You also have the internal conflicts that the characters experience. The first Catherine is torn between her love for Heathcliff and what Edgar Linton can offer her. Later, Catherine refuses to answer Edgar when he tells her to choose between the two men. Her inability to choose eventually leads to her death.
Heathcliff's inner conflict is the jealousy he feels when Catherine begins her friendhsip with Edgar. Then when he overhears Catherine say she would be "degraded" if she married Heathcliff, he leaves Wuthering Heights, hurt and ashamed. His love for Catherine becomes an obsession that only grows as he grows older. He's never able to control what he feels for Catherine. When he does return, he vows vengeance on everyone. Heathcliff spends the rest of his life struggling with the hate he feels for everyone at Wuthering Heights and Thrushcross Grange. His obsessive love for Catherine and his hateful revenge control him, and he's never able to rise above them.
These inner conflicts reflect the themes of love and passion, revenge, and cruelty.
Class conflict is one of the major themes. Catherine is very wealthy and Heathcliff, an orphan, has nothing. Bronte asks the reader to consider whether property ownership and money should have any bearing on determining a person's worth.
Another conflict is cruelty, which can manifest it self both physically and emotionally. Bronte argues that violence begets violence. This cycle of cruelty is so prevalent that it can be considered a major theme. For example, Heathcliff's rough treatment of Hareton is really a result of Hindley brutality to him. Emotionally, the sadist-maschostic relationship between Catherine and Heathcliff is one infused with cruelty.
For more on the themes of "Wuthering Heights" please visit the link below.