Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
984 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 330 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×Q8 | C2 | semidirect |
| 2. C5×#3832 | C2 | direct (N × H) |
| 3. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 7. C32×C5×Q8 | C22 | semidirect |
| 10. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 11. C4×C5×C3⋊D3 | C22 | semidirect |
| 12. C2×#3832 | C5 | direct (N × H) |
| 13. C2×C3×C5×Q8 | D3 | semidirect |
| 23. C2×C32×Q8 | C2×C5 | semidirect |
| 24. #3832 | C2×C5 | direct (N × H) |
| 25. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 26. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 28. C3×C5×Q8 | C2×D3 | semidirect |
| 34. C2×C32×C5 | #41 | semidirect |
| 38. C2×C5×Q8 | C3⋊D3 | semidirect |
| 42. C32×Q8 | C22×C5 | semidirect |
| 45. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 46. C4×C3⋊D3 | C22×C5 | semidirect |
| 52. C2×C3×Q8 | C5×D3 | semidirect |
| 56. C32×C5 | C2×#41 | semidirect |
| 58. C5×Q8 | C2×C3⋊D3 | semidirect |
| 69. C2×C3×C5 | #239 | semidirect |
| 73. C3×Q8 | C2×C5×D3 | semidirect |
| 83. C2×C32 | C5×#41 | semidirect |
| 87. C2×Q8 | C5×C3⋊D3 | semidirect |
| 90. C3×C5 | C2×#239 | semidirect |
| 97. C2×C5 | #3832 | direct (N × H) |
| 99. C32 | C2×C5×#41 | semidirect |
| 101. Q8 | C2×C5×C3⋊D3 | semidirect |
| 106. C2×C3 | C5×#239 | semidirect |
| 109. C5 | C2×#3832 | direct (N × H) |
| 115. C3 | C2×C5×#239 | semidirect |
| 117. C2 | C5×#3832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C5×#3832 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C5×#239 | 3 |
| C2×#3832 | 5 |