Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 3. C32×C5×C4⋊C4 | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 6. C5×#3752 | C2 | semidirect |
| 7. C5×#3750 | C2 | semidirect |
| 18. #64103 | C5 | direct (N × H) |
| 21. C3×C5×C4⋊C4 | D3 | semidirect |
| 40. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 41. C32×C4⋊C4 | C2×C5 | semidirect |
| 42. #3752 | C2×C5 | semidirect |
| 43. #3752 | C2×C5 | semidirect |
| 44. #3752 | C2×C5 | semidirect |
| 45. #3750 | C2×C5 | semidirect |
| 64. C5×C4⋊C4 | C3⋊D3 | semidirect |
| 91. C3×C4⋊C4 | C5×D3 | semidirect |
| 96. C32×C5 | #123 | semidirect |
| 153. C4⋊C4 | C5×C3⋊D3 | semidirect |
| 157. C3×C5 | #894 | semidirect |
| 175. C32 | C5×#123 | semidirect |
| 190. C5 | #64103 | direct (N × H) |
| 203. C3 | C5×#894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C32×C5×C4⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×#3750 | 2 |
| C5×#894 | 3 |
| #64103 | 5 |