Generally speaking, as the Prophet, peace be upon him, has reportedly stated, “Divorce is the most hated of all permissible things”. If one has no valid ground or reason for resorting to it, it may, therefore, be considered either undesirable or sinful.
However, there are certain exceptional cases, when divorce is considered as either desirable or even obligatory. If, for instance, one of the couple leaves Islam altogether, divorce becomes obligatory; it will be considered desirable when one of the spouses is leading an un-Islamic life-style and is neglectful of the pillars of Islam. Your case falls under this category.
Based on what is stated above, if you find your husband’s un-Islamic life-style intolerable you are permitted to divorce him if he is not willing to change. Being an alcoholic or consistently neglecting obligatory prayers are considered genuine reasons for seeking divorce.
Having said this, however, I must advise you not to rush to seek a divorce from him. You should first try to seek proper Islamic counseling. If no one is available for counseling, you may at least some wise people in the community to try to advise him. If all attempts fail to convince him to change, then you are entitled to seek a divorce from him.
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