Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 3. C5×#3724 | C2 | direct (N × H) |
| 6. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 10. C2×#3724 | C5 | direct (N × H) |
| 20. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 25. #3724 | C2×C5 | direct (N × H) |
| 37. C2×C32×C5 | C4⋊C4 | semidirect |
| 45. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 66. C32×C5 | C2×C4⋊C4 | semidirect |
| 76. C3⋊Dic3 | C2×C4×C5 | semidirect |
| 83. C2×C3×C5 | Dic3⋊C4 | semidirect |
| 103. C2×C32 | C5×C4⋊C4 | semidirect |
| 111. C3×C5 | C2×Dic3⋊C4 | semidirect |
| 124. C2×C5 | #3724 | direct (N × H) |
| 128. C32 | C2×C5×C4⋊C4 | semidirect |
| 138. C2×C3 | C5×Dic3⋊C4 | semidirect |
| 142. C5 | C2×#3724 | direct (N × H) |
| 150. C3 | C2×C5×Dic3⋊C4 | semidirect |
| 151. C2 | C5×#3724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C5×#3724 | 2 |
| C2×C5×Dic3⋊C4 | 3 |
| C2×#3724 | 5 |