Fiqh-us-Sunnah Volume 1, Purification and Prayer, Fiqh 1.087.

It is most virtuous to delay the night prayer until the end of the preferred time for it, which is half the night. Reported ‘Aishah, “One night the Prophet, upon whom be peace, prayed the night prayer after most of the night had gone and most of the people in the mosque had fallen asleep. Then he came out, prayed, and said, “This would be the proper time if it were not a hardship on my nation.”‘ (Related by Muslim and an-Nasa’i.) The Prophet, upon whom be peace, did not do this on a regular basis, as he heard that it would be a hardship on his nation. He would take into consideration the situation of those in the mosque. Sometimes he would hasten in performing the prayer and at other times he would delay it. Said Jabir, “The Messenger of Allah would pray the noon prayer during the hottest time of noon, the afternoon prayer when the sun was clear, the sunset prayer when the sun had gone down, and the night prayer he would sometimes delay and sometimes hasten if he found people gathered (in the mosque). If he noticed that they were lingering, he would delay it. He would pray the morning prayer while it was still dark.” (Related by al-Bukhari and Muslim.)