Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C5×PSU(3,𝔽2) #72217491
Order 2160.
180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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. C3×C5×PSU(3,𝔽2) | C2 | direct (N × H) |
| 3. C2×C5×PSU(3,𝔽2) | C3 | direct (N × H) |
| 6. C2×C3×PSU(3,𝔽2) | C5 | direct (N × H) |
| 8. C5×PSU(3,𝔽2) | C2×C3 | direct (N × H) |
| 9. C2×C33×C5 | Q8 | semidirect |
| 10. C3×C5×C3⋊D3 | Q8 | semidirect |
| 14. C3×PSU(3,𝔽2) | C2×C5 | direct (N × H) |
| 18. C2×PSU(3,𝔽2) | C3×C5 | direct (N × H) |
| 19. C33×C5 | C2×Q8 | semidirect |
| 26. C2×C32×C5 | C3×Q8 | semidirect |
| 27. C5×C3⋊D3 | C3×Q8 | semidirect |
| 33. PSU(3,𝔽2) | C2×C3×C5 | direct (N × H) |
| 37. C2×C33 | C5×Q8 | semidirect |
| 38. C3×C3⋊D3 | C5×Q8 | semidirect |
| 43. C32×C5 | C2×C3×Q8 | semidirect |
| 53. C2×C3×C5 | PSU(3,𝔽2) | direct (N × H) |
| 56. C33 | C2×C5×Q8 | semidirect |
| 63. C2×C32 | C3×C5×Q8 | semidirect |
| 64. C3⋊D3 | C3×C5×Q8 | semidirect |
| 71. C3×C5 | C2×PSU(3,𝔽2) | direct (N × H) |
| 77. C2×C5 | C3×PSU(3,𝔽2) | direct (N × H) |
| 80. C32 | C2×C3×C5×Q8 | semidirect |
| 87. C2×C3 | C5×PSU(3,𝔽2) | direct (N × H) |
| 90. C5 | C2×C3×PSU(3,𝔽2) | direct (N × H) |
| 95. C3 | C2×C5×PSU(3,𝔽2) | direct (N × H) |
| 98. C2 | C3×C5×PSU(3,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#157 | 2 |
| C3×C5×PSU(3,𝔽2) | 2 |
| C2×C5×PSU(3,𝔽2) | 3 |
| C2×C3×PSU(3,𝔽2) | 5 |
| C2×C3×C5×Q8 | 9 |