Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 162 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×C32×C5×D4 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 13. #64149 | C5 | direct (N × H) |
| 14. C2×C3×C5×D4 | D3 | semidirect |
| 23. C32×C4×C5 | D4 | semidirect |
| 24. C5×C3⋊Dic3 | D4 | semidirect |
| 26. C2×C32×D4 | C2×C5 | semidirect |
| 27. C2×#638 | C2×C5 | semidirect |
| 28. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 29. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 44. C2×C5×D4 | C3⋊D3 | semidirect |
| 58. C3×C4×C5 | #67 | semidirect |
| 60. C2×C3×D4 | C5×D3 | semidirect |
| 64. C32×C5 | #127 | semidirect |
| 77. C32×C4 | C5×D4 | semidirect |
| 78. C3⋊Dic3 | C5×D4 | semidirect |
| 97. C4×C5 | #638 | semidirect |
| 104. C2×D4 | C5×C3⋊D3 | semidirect |
| 106. C3×C5 | #940 | semidirect |
| 112. C3×C4 | C5×#67 | semidirect |
| 118. C32 | C5×#127 | semidirect |
| 130. C5 | #64149 | direct (N × H) |
| 137. C4 | C5×#638 | semidirect |
| 138. C3 | C5×#940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C5×#638 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#940 | 3 |
| #64149 | 5 |