Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
168 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 1. C2×C5×PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×C5×AGL(1,𝔽9) | C2 | semidirect |
| 4. C5×AΓL(1,𝔽9) | C2 | direct (N × H) |
| 9. C5×PSU(3,𝔽2) | C22 | semidirect |
| 12. C5×AGL(1,𝔽9) | C22 | semidirect |
| 13. C2×AΓL(1,𝔽9) | C5 | direct (N × H) |
| 22. C2×PSU(3,𝔽2) | C2×C5 | semidirect |
| 24. C2×AGL(1,𝔽9) | C2×C5 | semidirect |
| 25. AΓL(1,𝔽9) | C2×C5 | direct (N × H) |
| 27. C2×C32×C5 | SD16 | semidirect |
| 28. C5×C3⋊D3 | SD16 | semidirect |
| 39. PSU(3,𝔽2) | C22×C5 | semidirect |
| 42. AGL(1,𝔽9) | C22×C5 | semidirect |
| 48. C32×C5 | C2×SD16 | semidirect |
| 78. C2×C32 | C5×SD16 | semidirect |
| 79. C3⋊D3 | C5×SD16 | semidirect |
| 95. C2×C5 | AΓL(1,𝔽9) | direct (N × H) |
| 96. C32 | C2×C5×SD16 | semidirect |
| 110. C5 | C2×AΓL(1,𝔽9) | direct (N × H) |
| 122. C2 | C5×AΓL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×PSU(3,𝔽2) | 2 |
| C2×C5×GO+(4,𝔽2) | 2 |
| C2×C5×AGL(1,𝔽9) | 2 |
| C5×AΓL(1,𝔽9) | 2 |
| C2×AΓL(1,𝔽9) | 5 |
| C2×C5×SD16 | 9 |