Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
| 3. C5×#3755 | C2 | direct (N × H) |
| 4. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 8. C32×C5×Q8 | C22 | semidirect |
| 13. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 14. C2×#3755 | C5 | direct (N × H) |
| 15. C2×C3×C5×Q8 | D3 | semidirect |
| 26. C2×C32×Q8 | C2×C5 | semidirect |
| 28. #3755 | C2×C5 | direct (N × H) |
| 29. C2×C3⋊(C3⋊C8) | C2×C5 | semidirect |
| 32. C3×C5×Q8 | C2×D3 | semidirect |
| 39. C2×C32×C5 | SD16 | semidirect |
| 42. C2×C5×Q8 | C3⋊D3 | semidirect |
| 48. C32×Q8 | C22×C5 | semidirect |
| 53. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 60. C2×C3×Q8 | C5×D3 | semidirect |
| 64. C32×C5 | C2×SD16 | semidirect |
| 67. C5×Q8 | C2×C3⋊D3 | semidirect |
| 80. C2×C3×C5 | #215 | semidirect |
| 85. C3×Q8 | C2×C5×D3 | semidirect |
| 97. C2×C32 | C5×SD16 | semidirect |
| 100. C2×Q8 | C5×C3⋊D3 | semidirect |
| 104. C3×C5 | C2×#215 | semidirect |
| 112. C2×C5 | #3755 | direct (N × H) |
| 114. C32 | C2×C5×SD16 | semidirect |
| 117. Q8 | C2×C5×C3⋊D3 | semidirect |
| 123. C2×C3 | C5×#215 | semidirect |
| 126. C5 | C2×#3755 | direct (N × H) |
| 133. C3 | C2×C5×#215 | semidirect |
| 135. C2 | C5×#3755 | 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 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C5×#3755 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| C2×C5×#215 | 3 |
| C2×#3755 | 5 |