Not to worry I will get the list of Active Ships of Indian Navy so that you can have idea and go though it easily.

Here is the list

Submarine fleet
INS Chakra (S71)

Conventionally-powered submarines
INS Sindhughosh (S55)
INS Sindhudhvaj (S56)
INS Sindhuraj (S57)
INS Sindhuvir (S58)
INS Sindhuratna (S59)
INS Sindhukesari (S60)
INS Sindhukirti (S61)
INS Sindhuvijay (S62)
INS Sindhurashtra (S65)
INS Shishumar (S44)
INS Shankush (S45)
INS Shalki (S46)
INS Shankul (S47)

Surface fleet
INS Vikramaditya (R33)
INS Viraat (R22)

Destroyers
INS Kolkata (D63)
INS Kochi (D64)
INS Delhi (D61)
INS Mysore (D60)
INS Mumbai (D62)
INS Rajput (D51)
INS Rana (D52)
INS Ranjit (D53)
INS Ranvir (D54)
INS Ranvijay (D55)

Frigates
INS Shivalik (F47)
INS Satpura (F48)
INS Sahyadri (F49)
INS Talwar (F40)
INS Trishul (F43)
INS Tabar (F44)
INS Teg (F45)
INS Tarkash (F50)
INS Trikand (F51)
INS Brahmaputra (F31)
INS Betwa (F39)
INS Beas (F37)

Amphibious warfare ships
INS Jalashwa (L41)
INS Shardul (L16)
INS Kesari (L15)
INS Airavat (L24)
INS Magar (L20)
INS Gharial (L23)
INS Cheetah (L18)
INS Mahish (L19)
INS Guldar (L21)
INS Kumbhir (L22)