Geodesic
An expression for the number of subgroups of a given order of a finite $p$-group
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 561-568 
V. N. Shokuev. An expression for the number of subgroups of a given order of a finite $p$-group. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 561-568. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a8/
@article{MZM_1972_12_5_a8,
     author = {V. N. Shokuev},
     title = {An expression for the number of subgroups of a given order of a finite $p$-group},
     journal = {Matemati\v{c}eskie zametki},
     pages = {561--568},
     year = {1972},
     volume = {12},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We find an exact expression for the number of subgroups of any (possible) order of an arbitrary finite $p$-group.