  The recently discovered layered kagome metals AV$_3$Sb$_5$ (A=K, Rb, Cs)
exhibit diverse correlated phenomena, which are intertwined with a topological
electronic structure with multiple van Hove singularities (VHSs) in the
vicinity of the Fermi level. As the VHSs with their large density of states
enhance correlation effects, it is of crucial importance to determine their
nature and properties. Here, we combine polarization-dependent angle-resolved
photoemission spectroscopy with density functional theory to directly reveal
the sublattice properties of 3d-orbital VHSs in CsV$_3$Sb$_5$. Four VHSs are
identified around the M point and three of them are close to the Fermi level,
with two having sublattice-pure and one sublattice-mixed nature. Remarkably,
the VHS just below the Fermi level displays an extremely flat dispersion along
MK, establishing the experimental discovery of higher-order VHS. The
characteristic intensity modulation of Dirac cones around K further
demonstrates the sublattice interference embedded in the electronic structure.
The crucial insights into the electronic structure, revealed by our work,
provide a solid starting point for the understanding of the intriguing
correlation phenomena in the kagome metals AV$_3$Sb$_5$.
