Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 158 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×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 4. C32×C5×C4⋊C4 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 15. #64104 | C5 | direct (N × H) |
| 19. C3×C5×C4⋊C4 | D3 | semidirect |
| 27. C2×C5×C3⋊D3 | D4 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 32. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 33. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 34. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 35. C32×C4⋊C4 | C2×C5 | semidirect |
| 36. #3752 | C2×C5 | semidirect |
| 54. C5×C4⋊C4 | C3⋊D3 | semidirect |
| 72. C3×C4×C5 | D12 | semidirect |
| 77. C3×C4⋊C4 | C5×D3 | semidirect |
| 79. C32×C5 | #121 | semidirect |
| 94. C2×C3⋊D3 | C5×D4 | semidirect |
| 96. C32×C4 | C5×D4 | semidirect |
| 121. C4×C5 | C4⋊(C3⋊D3) | semidirect |
| 130. C4⋊C4 | C5×C3⋊D3 | semidirect |
| 132. C3×C5 | #895 | semidirect |
| 141. C3×C4 | C5×D12 | semidirect |
| 148. C32 | C5×#121 | semidirect |
| 162. C5 | #64104 | direct (N × H) |
| 172. C4 | C5×C4⋊(C3⋊D3) | semidirect |
| 173. C3 | C5×#895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C32×C5×C4⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×#895 | 3 |
| #64104 | 5 |