If you are concerned about inbreeding the size of the animal (or its feet) or not too important. Generation time can be of interest.
The important factors are population bottlenecks, how well they are suited to their environment, and how much or how soon they might be required to evolve.
Bottleneck reduce the effective population size (statistical equivalent of the number of adults contributing to the next generation). The genetic diversity of the next generation has an upper limit of 2 x the number of (ideally unrelated) individuals (for diploid animals). No more genetic diversity will be available than that. Longer periods of small populations will be a bit worse, but a single generation does a lot of damage to diversity. Because individuals in a population are likely related, calculating the effective population size usually produces a smaller number than the actual number of breeding individuals.
As genetic lines expand and accumulate mutations, their genetic diversity will increase, which should relieve these kind of problems. This will involve rate of natural (or artificial) mutagenesis and the kinds of mutations produced.
Can't answer your question directly, but here are some related cases:
Completely inbred mouse lines exist and are viable. The size of their broods are about 1/3 of normal and they are living in optimal laboratory conditions.
During the creation of these lines, there were probably many other lines that did not fair so well and were dropped (at least that's the way I would have done it).
I used to maintain genetic lines of zebrafish and inbreeding was quite a concern for us.
Our generations were usually around 100 fish (maybe 60 male and 40 female). The smaller number of the sex is the limiting factor.
We forced breeding to occur as we desired by collecting sperm and performing in vitro fertilizations.
There was a generation that had less than 20 fish (all female using genetic tricks).
The line was inbred, but viable and was subsequently improved by more directed breeding (towards fish able to breed naturally and give larger clutches of eggs).
Cheetahs (a viable species existing on its own in the wild) went through a population bottleneck estimated at 10,000 (so I understand). Their genetic diversity is low, but they work OK for now (survive in the wild). If some sudden change required them to evolve rapidly, they might not do so well due to their lack of genetic diversity which is fodder for evolution. Now their population is smaller due to habitat loss, but that seems to be a different problem.
My guess would be more than 100, more that 1,000 would be better.
It would depend on how the society dealt with these things. Maybe they have very strict incest rules, or none at all.