As far as Islamic Shariah is concerned, it is preferable to perform Tahajjud Prayer individually in the last part of the night. However, there is nothing wrong in performing it in congregation especially there is are benefit in it
On this, a detailed explanation was given by a prominent scholar, Sheikh `Abdul-Majeed Subh as those:
As for praying Tahajjud in congregation, there is nothing wrong with that. It is also permissible to offer other voluntary prayers in congregation. However, it is preferable to offer Tahajjud and voluntary prayers individually. Prophet Muhammad (peace and blessings be upon him) did that this way. The one who wakes up during night and performs Tahajjud individually feels the tranquility and comfort that he or she may not find in congregational prayers.
It is also reported in the hadith that Almighty Allah will be pleased of the behavior of two persons as one of them woke up in the middle of the night and offered prayer. Prophet Muhammad (peace and blessings be upon him) said, “Almighty Allah says, ‘O my angels, look at My servant. He stands in Prayer with no one seeing him except Me.’ Allah is also pleased due to the behavior of another man who, while unshielded, met an enemy and fought that enemy until he was killed.”
Moreover, Wael`Abdel-Mut`aal Shihab , a Shariah researcher at Al-Azhar University, added,
Tahajjud Prayer entails great rewards, and a Muslim should be keen on being constant in performing it.
Tahajjud Prayer can be performed individually or in congregation. This is applicable to Ramadan and any other time of the year. Though the Prophet (peace and blessings be upon him) offered Tahajjud and other optional prayers individually and in congregation, in most times he offered them individually. So, offering Tahajjud individually is preferable, and there is nothing wrong in performing it or any other optional prayers in congregation.
Here, I cite the hadith reported by Ibn `Abbas as a proof for this. Ibn `Abbas (may Allah be pleased with them) said, “I stayed overnight in the house of my aunt Maymunah bint Al-Harith (a wife of the Prophet) while the Prophet (peace and blessings be upon him) was there. The Prophet (peace and blessings be upon him) offered the `Ishaa‘ Prayer (in the mosque), returned home, and after having prayed four rak`ahs slept. Later on, he got up at night and then asked whether the boy (or he used a similar word) had slept? Then he got up for the Prayer and I stood up by his left side but he made me stand to his right and offered five rak`at followed by two more rak`ahs. Then, he slept … and then (after a while) he left for the (Fajr) Prayer” (Al-Bukhari).
Thus, the Prophet (peace and blessings be upon him) led Ibn `Abbas in congregational Tahajjud Prayer. He (peace and blessings be on him) also did this with other Companions.