Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
792 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 335 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. C22×C3⋊Dic15 | C2 | semidirect |
| 3. #10623913 | C2 | direct (N × H) |
| 6. C23×C32×C5 | C4 | semidirect |
| 10. C2×C3⋊Dic15 | C22 | semidirect |
| 18. C22×C32×C5 | C2×C4 | semidirect |
| 27. C23×C3×C5 | Dic3 | semidirect |
| 34. C2×C32×C5 | C22⋊C4 | semidirect |
| 41. C23×C32 | Dic5 | semidirect |
| 49. C22×C3×C5 | C2×Dic3 | semidirect |
| 56. C32×C5 | C2×C22⋊C4 | semidirect |
| 58. C23×C5 | C3⋊Dic3 | semidirect |
| 66. C22×C32 | C2×Dic5 | semidirect |
| 72. C2×C3×C5 | #217 | semidirect |
| 76. C23×C3 | Dic15 | semidirect |
| 84. C22×C5 | C2×C3⋊Dic3 | semidirect |
| 89. C2×C32 | C22⋊Dic5 | semidirect |
| 95. C3×C5 | C2×#217 | semidirect |
| 99. C22×C3 | C2×Dic15 | semidirect |
| 104. C2×C5 | #3757 | semidirect |
| 107. C32 | C2×C22⋊Dic5 | semidirect |
| 109. C23 | C3⋊Dic15 | semidirect |
| 115. C2×C3 | #6719 | semidirect |
| 118. C5 | C2×#3757 | semidirect |
| 122. C22 | C2×C3⋊Dic15 | semidirect |
| 126. C3 | C2×#6719 | semidirect |
| 128. C2 | #10623913 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C5 | 2 |
| C22×C3⋊Dic15 | 2 |
| #10623913 | 2 |
| C2×#6719 | 3 |
| C2×#3757 | 5 |