Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 244 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×C3⋊Dic15 | C2 | semidirect |
| 4. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 5. Dic5×C3⋊Dic3 | C2 | semidirect |
| 12. C32×C4×D5 | C4 | semidirect |
| 13. D5×C3⋊Dic3 | C4 | direct (N × H) |
| 23. C32×C4×C5 | C2×C4 | semidirect |
| 24. C3⋊Dic15 | C2×C4 | semidirect |
| 25. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 26. C32×Dic5 | C2×C4 | semidirect |
| 32. C4×C3⋊Dic3 | D5 | direct (N × H) |
| 38. C3×C4×D5 | Dic3 | semidirect |
| 43. C32×D5 | C42 | semidirect |
| 59. C3×C4×C5 | C2×Dic3 | semidirect |
| 61. C3×Dic5 | C2×Dic3 | semidirect |
| 68. C32×C5 | C2×C42 | semidirect |
| 75. C4×D5 | C3⋊Dic3 | direct (N × H) |
| 80. C32×C4 | C4×D5 | semidirect |
| 82. C3⋊Dic3 | C4×D5 | direct (N × H) |
| 86. C3×D5 | C4×Dic3 | semidirect |
| 98. C4×C5 | C2×C3⋊Dic3 | semidirect |
| 100. Dic5 | C2×C3⋊Dic3 | semidirect |
| 109. C3×C5 | C2×C4×Dic3 | semidirect |
| 114. C3×C4 | D5×Dic3 | semidirect |
| 119. D5 | C4×C3⋊Dic3 | direct (N × H) |
| 120. C32 | C42×D5 | semidirect |
| 131. C5 | C2×C4×C3⋊Dic3 | semidirect |
| 138. C4 | D5×C3⋊Dic3 | direct (N × H) |
| 139. C3 | C4×D5×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D5 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C4×C3⋊Dic15 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| Dic5×C3⋊Dic3 | 2 |
| C4×D5×Dic3 | 3 |
| C2×C4×C3⋊Dic3 | 5 |