Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
760 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 172 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. C4×C5×#41⋊C3 | C2 | semidirect |
| 4. C4×C5×H(5,𝔽2) | C3 | semidirect |
| 5. C5×#994 | C4 | direct (N × H) |
| 8. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. C4×#994 | C5 | direct (N × H) |
| 19. C5×#41⋊C3 | C2×C4 | semidirect |
| 24. #520⋊C3 | C2×C5 | semidirect |
| 25. C4×#41⋊C3 | C2×C5 | semidirect |
| 27. C5×H(5,𝔽2) | C3×C4 | semidirect |
| 47. C4×H(5,𝔽2) | C3×C5 | semidirect |
| 52. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 53. #994 | C4×C5 | direct (N × H) |
| 56. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 57. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 96. #41⋊C3 | C2×C4×C5 | semidirect |
| 122. H(5,𝔽2) | C3×C4×C5 | semidirect |
| 149. SL(2,𝔽3) | C22×C4×C5 | semidirect |
| 161. C4×C5 | #994 | direct (N × H) |
| 221. C5 | C4×#994 | direct (N × H) |
| 233. C4 | C5×#994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#994 | 2 |
| C5×#520⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C4×C5×H(5,𝔽2) | 3 |
| C3×C4×C5×Q8 | 4 |
| C4×#994 | 5 |