Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 378 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 |
|---|---|---|
| 3. C4×C5×C3⋊Dic3 | C2 | direct (N × H) |
| 6. C2×C32×C4×C5 | C4 | semidirect |
| 8. C2×C5×C3⋊Dic3 | C4 | direct (N × H) |
| 10. C2×C4×C3⋊Dic3 | C5 | direct (N × H) |
| 17. C32×C4×C5 | C2×C4 | semidirect |
| 18. C5×C3⋊Dic3 | C2×C4 | direct (N × H) |
| 22. C4×C3⋊Dic3 | C2×C5 | direct (N × H) |
| 24. C2×C3×C4×C5 | Dic3 | semidirect |
| 29. C2×C32×C5 | C42 | semidirect |
| 36. C2×C32×C4 | C4×C5 | semidirect |
| 38. C2×C3⋊Dic3 | C4×C5 | direct (N × H) |
| 43. C3×C4×C5 | C2×Dic3 | semidirect |
| 48. C32×C5 | C2×C42 | semidirect |
| 52. C2×C4×C5 | C3⋊Dic3 | direct (N × H) |
| 57. C32×C4 | C2×C4×C5 | semidirect |
| 58. C3⋊Dic3 | C2×C4×C5 | direct (N × H) |
| 60. C2×C3×C5 | C4×Dic3 | semidirect |
| 64. C2×C3×C4 | C5×Dic3 | semidirect |
| 72. C4×C5 | C2×C3⋊Dic3 | direct (N × H) |
| 73. C2×C32 | C42×C5 | semidirect |
| 79. C3×C5 | C2×C4×Dic3 | semidirect |
| 83. C3×C4 | C2×C5×Dic3 | semidirect |
| 85. C2×C5 | C4×C3⋊Dic3 | direct (N × H) |
| 88. C32 | C2×C42×C5 | semidirect |
| 92. C2×C4 | C5×C3⋊Dic3 | direct (N × H) |
| 94. C2×C3 | C4×C5×Dic3 | semidirect |
| 97. C5 | C2×C4×C3⋊Dic3 | direct (N × H) |
| 102. C4 | C2×C5×C3⋊Dic3 | direct (N × H) |
| 103. C3 | C2×C4×C5×Dic3 | semidirect |
| 104. C2 | C4×C5×C3⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C2×C4×C5×Dic3 | 3 |
| C2×C4×C3⋊Dic3 | 5 |