The Fermi decays () are often referred to as the "superallowed" decays while Gamow–Teller () decays are simple "allowed" decays.
Forbidden decays are those which are substantially more improbable, due to parity violation, and as a result have long decay times.
Now the angular momentum (L) of the  systems can be non-zero (in the center-of-mass frame of the system).
Below are the Observed Selection Rules for Nuclear Beta-Decay:
Each of the above have Fermi () and Gamow–Teller () decays.
So for the "first-forbidden" transitions you have
: Fermi
and
: Gamow–Teller
systems.
Notice that  (parity violating transition).
The half life of the decay increases with each order: