Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 456 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×C5×#634 | C2 | semidirect |
| 3. C32×C5×C22⋊C4 | C2 | semidirect |
| 4. C5×#3757 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 6. C5×#3752 | C2 | semidirect |
| 7. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 18. #64094 | C5 | direct (N × H) |
| 21. C3×C5×C22⋊C4 | D3 | semidirect |
| 40. C2×#634 | C2×C5 | semidirect |
| 41. C32×C22⋊C4 | C2×C5 | semidirect |
| 42. #3757 | C2×C5 | semidirect |
| 43. #3752 | C2×C5 | semidirect |
| 44. #3752 | C2×C5 | semidirect |
| 45. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 66. C5×C22⋊C4 | C3⋊D3 | semidirect |
| 91. C3×C22⋊C4 | C5×D3 | semidirect |
| 96. C32×C5 | #124 | semidirect |
| 155. C22⋊C4 | C5×C3⋊D3 | semidirect |
| 157. C3×C5 | #885 | semidirect |
| 175. C32 | C5×#124 | semidirect |
| 190. C5 | #64094 | direct (N × H) |
| 203. C3 | C5×#885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C2×C5×#634 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C5×#3757 | 2 |
| C5×#3752 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#885 | 3 |
| #64094 | 5 |