Is it permissible for my mother, who is fifty years old and has never performed the Hajj or Umrah, to go for Hajj without a mahram?

It is permissible for a woman to travel for Hajj with a safe company of righteous men and women, even if she does not have a mahram (unmarriageable kin) with her. This is the view of the Maliki and Shafi'i schools of thought. An exception to this is a young or beautiful woman, or one who is not religious and modest; for her, it is not permissible to travel without a mahram. It is preferable for a mahram to travel with her if possible; if not possible, she may travel with the safe company.