Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
984 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 310 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. C32×C5×#41 | C2 | semidirect |
| 2. C5×#3832 | C2 | semidirect |
| 3. C5×Q8×C3⋊D3 | C2 | semidirect |
| 4. C5×#3830 | C2 | semidirect |
| 5. C5×D4×C3⋊D3 | C2 | semidirect |
| 6. C5×#3828 | C2 | semidirect |
| 7. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 10. C32×C5×Q8 | C22 | semidirect |
| 11. C32×C5×D4 | C22 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 13. C5×#638 | C22 | semidirect |
| 14. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 15. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 18. C4×C5×C3⋊D3 | C22 | semidirect |
| 19. C4×C5×C3⋊D3 | C22 | semidirect |
| 20. C5×#634 | C22 | semidirect |
| 21. #41×C3⋊D3 | C5 | direct (N × H) |
| 22. C3×C5×#41 | D3 | semidirect |
| 38. C32×#41 | C2×C5 | semidirect |
| 39. #3832 | C2×C5 | semidirect |
| 40. Q8×C3⋊D3 | C2×C5 | semidirect |
| 41. #3830 | C2×C5 | semidirect |
| 42. D4×C3⋊D3 | C2×C5 | semidirect |
| 43. #3828 | C2×C5 | semidirect |
| 44. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 46. C3×C5×Q8 | C2×D3 | semidirect |
| 47. C3×C5×D4 | C2×D3 | semidirect |
| 48. C2×C3×C4×C5 | C2×D3 | semidirect |
| 61. C5×C3⋊D3 | #41 | direct (N × H) |
| 65. C5×#41 | C3⋊D3 | direct (N × H) |
| 70. C32×Q8 | C22×C5 | semidirect |
| 71. C32×D4 | C22×C5 | semidirect |
| 72. C2×C32×C4 | C22×C5 | semidirect |
| 73. #638 | C22×C5 | semidirect |
| 74. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 75. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 78. C4×C3⋊D3 | C22×C5 | semidirect |
| 79. C4×C3⋊D3 | C22×C5 | semidirect |
| 80. #634 | C22×C5 | semidirect |
| 89. C3×#41 | C5×D3 | semidirect |
| 96. C32×C5 | C2×#41 | semidirect |
| 99. C5×Q8 | C2×C3⋊D3 | semidirect |
| 102. C5×D4 | C2×C3⋊D3 | semidirect |
| 108. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 123. C3×Q8 | C2×C5×D3 | semidirect |
| 124. C3×D4 | C2×C5×D3 | semidirect |
| 125. C2×C3×C4 | C2×C5×D3 | semidirect |
| 145. C3⋊D3 | C5×#41 | direct (N × H) |
| 149. #41 | C5×C3⋊D3 | direct (N × H) |
| 153. C3×C5 | D3×#41 | semidirect |
| 166. C32 | C2×C5×#41 | semidirect |
| 169. Q8 | C2×C5×C3⋊D3 | semidirect |
| 172. D4 | C2×C5×C3⋊D3 | semidirect |
| 178. C2×C4 | C2×C5×C3⋊D3 | semidirect |
| 183. C5 | #41×C3⋊D3 | direct (N × H) |
| 192. C3 | C5×D3×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C5×#3832 | 2 |
| C5×Q8×C3⋊D3 | 2 |
| C5×#3830 | 2 |
| C5×D4×C3⋊D3 | 2 |
| C5×#3828 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C5×D3×#41 | 3 |
| #41×C3⋊D3 | 5 |