Histone methyltransferase that specifically trimethylates 'Lys-20' of histone H4. H4 'Lys-20' trimethylation represents a specific tag for epigenetic transcriptional repression. Mainly functions in pericentric heterochromatin regions; thereby playing a central role in the establishment of constitutive heterochromatin in these regions. SUV420H1 is targeted to histone H3 via its interaction with RB1 family proteins (RB1; RBL1 and RBL2) (By similarity). Plays a role in myogenesis by regulating the expression of target genes; such as EID3. {ECO:0000250; ECO:0000269|PubMed:23720823}.