Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. C2×C5×#634 | C2 | semidirect |
| 3. C32×C5×C4⋊C4 | C2 | semidirect |
| 6. C5×#3750 | C2 | semidirect |
| 7. C5×#3750 | C2 | semidirect |
| 18. #64105 | C5 | direct (N × H) |
| 21. C3×C5×C4⋊C4 | D3 | semidirect |
| 29. C2×C5×C3⋊D3 | Q8 | semidirect |
| 38. C2×#634 | C2×C5 | semidirect |
| 39. C32×C4⋊C4 | C2×C5 | semidirect |
| 42. #3750 | C2×C5 | semidirect |
| 43. #3750 | C2×C5 | semidirect |
| 62. C5×C4⋊C4 | C3⋊D3 | semidirect |
| 86. C3×C4⋊C4 | C5×D3 | semidirect |
| 91. C32×C5 | C22⋊Q8 | semidirect |
| 104. C2×C3⋊D3 | C5×Q8 | semidirect |
| 143. C4⋊C4 | C5×C3⋊D3 | semidirect |
| 146. C3×C5 | #896 | semidirect |
| 161. C32 | C5×C22⋊Q8 | semidirect |
| 175. C5 | #64105 | direct (N × H) |
| 186. C3 | C5×#896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C5×#634 | 2 |
| C32×C5×C4⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×#3750 | 2 |
| C5×#896 | 3 |
| #64105 | 5 |