  We study the structure of parabolic inductions of a pro-$p$-Iwahori Hecke
algebra. In particular, we give a classification of irreducible modulo $p$
representations of pro-$p$-Iwahori Hecke algebra in terms of supersingular
representations. Since supersingular representations are classified by Ollivier
and Vigneras, it completes the classification of irreducible modulo $p$
representations.
