Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
608 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 77 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. Dic5×#41⋊C3 | C2 | semidirect |
| 3. #11752145 | C2 | semidirect |
| 4. Dic5×GL(2,𝔽3) | C2 | semidirect |
| 5. #11751600 | C2 | semidirect |
| 8. C5×#986 | C4 | semidirect |
| 11. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 12. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 13. #91184 | C22 | semidirect |
| 16. #41×Dic5 | D3 | semidirect |
| 27. C5×#41⋊C3 | C2×C4 | semidirect |
| 30. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 75. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 78. #986 | Dic5 | direct (N × H) |
| 86. C5×#41 | C4×D3 | semidirect |
| 139. #41⋊C3 | C2×Dic5 | semidirect |
| 141. GL(2,𝔽3) | C2×Dic5 | semidirect |
| 213. SL(2,𝔽3) | C22×Dic5 | semidirect |
| 229. Dic5 | #986 | direct (N × H) |
| 232. #41 | D3×Dic5 | semidirect |
| 310. C5 | C4×#986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| Dic5×#41⋊C3 | 2 |
| #11752145 | 2 |
| Dic5×GL(2,𝔽3) | 2 |
| #11751600 | 2 |
| Dic5×AGL(1,ℤ/8) | 3 |
| Dic5×D12 | 4 |
| C4×#986 | 5 |