aviator, here is a list of Soviet nuclear powered submarines that were commissioned by 1990 and which were serving with the Northern Fleet at the time:
Project 627 (NATO November) SSN: K-3, K-5 (decommissioned in January 1990), K-11, K-21, K-50; decommissioned in April 1990: K-11, K-21, K-50
Pr 658 (Hotel) SSBN: K-16, K-19 (in reserve since 1979, decommissioned April 1990), K-33, K-40, K-145, K-149 (went into reserve fleet in March 1990)
Pr 667A (Yankee) SSBN: K-32 (did not deploy after 1986 due to reactor accident), K-137 Leninets (on missile patrol in the North Atlantic from 19 October to 31 December 1990), K-140 (out of service by 17 December 1990), K-214, K-228, K-241, K-245, K-249, K-253 (Yankee Notch conversion), K-395 (in drydock for Yankee Notch conversion), K-403 (sea trials of towed array pod), K-411 (completed Yankee Stretch conversion in 1990), K-418 (removed from active service in 1989), K-420 (Yankee Sidecar SSGN conversion, but torpedoes only by 1989), K-423, K-426, K-444; decommissioned in April 1990: K-32, K-140, K-426
[Note: In 1988 the director of US naval intelligence Adm Studeman told Congress that Yankee class SSBNs had ceased patrols off the US coast in late 1987 and were instead conducting "combat service patrols against theater targets" (i.e. staying close to home), presumably to compensate for the loss of the SS-20 under the INF Treaty.]
Pr 667B (Delta I) SSBN: K-279, K-385, K-447, K-450, K-457, K-460, K-465, K-472, K-475
Pr 667BD (Delta II) SSBN: K-92, K-182, K-193, K-421
Pr 667BDR (Delta III) SSBN: K-44 (in post drydock sea trials), K-129 (had powerplant failure in June 1989, may not have been available), K-424, K-449 (went to Pacific Fleet in November 1990), K-487, K-496
Pr 667BDRM (Delta IV) SSBN: K-18, -51, -64, -84, -114, -117, -407 (not commissioned until late November 1990)
Pr 670M (Charlie II) SSGN: K-209, -452, -458, -479, -503, -508
Pr 671 (Victor I) SSN: K-38, -53, -69, -147, -306, -323, -367 (did not deploy again after a reactor accident in 1985), -370 (may not have been available for deployment), -398, -438, -462, -481
Pr 671RT (Victor II) SSN: K-371, -387, -467, -488 (never returned to sea after 1988 drydock), -495, -513, -517
Pr 671RTM (Victor III) SSN: K-218, -244, -254, -298, -299, -358, -502, -524, -527
Pr 671RTMK (Improved Victor III) SSN: K-292, K-388, K-138 (operational from January 1990), K-414 (not commissioned until 30 December 1990)
Pr 675 (Echo II) SSGN: К-1 (may not have deployed after 1989), K-22, K-28, K-35 (final deployment in 1989), K-47 (in refuel and overhaul, did not return until 1992), K-74, K-104, K-125, K-128 (not in active service after 1989), K-131 (did not deploy after 1984), K-170 (may not have been operational after turbine accident in 1988), K-172 (stayed in port after reactor leak in June 1989); decommissioned in 1990: K-28, K-74, K-128, K-172 (in April)
Pr 705 (Alfa) SSN: K-123 (received a new reactor in 1990, probably not operational until 1992), K-316, K-373, K-432, K-463, K-493 (all but K-123 decommissioned in April 1990)
Pr 941 (Typhoon) SSBN: TK-12, TK-13, TK-17, TK-20, TK-202, TK-208
Pr 945 (Sierra I) SSN: K-239, K-276
Pr 945A (Sierra II) SSN: K-534 (not commissioned until 26 December 1990)
Pr 949 (Oscar I) SSGN: K-206 Minsky Komsomolets, K-525
Pr 949A (Oscar II) SSGN: K-119, K-132 (transferred to Pacific Fleet in late October 1990), K-148, K-410 (not commissioned until 22 December 1990), K-442 (not commissioned until 28 December 1990)
Pr 971 (Akula) SSN: K-154 (commissioned but reportedly not operational until December 1993), K-157 (commissioned but reportedly not operational until November 1995), K-317 Pantera (not commissioned until 27 December 1990), K-328 (commissioned but reportedly not operational until December 1992), K-461 (commissioned but reportedly not operational until December 1991), K-480
I will further update this list with information about which boats might have actually been available for service.