Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
606 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 92 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. C5×#5420 | C2 | semidirect |
| 4. C5×#5394 | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 8. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 13. C5×#859 | C22 | semidirect |
| 14. #85353 | C5 | direct (N × H) |
| 16. C5×#519 | D3 | semidirect |
| 28. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 30. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 31. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 36. #519⋊C3 | C2×C5 | semidirect |
| 37. #5420 | C2×C5 | semidirect |
| 38. #5394 | C2×C5 | semidirect |
| 39. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 51. C4×C5×Q8 | C2×D3 | semidirect |
| 79. C2×GL(2,𝔽3) | C4×C5 | semidirect |
| 83. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 84. #859 | C22×C5 | semidirect |
| 88. C2×C5×Q8 | C4×D3 | semidirect |
| 121. #519 | C5×D3 | semidirect |
| 143. C2×SL(2,𝔽3) | C2×C4×C5 | semidirect |
| 145. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 146. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 187. C4×Q8 | C2×C5×D3 | semidirect |
| 235. C2×Q8 | C4×C5×D3 | semidirect |
| 314. C5 | #85353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×GL(2,𝔽3) | 2 |
| C5×#519⋊C3 | 2 |
| C5×#5420 | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#2949 | 3 |
| C5×D3×C22⋊C4 | 4 |
| #85353 | 5 |