How do the subplots in Hamlet support the main plot?how it supports to main plot
I'm not sure what you want to know about subplots in Hamlet, but I'll try. There are three families in Hamlet. The first, of course, is Hamlet, Claudius, and Gertrude. The second is Polonius, Laertes, and Ophelia. The third is Fortinbras and Old Fortinbras. Each of these families has avenging sons interested in restoring family honor. How each son goes about seeking revenge helps to understand Shakespeare's ideas about the effects of revenge on the avenger. We see Fortinbras who is interested in restoring the lands that his father lost to Denmark. He is blustery and rash and easily prevented by a collusion between Claudius and his uncle. We see Laertes, hot-headed, and vengeful, eager to kill the murderer of his father. He too is easily manipulated as Claudius talks him into murdering Hamlet in a dishonorable way. Then of course we see Hamlet, whose mission is to kill the murderer of his father: Claudius. Hamlet, unlike the other two, is cautious in his proceedings and probably more effective. Each son is successful in a way. Laertes kills Hamlet, the killer of his father. Fortinbras takes over Denmark, and Hamlet kills Claudius. But each also loses. Laertes loses his honor and his life. Fortinbras gains lands that are crippled by corruption; and Hamlet loses his life. Through these contrasts we see how difficult Hamlet's task is to accomplish, and we see different ways of seeking revenge.
Two subplots in particular support the main plot in Shakespeare's Hamlet.
First, Fortinbras has a father to revenge and an uncle for a king just like Hamlet. Fortinbras is in the process of attacking Denmark without his uncle's blessing when the uncle finds out and puts a stop to it. Later, Fortinbras leads an army against Poland in order to capture a worthless piece of land.
Second, Laertes storms into the castle ready to kill Claudius as revenge for his father's murder. Laertes stops only when he is convinced by the king that Hamlet is responsible for the murder of Polonius. Laertes then teams with Claudius in a plot to kill Hamlet.
These subplots support the main plot by providing foils for Hamlet. Fortinbras and Laertes reveal how quick revenge for a father's death could be taken, in contrast to Hamlet's delaying his revenge.