Torus package on a torus

Let $$G$$ to be a nilpotent Lie group and $$H to be two closed subgroups such as
$$G / H to G / J$$ is a bundle of fibers with fibers $$J / H$$.

Assume that $$G / J = (S ^ 1) ^ m$$ and $$J / H = (S ^ 1) ^ m$$. Is the package trivial?