Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 174 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×C4×C5×C3⋊D3 | C2 | semidirect |
| 3. C32×C5×C4⋊C4 | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 12. C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 14. #64102 | C5 | direct (N × H) |
| 17. C3×C5×C4⋊C4 | D3 | semidirect |
| 23. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 25. C32×C4×C5 | C2×C4 | semidirect |
| 27. C5×C3⋊Dic3 | D4 | semidirect |
| 30. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 31. C32×C4⋊C4 | C2×C5 | semidirect |
| 32. #3752 | C2×C5 | semidirect |
| 33. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 48. C5×C4⋊C4 | C3⋊D3 | semidirect |
| 56. C4⋊(C3⋊D3) | C4×C5 | semidirect |
| 63. C3×C4×C5 | C4×D3 | semidirect |
| 68. C3×C4⋊C4 | C5×D3 | semidirect |
| 71. C32×C5 | C4×D4 | semidirect |
| 82. C2×C3⋊D3 | C2×C4×C5 | semidirect |
| 84. C32×C4 | C2×C4×C5 | semidirect |
| 86. C3⋊Dic3 | C5×D4 | semidirect |
| 106. C4×C5 | C4×C3⋊D3 | semidirect |
| 113. C4⋊C4 | C5×C3⋊D3 | semidirect |
| 116. C3×C5 | #893 | semidirect |
| 122. C3×C4 | C4×C5×D3 | semidirect |
| 129. C32 | C4×C5×D4 | semidirect |
| 141. C5 | #64102 | direct (N × H) |
| 149. C4 | C4×C5×C3⋊D3 | semidirect |
| 150. C3 | C5×#893 | 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 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#893 | 3 |
| #64102 | 5 |