Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
718 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 91 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×#91185 | C2 | semidirect |
| 3. C2×C5×GU(2,𝔽3) | C2 | semidirect |
| 4. D5×GU(2,𝔽3) | C2 | direct (N × H) |
| 7. D5×#41⋊C3 | C4 | semidirect |
| 9. C2×D5×SL(2,𝔽3) | C4 | semidirect |
| 10. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 12. #91185 | C22 | semidirect |
| 13. C5×GU(2,𝔽3) | C22 | semidirect |
| 25. C5×#41⋊C3 | C2×C4 | semidirect |
| 27. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 28. D5×SL(2,𝔽3) | C2×C4 | semidirect |
| 29. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 36. C2×GU(2,𝔽3) | D5 | direct (N × H) |
| 72. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 82. GU(2,𝔽3) | C2×D5 | direct (N × H) |
| 151. #41⋊C3 | C4×D5 | semidirect |
| 154. C2×SL(2,𝔽3) | C4×D5 | semidirect |
| 237. SL(2,𝔽3) | C2×C4×D5 | semidirect |
| 248. C2×D5 | GU(2,𝔽3) | direct (N × H) |
| 318. C2×C5 | C2×GU(2,𝔽3) | semidirect |
| 321. D5 | C2×GU(2,𝔽3) | direct (N × H) |
| 367. C5 | C22×GU(2,𝔽3) | semidirect |
| 391. C2 | D5×GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41⋊C3 | 2 |
| C2×#91185 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| D5×GU(2,𝔽3) | 2 |
| C2×D5×#104 | 3 |
| C2×D5×C3⋊C8 | 4 |
| C22×GU(2,𝔽3) | 5 |