Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 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×#4094⋊C3 | C2 | semidirect |
| 3. C2×#91185 | C2 | semidirect |
| 4. #11751615 | C2 | direct (N × H) |
| 7. C5×#985 | C4 | semidirect |
| 9. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 10. C2×C5×#226 | C4 | semidirect |
| 12. #4094⋊C3 | C22 | semidirect |
| 13. #91185 | C22 | semidirect |
| 17. C2×#4094 | D3 | semidirect |
| 28. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 29. C5×#226 | C2×C4 | semidirect |
| 51. #4094 | C2×D3 | semidirect |
| 73. #985 | Dic5 | semidirect |
| 75. C2×GL(2,𝔽3) | Dic5 | semidirect |
| 76. C2×#226 | Dic5 | semidirect |
| 140. GL(2,𝔽3) | C2×Dic5 | semidirect |
| 141. #226 | C2×Dic5 | semidirect |
| 274. C2×C5 | #5404 | semidirect |
| 308. C5 | C2×#5404 | semidirect |
| 325. C2 | #11751615 | 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×#4094⋊C3 | 2 |
| C2×#91185 | 2 |
| #11751615 | 2 |
| C2×#65485 | 3 |
| C2×D3×#168 | 4 |
| C2×#5404 | 5 |