Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
792 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 266 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 |
|---|---|---|
| 2. C22×C32×C4×C5 | C2 | semidirect |
| 3. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 4. C5×#3752 | C2 | direct (N × H) |
| 9. C22×C5×C3⋊D3 | C4 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 14. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 15. C2×#3752 | C5 | direct (N × H) |
| 17. C22×C3×C4×C5 | D3 | semidirect |
| 27. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 32. C22×C32×C4 | C2×C5 | semidirect |
| 33. C22×C3⋊Dic3 | C2×C5 | semidirect |
| 34. #3752 | C2×C5 | direct (N × H) |
| 41. C2×C3×C4×C5 | C2×D3 | semidirect |
| 45. C2×C32×C5 | C22⋊C4 | semidirect |
| 52. C22×C4×C5 | C3⋊D3 | semidirect |
| 57. C22×C3⋊D3 | C4×C5 | semidirect |
| 60. C2×C32×C4 | C22×C5 | semidirect |
| 62. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 74. C22×C3×C4 | C5×D3 | semidirect |
| 77. C32×C5 | C2×C22⋊C4 | semidirect |
| 86. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 94. C2×C3⋊D3 | C2×C4×C5 | semidirect |
| 98. C2×C3×C5 | (C2×D3)⋊C4 | semidirect |
| 109. C2×C3×C4 | C2×C5×D3 | semidirect |
| 122. C2×C32 | C5×C22⋊C4 | semidirect |
| 129. C22×C4 | C5×C3⋊D3 | semidirect |
| 131. C3×C5 | C2×(C2×D3)⋊C4 | semidirect |
| 143. C2×C5 | #3752 | direct (N × H) |
| 147. C32 | C2×C5×C22⋊C4 | semidirect |
| 156. C2×C4 | C2×C5×C3⋊D3 | semidirect |
| 157. C2×C3 | C5×(C2×D3)⋊C4 | semidirect |
| 162. C5 | C2×#3752 | direct (N × H) |
| 173. C3 | C2×C5×(C2×D3)⋊C4 | semidirect |
| 175. C2 | C5×#3752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C22×C32×C4×C5 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C5×#3752 | 2 |
| C2×C5×(C2×D3)⋊C4 | 3 |
| C2×#3752 | 5 |