Fermi-surface topology governs the relationship between magnetism and superconductivity in iron-based materials. Using low-temperature transport, angle-resolved photoemission, and x-ray diffraction, we show unambiguous evidence of large Fermi-surface reconstruction in at magnetic spin-density-wave and nonmagnetic collapsed-tetragonal () transitions. For the transition, the change in the Fermi-surface topology has a different character with no contribution from the hole part of the Fermi surface. In addition, the results suggest that the pressure effect in is mainly leading to a rigid-band-like change of the valence electronic structure. We discuss these results and their implications for magnetism and superconductivity in this material.