Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 136 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. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 4. C5×#3724 | C2 | semidirect |
| 9. C4×C5×C3⋊D3 | C4 | semidirect |
| 12. #63900 | C5 | direct (N × H) |
| 17. C5×C4⋊Dic3 | D3 | semidirect |
| 23. C32×C4×C5 | C2×C4 | semidirect |
| 24. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 29. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 30. #3724 | C2×C5 | semidirect |
| 46. C5×C3⋊D3 | C4⋊C4 | semidirect |
| 54. C4×C3⋊D3 | C4×C5 | semidirect |
| 67. C3×C4×C5 | C4×D3 | semidirect |
| 75. C4⋊Dic3 | C5×D3 | semidirect |
| 77. C32×C5 | C2×C4⋊C4 | semidirect |
| 88. C32×C4 | C2×C4×C5 | semidirect |
| 89. C3⋊Dic3 | C2×C4×C5 | semidirect |
| 117. C4×C5 | #624 | semidirect |
| 121. C3⋊D3 | C5×C4⋊C4 | semidirect |
| 127. C3×C5 | D3×C4⋊C4 | semidirect |
| 138. C3×C4 | C4×C5×D3 | semidirect |
| 146. C32 | C2×C5×C4⋊C4 | semidirect |
| 161. C5 | #63900 | direct (N × H) |
| 168. C4 | C5×#624 | semidirect |
| 170. C3 | C5×D3×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C5×#624 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C5×#3724 | 2 |
| C5×D3×C4⋊C4 | 3 |
| #63900 | 5 |