1. allow that = admit
2. allow of sg = permit, make it possible
3. allow for sg = take it into account

There are certain cases in which it is preferable to use "that" instead of "which" or "who". If the noun is preceded by one of the following, we use "that" instead of "which" or "who":
1-"all,"
2-"any(thing),"
3-"every(thing),"
4-"some(thing)"
5- "no(thing),"
"little," 6-
7-"few,"
8-"many,"
9-"much,"
10-"none,"
11-after the opening (it is.../is it.../it was)
12-after cardinals (first/second/third, etc.)
13-only
14-next
15-last
16- after superlative adjectives(best/easiest/coldest, etc.)