Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
346 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 132 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×C5×Dic3 | C2 | semidirect |
| 3. C32×C5×C22⋊C4 | C2 | semidirect |
| 4. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 7. C5×#886 | C3 | direct (N × H) |
| 15. C3×#886 | C5 | direct (N × H) |
| 19. C22×C5×Dic3 | C2×C3 | semidirect |
| 23. C3×C5×C22⋊C4 | D3 | semidirect |
| 24. C3×C5×C22⋊C4 | C2×C3 | semidirect |
| 25. C5×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 26. C5×C4⋊Dic3 | C2×C3 | semidirect |
| 37. C22×C3×Dic3 | C2×C5 | semidirect |
| 38. C32×C22⋊C4 | C2×C5 | semidirect |
| 39. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 40. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 58. #886 | C3×C5 | direct (N × H) |
| 67. C5×C22⋊C4 | C3×D3 | semidirect |
| 98. C22×Dic3 | C2×C3×C5 | semidirect |
| 102. C3×C22⋊C4 | C5×D3 | semidirect |
| 103. C3×C22⋊C4 | C2×C3×C5 | semidirect |
| 104. (C2×D3)⋊C4 | C2×C3×C5 | semidirect |
| 105. C4⋊Dic3 | C2×C3×C5 | semidirect |
| 106. C32×C5 | #123 | semidirect |
| 166. C22⋊C4 | C3×C5×D3 | semidirect |
| 168. C3×C5 | #886 | direct (N × H) |
| 169. C3×C5 | C3×#123 | semidirect |
| 194. C32 | C5×#123 | semidirect |
| 213. C5 | C3×#886 | direct (N × H) |
| 223. C3 | C5×#886 | direct (N × H) |
| 224. C3 | C3×C5×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#67 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C3×C5×#123 | 3 |
| C5×#886 | 3 |
| C3×#886 | 5 |