Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
780 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 162 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. C23×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C32×C5×D4 | C2 | semidirect |
| 3. C2×C5×#638 | C2 | semidirect |
| 4. C5×#3757 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 8. C23×C32×C5 | C22 | semidirect |
| 13. C2×C32×C4×C5 | C22 | semidirect |
| 15. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 16. #64146 | C5 | direct (N × H) |
| 18. C2×C3×C5×D4 | D3 | semidirect |
| 25. C22×C32×C5 | D4 | semidirect |
| 30. C2×C5×C3⋊D3 | D4 | semidirect |
| 34. C23×C3⋊D3 | C2×C5 | semidirect |
| 35. C2×C32×D4 | C2×C5 | semidirect |
| 36. C2×#638 | C2×C5 | semidirect |
| 37. #3757 | C2×C5 | semidirect |
| 38. #3752 | C2×C5 | semidirect |
| 40. C23×C3×C5 | C2×D3 | semidirect |
| 45. C2×C3×C4×C5 | C2×D3 | semidirect |
| 56. C2×C5×D4 | C3⋊D3 | semidirect |
| 60. C23×C32 | C22×C5 | semidirect |
| 65. C2×C32×C4 | C22×C5 | semidirect |
| 67. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 71. C22×C3×C5 | #67 | semidirect |
| 80. C2×C3×D4 | C5×D3 | semidirect |
| 84. C32×C5 | #120 | semidirect |
| 89. C23×C5 | C2×C3⋊D3 | semidirect |
| 93. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 97. C22×C32 | C5×D4 | semidirect |
| 102. C2×C3⋊D3 | C5×D4 | semidirect |
| 112. C23×C3 | C2×C5×D3 | semidirect |
| 117. C2×C3×C4 | C2×C5×D3 | semidirect |
| 127. C22×C5 | #638 | semidirect |
| 138. C2×D4 | C5×C3⋊D3 | semidirect |
| 141. C3×C5 | #937 | semidirect |
| 145. C22×C3 | C5×#67 | semidirect |
| 158. C32 | C5×#120 | semidirect |
| 163. C23 | C2×C5×C3⋊D3 | semidirect |
| 167. C2×C4 | C2×C5×C3⋊D3 | semidirect |
| 173. C5 | #64146 | direct (N × H) |
| 181. C22 | C5×#638 | semidirect |
| 185. C3 | C5×#937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C2×C32×C5×D4 | 2 |
| C2×C5×#638 | 2 |
| C5×#3757 | 2 |
| C5×#3752 | 2 |
| C5×#937 | 3 |
| #64146 | 5 |