  We investigate here various kinds of semi-product subgroups of Poincar\'e
group in the scheme of Cohen-Glashow's very special relativity along the
deformation approach by Gibbons- Gomis-Pope. For each proper Poincar\'e
subgroup which is a semi-product of proper lorentz group with the spacetime
translation group T(4), we investigate all possible deformations and obtain all
the possible natural representations which inherit from the $5-d$
representation of Poincar\'e group. We find from the obtained natural
representation that rotation operation may have additional accompanied scale
transformation in the case of the original Lorentz subgroup is deformed and the
boost operation get the additional accompanied scale transformation in all the
deformation cases. The additional accompanied scale transformation has strong
constrain on the possible invariant metric function of the corresponding
geometry and the field theories in the spacetime with the corresponding
geometry.
