Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 158 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×D4 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 4. C5×#3757 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 15. #64147 | C5 | direct (N × H) |
| 16. C2×C3×C5×D4 | D3 | semidirect |
| 27. C2×C5×C3⋊D3 | D4 | semidirect |
| 28. C32×C4×C5 | D4 | semidirect |
| 32. C2×C32×D4 | C2×C5 | semidirect |
| 33. C2×#638 | C2×C5 | semidirect |
| 34. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 35. #3757 | C2×C5 | semidirect |
| 36. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 52. C2×C5×D4 | C3⋊D3 | semidirect |
| 71. C3×C4×C5 | #67 | semidirect |
| 74. C2×C3×D4 | C5×D3 | semidirect |
| 79. C32×C5 | #121 | semidirect |
| 94. C2×C3⋊D3 | C5×D4 | semidirect |
| 95. C32×C4 | C5×D4 | semidirect |
| 121. C4×C5 | #638 | semidirect |
| 128. C2×D4 | C5×C3⋊D3 | semidirect |
| 132. C3×C5 | #938 | semidirect |
| 140. C3×C4 | C5×#67 | semidirect |
| 148. C32 | C5×#121 | semidirect |
| 162. C5 | #64147 | direct (N × H) |
| 172. C4 | C5×#638 | semidirect |
| 173. C3 | C5×#938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C5×#638 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C5×#3757 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C5×#938 | 3 |
| #64147 | 5 |