Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
780 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 222 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×C32×D5 | C2 | semidirect |
| 2. C2×C32×C22⋊D5 | C2 | semidirect |
| 3. C2×C32×D20 | C2 | semidirect |
| 4. C32×C5×C22⋊C4 | C2 | semidirect |
| 5. C32×#685 | C2 | semidirect |
| 6. C3×#4028 | C3 | direct (N × H) |
| 11. C22×C32×D5 | C22 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 14. C2×C32×Dic5 | C22 | semidirect |
| 17. C23×C3×D5 | C2×C3 | semidirect |
| 18. C2×C3×C22⋊D5 | C2×C3 | semidirect |
| 19. C2×C3×D20 | C2×C3 | semidirect |
| 20. C3×C5×C22⋊C4 | C2×C3 | semidirect |
| 21. C3×#685 | C2×C3 | semidirect |
| 23. C22×C32×C5 | D4 | semidirect |
| 30. C2×C32×D5 | D4 | semidirect |
| 33. #4028 | C32 | direct (N × H) |
| 38. C32×C22⋊C4 | D5 | semidirect |
| 43. C22×C3×D5 | C22×C3 | semidirect |
| 44. C2×C3×C4×C5 | C22×C3 | semidirect |
| 46. C2×C3×Dic5 | C22×C3 | semidirect |
| 54. C23×D5 | C2×C32 | semidirect |
| 55. C2×C22⋊D5 | C2×C32 | semidirect |
| 56. C2×D20 | C2×C32 | semidirect |
| 57. C5×C22⋊C4 | C2×C32 | semidirect |
| 58. #685 | C2×C32 | semidirect |
| 67. C2×C32×C4 | C2×D5 | semidirect |
| 69. C22×C3×C5 | C3×D4 | semidirect |
| 76. C2×C3×D5 | C3×D4 | semidirect |
| 83. C3×C22⋊C4 | C3×D5 | semidirect |
| 84. C32×C5 | #120 | semidirect |
| 89. C22×D5 | C22×C32 | semidirect |
| 90. C2×C4×C5 | C22×C32 | semidirect |
| 92. C2×Dic5 | C22×C32 | semidirect |
| 101. C22×C32 | D20 | semidirect |
| 119. C2×C3×C4 | C2×C3×D5 | semidirect |
| 121. C22×C5 | C32×D4 | semidirect |
| 128. C2×D5 | C32×D4 | semidirect |
| 140. C22⋊C4 | C32×D5 | semidirect |
| 141. C3×C5 | C3×#120 | semidirect |
| 149. C22×C3 | C3×D20 | semidirect |
| 158. C32 | #4028 | direct (N × H) |
| 167. C2×C4 | C2×C32×D5 | semidirect |
| 173. C5 | C32×#120 | semidirect |
| 181. C22 | C32×D20 | semidirect |
| 185. C3 | C3×#4028 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×D5 | 2 |
| C2×C32×C22⋊D5 | 2 |
| C2×C32×D20 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C32×#685 | 2 |
| C3×#4028 | 3 |
| C32×#120 | 5 |