Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
546 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 546 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×#520⋊C3 | C2 | semidirect |
| 3. C5×#5426 | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C5×#5388 | C2 | semidirect |
| 8. C5×#985 | C4 | semidirect |
| 14. #85364 | C5 | direct (N × H) |
| 17. C5×#520 | D3 | semidirect |
| 28. C5×#41⋊C3 | C2×C4 | semidirect |
| 30. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 31. C5×#226 | C2×C4 | semidirect |
| 36. #520⋊C3 | C2×C5 | semidirect |
| 37. #5426 | C2×C5 | semidirect |
| 38. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 39. #5388 | C2×C5 | semidirect |
| 78. #985 | C4×C5 | semidirect |
| 87. C5×#41 | C4×D3 | semidirect |
| 121. #520 | C5×D3 | semidirect |
| 140. #41⋊C3 | C2×C4×C5 | semidirect |
| 142. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 143. #226 | C2×C4×C5 | semidirect |
| 230. #41 | C4×C5×D3 | semidirect |
| 306. C5 | #85364 | 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 |
| C5×#520⋊C3 | 2 |
| C5×#5426 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5388 | 2 |
| C5×#2952 | 3 |
| C5×D3×C4⋊C4 | 4 |
| #85364 | 5 |