We have studied the variations in stability, bifurcation, critical velocity, Lagrange points, and critical periodic orbits in the context of the transition from the Sitnikov four-body system (as analyzed by Soulis et al. (Celest. Mech. Dyn. Astron. 100:251–266, 2008)) to the Sitnikov five-body system. The incorporation of one primary body results in a reduction in critical velocity and an increase in the number of stability intervals. We applied Floquet’s theory to study the stability/instability of the motion of negligible mass. For this, we assume $z_{in}$ as family parameter and vary it in the interval $[0, 10]$ . Upon slightly perturbing the negligible mass from the z-axis, we obtained 13 Lagrange points. We have determined three-dimensional families of periodic orbits which bifurcate from the critical points/bifurcation points. We observed that the bifurcation points lie within the interval $[1.0709360, 2.7944120]$ . We have discussed stability/instability of periodic orbits bifurcating from the critical points.
