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. C2×C32×C5×D4 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C5×#3830 | C2 | semidirect |
| 4. C5×D4×C3⋊D3 | C2 | semidirect |
| 5. C5×#3828 | C2 | semidirect |
| 7. C23×C32×C5 | C22 | semidirect |
| 8. C22×C5×C3⋊D3 | C22 | semidirect |
| 9. C32×C5×D4 | C22 | semidirect |
| 10. C2×C32×C4×C5 | C22 | semidirect |
| 11. C5×#638 | C22 | semidirect |
| 12. C5×#638 | C22 | semidirect |
| 13. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 14. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C4×C5×C3⋊D3 | C22 | semidirect |
| 16. C5×#634 | C22 | semidirect |
| 17. #64361 | C5 | direct (N × H) |
| 18. C2×C3×C5×D4 | D3 | semidirect |
| 31. C2×C32×D4 | C2×C5 | semidirect |
| 32. C2×#638 | C2×C5 | semidirect |
| 33. #3830 | C2×C5 | semidirect |
| 34. D4×C3⋊D3 | C2×C5 | semidirect |
| 35. #3828 | C2×C5 | semidirect |
| 36. C23×C3×C5 | C2×D3 | semidirect |
| 38. C3×C5×D4 | C2×D3 | semidirect |
| 39. C2×C3×C4×C5 | C2×D3 | semidirect |
| 55. C2×C5×D4 | C3⋊D3 | semidirect |
| 56. C23×C32 | C22×C5 | semidirect |
| 57. C22×C3⋊D3 | C22×C5 | semidirect |
| 58. C32×D4 | C22×C5 | semidirect |
| 59. C2×C32×C4 | C22×C5 | semidirect |
| 60. #638 | C22×C5 | semidirect |
| 61. #638 | C22×C5 | semidirect |
| 62. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 63. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 64. C4×C3⋊D3 | C22×C5 | semidirect |
| 65. #634 | C22×C5 | semidirect |
| 73. C2×C3×D4 | C5×D3 | semidirect |
| 78. C32×C5 | H(5,𝔽2) | semidirect |
| 80. C23×C5 | C2×C3⋊D3 | semidirect |
| 85. C5×D4 | C2×C3⋊D3 | semidirect |
| 88. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 101. C23×C3 | C2×C5×D3 | semidirect |
| 103. C3×D4 | C2×C5×D3 | semidirect |
| 104. C2×C3×C4 | C2×C5×D3 | semidirect |
| 126. C2×D4 | C5×C3⋊D3 | semidirect |
| 127. C3×C5 | #1004 | semidirect |
| 139. C32 | C5×H(5,𝔽2) | semidirect |
| 141. C23 | C2×C5×C3⋊D3 | semidirect |
| 146. D4 | C2×C5×C3⋊D3 | semidirect |
| 149. C2×C4 | C2×C5×C3⋊D3 | semidirect |
| 154. C5 | #64361 | direct (N × H) |
| 162. C3 | C5×#1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C5×#638 | 2 |
| C5×#3830 | 2 |
| C5×D4×C3⋊D3 | 2 |
| C5×#3828 | 2 |
| C5×#1004 | 3 |
| #64361 | 5 |