Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 138 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×C5×#638 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 5. C32×C5×C22⋊C4 | C2 | semidirect |
| 6. C5×#3752 | C2 | semidirect |
| 7. C5×#3750 | C2 | semidirect |
| 20. #64093 | C5 | direct (N × H) |
| 25. C3×C5×C22⋊C4 | D3 | semidirect |
| 37. C2×C5×C3⋊D3 | D4 | semidirect |
| 41. C5×C3⋊Dic3 | D4 | semidirect |
| 43. C2×#638 | C2×C5 | semidirect |
| 44. C2×#638 | C2×C5 | semidirect |
| 45. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 46. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 47. C32×C22⋊C4 | C2×C5 | semidirect |
| 48. #3752 | C2×C5 | semidirect |
| 49. #3750 | C2×C5 | semidirect |
| 74. C5×C22⋊C4 | C3⋊D3 | semidirect |
| 104. C3×C22⋊C4 | C5×D3 | semidirect |
| 107. C32×C5 | #121 | semidirect |
| 128. C2×C3⋊D3 | C5×D4 | semidirect |
| 132. C3⋊Dic3 | C5×D4 | semidirect |
| 177. C22⋊C4 | C5×C3⋊D3 | semidirect |
| 178. C3×C5 | #884 | semidirect |
| 199. C32 | C5×#121 | semidirect |
| 217. C5 | #64093 | direct (N × H) |
| 232. C3 | C5×#884 | 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×C4⋊(C3⋊D3) | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×#3750 | 2 |
| C5×#884 | 3 |
| #64093 | 5 |