Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
406 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 1. C2×C3×C4×C5×D3 | C2 | semidirect |
| 3. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 4. C5×#3724 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 13. C5×#625 | C4 | direct (N × H) |
| 14. C4×#625 | C5 | direct (N × H) |
| 17. C2×C4×C5×D3 | D3 | semidirect |
| 26. C2×C3×C5×D3 | C2×C4 | semidirect |
| 27. C32×C4×C5 | D4 | semidirect |
| 29. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 32. C2×C3×C4×D3 | C2×C5 | semidirect |
| 34. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 35. #3724 | C2×C5 | semidirect |
| 36. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 66. #625 | C4×C5 | direct (N × H) |
| 74. C2×C5×D3 | C4×D3 | semidirect |
| 77. C3×C4×C5 | #67 | semidirect |
| 85. C2×C4×D3 | C5×D3 | semidirect |
| 91. C32×C5 | C4×D4 | semidirect |
| 102. C2×C3×D3 | C2×C4×C5 | semidirect |
| 103. C32×C4 | C5×D4 | semidirect |
| 105. C3⋊Dic3 | C2×C4×C5 | semidirect |
| 136. C4×C5 | #625 | direct (N × H) |
| 147. C3×C5 | C4×#67 | semidirect |
| 155. C2×D3 | C4×C5×D3 | semidirect |
| 158. C3×C4 | C5×#67 | semidirect |
| 168. C32 | C4×C5×D4 | semidirect |
| 184. C5 | C4×#625 | direct (N × H) |
| 192. C4 | C5×#625 | direct (N × H) |
| 194. C3 | C4×C5×#67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C2×C5×#625 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#3724 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C4×C5×#67 | 3 |
| C4×#625 | 5 |