We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale two-dimensional tensor network calculations. Our simulations reveal a period 4 stripe state with spin and weak charge order over an extended doping range beyond $\ensuremath{\delta}\ensuremath{\sim}0.12$ and stripes with larger periods at smaller doping. The period 4 stripe exhibits coexisting
d-wave superconductivity in the doping range $0.15\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, while at smaller doping around $\ensuremath{\delta}\ensuremath{\sim}1/8$ we find a strong competition between superconducting and nonsuperconducting stripes, including also pair density-wave states with an alternating sign structure on neighboring stripes, suggesting that the fate of superconductivity around 1/8 doping may be sensitive on the model parameters.
We study the competition between stripe states with different periods and a uniform
d-wave superconducting state in the extended two-dimensional Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping ${t}^{\ensuremath{'}}$, the preferred period of the stripe decreases. For the values of ${t}^{\ensuremath{'}}$ predicted for cuprate high-
Tc superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at
1/8 doping. Only at larger doping, $0.18\ensuremath{\lesssim}\ensuremath{\delta}<0.25$, the period 4 stripe exhibits coexisting
d-wave superconducting order. The uniform
d-wave state is only favored for sufficiently large positive ${t}^{\ensuremath{'}}$.