Yes its legal. A serializable class can be serialized even if its parent class is not serializable. This is from the javadocs of Serializable class
To allow subtypes of non-serializable classes to be serialized, the subtype may assume responsibility for saving and restoring the state of the supertype's public, protected, and (if accessible) package fields. The subtype may assume this responsibility only if the class it extends has an accessible no-arg constructor to initialize the class's state. It is an error to declare a class Serializable if this is not the case. The error will be detected at runtime.
Also serialization is not a part of
SCJP exam now...