Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
552 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 4. C5×#3750 | C2 | direct (N × H) |
| 10. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 13. C2×#3750 | C5 | direct (N × H) |
| 24. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 29. #3750 | C2×C5 | direct (N × H) |
| 38. C2×C32×C5 | C4⋊C4 | semidirect |
| 50. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 64. C32×C5 | C2×C4⋊C4 | semidirect |
| 78. C3⋊Dic3 | C2×C4×C5 | semidirect |
| 80. C2×C3×C5 | Dic3⋊C4 | semidirect |
| 98. C2×C32 | C5×C4⋊C4 | semidirect |
| 106. C3×C5 | C2×Dic3⋊C4 | semidirect |
| 114. C2×C5 | #3750 | direct (N × H) |
| 118. C32 | C2×C5×C4⋊C4 | semidirect |
| 126. C2×C3 | C5×Dic3⋊C4 | semidirect |
| 130. C5 | C2×#3750 | direct (N × H) |
| 138. C3 | C2×C5×Dic3⋊C4 | semidirect |
| 139. C2 | C5×#3750 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C5×#3750 | 2 |
| C2×C5×Dic3⋊C4 | 3 |
| C2×#3750 | 5 |