Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
420 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 16. #67141 | C4 | direct (N × H) |
| 26. C32×C4×C5 | Q8 | semidirect |
| 69. C3×C4×C5 | Dic6 | semidirect |
| 83. C32×C5 | C4×Q8 | semidirect |
| 95. C32×C4 | Dic10 | semidirect |
| 115. C4×C5 | #634 | semidirect |
| 130. C3×C5 | C4×Dic6 | semidirect |
| 134. C3×C4 | #1204 | semidirect |
| 142. C32 | C4×Dic10 | semidirect |
| 154. C5 | C4×#634 | semidirect |
| 162. C4 | #67141 | direct (N × H) |
| 163. C3 | C4×#1204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67141 | 2 |
| C4×C3⋊Dic15 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C32×C4×Dic5 | 2 |
| #10623775 | 2 |
| #10623774 | 2 |
| #10623773 | 2 |
| C4×#1204 | 3 |
| C4×#634 | 5 |