Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
996 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 306 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×D4×C3⋊D3 | C2 | semidirect |
| 4. C5×#3828 | C2 | semidirect |
| 5. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 7. C22×C5×C3⋊D3 | C22 | semidirect |
| 8. C32×C5×Q8 | C22 | semidirect |
| 9. C32×C5×D4 | C22 | semidirect |
| 10. C2×C32×C4×C5 | C22 | semidirect |
| 11. C5×#638 | C22 | semidirect |
| 12. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 14. C4×C5×C3⋊D3 | C22 | semidirect |
| 15. C5×#634 | C22 | semidirect |
| 16. #64366 | C5 | direct (N × H) |
| 17. C3×C5×#41 | D3 | semidirect |
| 29. C32×#41 | C2×C5 | semidirect |
| 30. #3832 | C2×C5 | semidirect |
| 31. D4×C3⋊D3 | C2×C5 | semidirect |
| 32. #3828 | C2×C5 | semidirect |
| 33. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 35. C3×C5×Q8 | C2×D3 | semidirect |
| 36. C3×C5×D4 | C2×D3 | semidirect |
| 37. C2×C3×C4×C5 | C2×D3 | semidirect |
| 49. C5×#41 | C3⋊D3 | semidirect |
| 52. C22×C3⋊D3 | C22×C5 | semidirect |
| 53. C32×Q8 | C22×C5 | semidirect |
| 54. C32×D4 | C22×C5 | semidirect |
| 55. C2×C32×C4 | C22×C5 | semidirect |
| 56. #638 | C22×C5 | semidirect |
| 57. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 58. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 59. C4×C3⋊D3 | C22×C5 | semidirect |
| 60. #634 | C22×C5 | semidirect |
| 67. C3×#41 | C5×D3 | semidirect |
| 72. C32×C5 | H(5,𝔽2) | semidirect |
| 75. C5×Q8 | C2×C3⋊D3 | semidirect |
| 79. C5×D4 | C2×C3⋊D3 | semidirect |
| 81. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 93. C3×Q8 | C2×C5×D3 | semidirect |
| 94. C3×D4 | C2×C5×D3 | semidirect |
| 95. C2×C3×C4 | C2×C5×D3 | semidirect |
| 112. #41 | C5×C3⋊D3 | semidirect |
| 115. C3×C5 | #1009 | semidirect |
| 125. C32 | C5×H(5,𝔽2) | semidirect |
| 128. Q8 | C2×C5×C3⋊D3 | semidirect |
| 132. D4 | C2×C5×C3⋊D3 | semidirect |
| 134. C2×C4 | C2×C5×C3⋊D3 | semidirect |
| 138. C5 | #64366 | direct (N × H) |
| 145. C3 | C5×#1009 | 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×D4×C3⋊D3 | 2 |
| C5×#3828 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C5×#1009 | 3 |
| #64366 | 5 |