Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
526 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 526 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. C2×C5×#131⋊C3 | C2 | semidirect |
| 3. C2×C5×GU(2,𝔽3) | C2 | semidirect |
| 4. C5×#5404 | C2 | direct (N × H) |
| 7. C5×#985 | C4 | semidirect |
| 9. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 10. C2×C5×#226 | C4 | semidirect |
| 12. C5×#131⋊C3 | C22 | semidirect |
| 13. C5×GU(2,𝔽3) | C22 | semidirect |
| 14. C2×#5404 | C5 | direct (N × H) |
| 17. C2×C5×#131 | D3 | semidirect |
| 28. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 29. C5×#226 | C2×C4 | semidirect |
| 34. C2×#131⋊C3 | C2×C5 | semidirect |
| 35. C2×GU(2,𝔽3) | C2×C5 | semidirect |
| 36. #5404 | C2×C5 | direct (N × H) |
| 50. C5×#131 | C2×D3 | semidirect |
| 73. #985 | C4×C5 | semidirect |
| 75. C2×GL(2,𝔽3) | C4×C5 | semidirect |
| 76. C2×#226 | C4×C5 | semidirect |
| 78. #131⋊C3 | C22×C5 | semidirect |
| 79. GU(2,𝔽3) | C22×C5 | semidirect |
| 123. C2×#131 | C5×D3 | semidirect |
| 140. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 141. #226 | C2×C4×C5 | semidirect |
| 187. #131 | C2×C5×D3 | semidirect |
| 274. C2×C5 | #5404 | direct (N × H) |
| 308. C5 | C2×#5404 | direct (N × H) |
| 325. C2 | C5×#5404 | 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 |
| C2×C5×#131⋊C3 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#5404 | 2 |
| C2×C5×#443 | 3 |
| C2×C5×D3×C8 | 4 |
| C2×#5404 | 5 |