Intensive studies for more than three decades have elucidated multiple superconducting phases and odd-parity Cooper pairs in a heavy fermion superconductor UPt3. We identify a time-reversal invariant superconducting phase of UPt3 as a recently proposed topological nonsymmorphic superconductivity. Combining the band structure of UPt3, order parameter of E-2u representation allowed by P6(3)/mmc space group symmetry, and topological classification by K theory, we demonstrate the nontrivial Z(2)-invariant of three-dimensional DIII class enriched by glide symmetry. Correspondingly, double Majorana cone surface states appear at the surface Brillouin zone boundary. Furthermore, we show a variety of surface states and clarify the topological protection by crystal symmetry. Majorana arcs corresponding to tunable Weyl points appear in the time-reversal symmetry broken B phase. Majorana cone protected by mirror Chern number and Majorana flat band by glide-winding number are also revealed.