41⋊C3 | C2×C4 | semidirect |
| 30. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 35. C4×#41⋊C3 | C2×C5 | semidirect |
| 36. #5426 | C2×C5 | semidirect |
| 37. #5394 | C2×C5 | semidirect |
| 38. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 76. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 78. #986 | C4×C5 | direct (N × H) |
| 81. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 82. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 83. #859 | C22×C5 | semidirect |
| 86. C5×#41 | C4×D3 | semidirect |
| 119. C4×#41 | C5×D3 | semidirect |
| 139. #41⋊C3 | C2×C4×C5 | semidirect |
| 141. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 213. SL(2,𝔽3) | C22×C4×C5 | semidirect |
| 229. C4×C5 | #986 | direct (N × H) |
| 232. #41 | C4×C5×D3 | semidirect |
| 310. C5 | C4×#986 | direct (N × H) |
| 326. C4 | C5×#986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#5426 | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C4×C5×AGL(1,ℤ/8) | 3 |
| C4×C5×D12 | 4 |
| C4×#986 | 5 |