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Your question covers an entire industry and job place. Aviation sector is huge and has a lot of job profiles related to it. It depends on you where you want to go. Please clarify so that I can respond accordingly. That is a question asked about the industry and there is no mention of the job profile. Such questions require discussion as they look to elaborate an industry and not just a profile. I'll give you a brief about the main job portfolios that are hosted by the aviation industry:
For Pilot Training:
1. Indira Gandhi Rashtriya Udan Academy (IGRUA) - Rae Bareli is the only government-owned institute for pilot training. There are state flying clubs which run in collaboration with state governments:
2. Madhya Pradesh Flying Club - Indore & Bhopal
3. Nagpur Flying Club, etc. CAE Gondia is another premier institute which works in collaboration with some private airlines to train candidates to obtain a CPL or AME (Aircraft Maintenance Engineer) Course:
1. Indian Institute of Aeronautics (IIA)
2. Indian Aviation Academy
For Flight Dispatchers Course:
1. CTE Hyderabad - Run by Air India
For air hostess training:
There are no government-owned colleges. However, a number of private academies are operational in the market. This was an explanation that basically covers wider view about the main job roles in aviation industry, choose yours wisely and then proceed accordingly.

All the flying clubs are DGCA approved. No one can start or operate a flying club without DGCA's approval. You may look for clubs which have better facilities like Navigational systems, Availability of instructors, suitability of weather for training flights and aircrafts. As far as reputation is concerned you should look for IGRUA, NFTI, Chimes Aviation, MPFC, Carver Aviation, NFC Nagpur and BFC Mumbai. Mind it they don't repute in terms of placements it's just that the training is good there. And they also cover most of the above mentioned criteria. In flying clubs there is no placement assistance provided to any candidate. You will have to apply for vacancies on your own as per the notifications issued by various airlines.