Aside from the main settings of Hogwarts and the United Kingdom, there are several sub-settings that play a major part in Harry Potter and the Order of the Phoenix. 4 Privet Drive, Little Whinging, the home of the Dursleys, is a place of never ending torture for Harry. New settings are introduced in this book including Twelve Grimmauld Place, the former home of Sirius Black’s family. It is a place filled with dark magical items, but it is also the headquarters of the Order of the Phoenix. Even though filled with reminders of dark magic and of the war brewing, it is a happy place for Harry because it serves as a hiding place for his godfather Sirius, the closest thing to family that he has and the Weasley family, who have always treated Harry like a son. At Hogwarts, a new setting is the Room of Requirement, which becomes anything the user requires it to be, where Harry leads the D.A. The Forbidden Forest is another sub-setting that plays a significant role in this book. Perhaps the most important sub-settings in the entire novel are the Ministry of Magic and the Department of Mysteries that play important roles in one of the many climaxes of the Order of the Phoenix.
I'm assuming by "subsettings" you are referring to more minor settings, and not just England, or Hogwarts. Harry Potter and the Order of the Phoenix takes place primarily in the house of Sirius Black and in the Halls of Hogwarts School of Witchcraft and Wizardry. However, there are some smaller, less oft visited setting that are certainly worth mentioning. For example, in the very beginning of the novel Harry and his cousin are in a park where they meet the dementors. Harry must use magic to fend them off. Normally, using magic outside of Hogwarts is forbidden and Harry end up in a great deal of trouble because of that encounter in a neighborhood park.
Another minor setting is the ministry of magic, though perhaps I am incorrect in calling it a minor setting. Harry first appears in the ministry for his hearing. After that, Harry, Hermione, Ron, Luna, and Ginny spend time in the ministry at the end trying to save Sirius.
Being such a long book, the Harry Potter and the Order of the Phoenix features many, many different settings. These include Sirius Black's old home, the headquarters of the titular Order of the Phoenix, and the many different rooms inside the Black House. Of course there are also the many rooms inside Hogwarts that were featured in the story. Some prominent sub-settings would include the Room of Requirement, where DA meetings were held, Dumbledore's office, where he fended off four Ministry officials before making his escape, Umbridge's office, where Harry was forced to undergo several torturous detentions and an illegal attempted questioning, and many more.
It would be hard to list every single one of the settings in Order of the Phoenix. This book, like all the other Harry Potter books, describes a year at Hogwarts on an almost daily basis, so there are bound to be a lot of different settings.