Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
216 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 84 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. C3×C4×C5×Dic3 | C2 | semidirect |
| 3. C3×C5×#208 | C2 | semidirect |
| 5. C5×#837 | C3 | direct (N × H) |
| 6. C32×C5×Q8 | C4 | semidirect |
| 8. C32×C5×D4 | C4 | semidirect |
| 13. C3×#837 | C5 | direct (N × H) |
| 19. C4×C5×Dic3 | C2×C3 | semidirect |
| 20. C5×#208 | C2×C3 | semidirect |
| 29. C3×C4×Dic3 | C2×C5 | semidirect |
| 30. C3×#208 | C2×C5 | semidirect |
| 32. C3×C5×Q8 | Dic3 | semidirect |
| 33. C3×C5×Q8 | C3×C4 | semidirect |
| 38. C3×C5×D4 | Dic3 | semidirect |
| 39. C3×C5×D4 | C3×C4 | semidirect |
| 51. #837 | C3×C5 | direct (N × H) |
| 58. C32×Q8 | C4×C5 | semidirect |
| 60. C32×D4 | C4×C5 | semidirect |
| 87. C4×Dic3 | C2×C3×C5 | semidirect |
| 88. #208 | C2×C3×C5 | semidirect |
| 89. C32×C5 | #104 | semidirect |
| 90. C5×Q8 | C3×Dic3 | semidirect |
| 92. C5×D4 | C3×Dic3 | semidirect |
| 114. C3×Q8 | C5×Dic3 | semidirect |
| 115. C3×Q8 | C3×C4×C5 | semidirect |
| 120. C3×D4 | C5×Dic3 | semidirect |
| 121. C3×D4 | C3×C4×C5 | semidirect |
| 145. C3×C5 | #837 | direct (N × H) |
| 146. C3×C5 | C3×#104 | semidirect |
| 167. C32 | C5×#104 | semidirect |
| 168. Q8 | C3×C5×Dic3 | semidirect |
| 170. D4 | C3×C5×Dic3 | semidirect |
| 184. C5 | C3×#837 | direct (N × H) |
| 192. C3 | C5×#837 | direct (N × H) |
| 193. C3 | C3×C5×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C3×C5×#208 | 2 |
| C3×C5×#104 | 3 |
| C5×#837 | 3 |
| C3×#837 | 5 |