Over it (the Hell-Fire) are appointed nineteen (wardens). (74:30)    

Commentary
NUMBER 19: When we analyze the verses of the Quran and the various topics which are covered within this Living Book, we see that out of the 6,000+ verses, almost 1/3 or over 2,000 of them speak about the Day of Judgement, and the eventual outcomes of Heaven and Hell. This should be a wakeup call for us to take our actions in this life more seriously as there will be a day of accountability.
However, much of what we read in the Quran about that Day and Paradise and Hell seem abstract, and truly much of it is steeped in metaphorical language which Allah has ‘watered down’ for us to better understand – and many times drawing from parallels in our world and how it works.
One such example is the verse in question from Surah al-Muddatthir in which Allah tells us that there are 19 wardens which are appointed to guard over the fire of Hell. 
We believe that Allah is All-Powerful and that He can do anything, yet we see that some of His workings, He appoints certain angels do carry out the tasks. For revelation, He relies on Jibrāʾil; for taking the souls of humanity, He tasks ʿIsrāʾīl; when He destroys communities, like he did to the people of Prophet Lūṭ, the Quran says that He employed two angels to carry out this task - but WHY the need for 19 angels to guard Hell – why not 18 or 20 angels to oversee the punishments?
From the commentaries of this verse, it seems that we have no related statements from the Prophet or Imams which explain WHY this specific number was chosen. Ayatullah Makarim Shirazi has given a possibility that it could be that the figure of 19 is made up of two numbers “1” and “9” – and “1” is the smallest number and “9” is the largest number – and from these (obviously apart from “0”) all other numbers are derived. Other scholars have stated that the sources of all negative ethical traits are 19, and since these adverse traits can lead to the punishment of Allah, thus the 19 levels of Hell are the same number and in each level, there is an angel or group of angels who are in charge of carrying out the punishments.
Ultimately however, there are some things which are still ambiguous in regards to this number and why Allah chose it, however we must submit that there is a meaning and wisdom behind it – even if we still are not acquainted with it.
Point of Reflection
If one angel has the power to take the souls of all of humanity; and two angels can destroy an entire city and all of its inhabitants; then indeed nineteen angels (or groups of angels) can over-see the punishments of all of those destined for Hell – this is not something challenging for Allah!