Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
| 4. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C5×#3750 | C2 | semidirect |
| 14. #64133 | C5 | direct (N × H) |
| 22. C22×C32×C5 | Q8 | semidirect |
| 30. C2×#634 | C2×C5 | semidirect |
| 32. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 33. #3750 | C2×C5 | semidirect |
| 60. C22×C3×C5 | Dic6 | semidirect |
| 71. C32×C5 | C22⋊Q8 | semidirect |
| 81. C22×C32 | C5×Q8 | semidirect |
| 101. C22×C5 | #634 | semidirect |
| 116. C3×C5 | #924 | semidirect |
| 119. C22×C3 | C5×Dic6 | semidirect |
| 129. C32 | C5×C22⋊Q8 | semidirect |
| 141. C5 | #64133 | direct (N × H) |
| 144. C22 | C5×#634 | semidirect |
| 150. C3 | C5×#924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C2×C5×#634 | 2 |
| C5×#3757 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C5×#3750 | 2 |
| C5×#924 | 3 |
| #64133 | 5 |