Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 564 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×D5×C3⋊Dic3 | C2 | semidirect |
| 3. C4×C3⋊Dic15 | C2 | semidirect |
| 4. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. #10623770 | C2 | semidirect |
| 12. C32×D20 | C4 | semidirect |
| 23. C2×C32×D5 | C2×C4 | semidirect |
| 24. C32×C4×C5 | C2×C4 | semidirect |
| 26. C3⋊Dic15 | D4 | semidirect |
| 32. C4⋊(C3⋊Dic3) | D5 | semidirect |
| 39. C3×D20 | Dic3 | semidirect |
| 61. C2×C3×D5 | C2×Dic3 | semidirect |
| 62. C3×C4×C5 | C2×Dic3 | semidirect |
| 71. C32×C5 | C4×D4 | semidirect |
| 77. D20 | C3⋊Dic3 | semidirect |
| 83. C32×C4 | C4×D5 | semidirect |
| 102. C2×D5 | C2×C3⋊Dic3 | semidirect |
| 104. C4×C5 | C2×C3⋊Dic3 | semidirect |
| 116. C3×C5 | D4×Dic3 | semidirect |
| 121. C3×C4 | D5×Dic3 | semidirect |
| 129. C32 | #4039 | semidirect |
| 141. C5 | D4×C3⋊Dic3 | semidirect |
| 149. C4 | D5×C3⋊Dic3 | semidirect |
| 150. C3 | #91434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D20 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C4×C3⋊Dic15 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| #10623770 | 2 |
| #91434 | 3 |
| D4×C3⋊Dic3 | 5 |