Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 241 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. C22×C3⋊Dic15 | C2 | semidirect |
| 3. #10623913 | C2 | semidirect |
| 4. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 5. C4×C3⋊Dic15 | C2 | semidirect |
| 8. C32×C5×D4 | C4 | semidirect |
| 22. C22×C32×C5 | C2×C4 | semidirect |
| 24. C32×C4×C5 | C2×C4 | semidirect |
| 27. C3⋊Dic15 | D4 | direct (N × H) |
| 35. C3×C5×D4 | Dic3 | semidirect |
| 52. C32×D4 | Dic5 | semidirect |
| 60. C22×C3×C5 | C2×Dic3 | semidirect |
| 62. C3×C4×C5 | C2×Dic3 | semidirect |
| 71. C32×C5 | C4×D4 | semidirect |
| 73. C5×D4 | C3⋊Dic3 | semidirect |
| 81. C22×C32 | C2×Dic5 | semidirect |
| 83. C32×C4 | C2×Dic5 | semidirect |
| 93. C3×D4 | Dic15 | semidirect |
| 101. C22×C5 | C2×C3⋊Dic3 | semidirect |
| 103. C4×C5 | C2×C3⋊Dic3 | semidirect |
| 116. C3×C5 | D4×Dic3 | semidirect |
| 119. C22×C3 | C2×Dic15 | semidirect |
| 121. C3×C4 | C2×Dic15 | semidirect |
| 129. C32 | D4×Dic5 | semidirect |
| 131. D4 | C3⋊Dic15 | direct (N × H) |
| 141. C5 | D4×C3⋊Dic3 | semidirect |
| 144. C22 | C2×C3⋊Dic15 | semidirect |
| 149. C4 | C2×C3⋊Dic15 | semidirect |
| 150. C3 | D4×Dic15 | 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 |
| C22×C3⋊Dic15 | 2 |
| #10623913 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C4×C3⋊Dic15 | 2 |
| D4×Dic15 | 3 |
| D4×C3⋊Dic3 | 5 |