Shulchan Arukh, Orach Chayim 199/שולחן ערוך·אורח חיים קצ״ט

1The waiter who ate an olive’s worth may be included in the zimun.

2Nowadays, Cutheans are the same as idolaters and are not included in a zimun

3Someone who is an absolute am ha’aretz is included in a zimun nowadays

44. A gentile is not included in a zimun. Even a convert who was circumcised but did not immerse may not be included in a zimun. Someone who is a full fledged convert is included in a zimun and he may recite birkas hamazon including the words Al Shehinchalta La'avoteinu

5An onen (on a weekday), that is exempt from blessing, may not be included in a zimun.

6We do not make a zimun with women, slaves or children but they may make a zimun by themselves. A zimun comprised of women, slaves and children should not be formed due to the promiscuity of the slaves, rather women should recite birkas hamazon by themselves and slaves by themselves but they may not use Hashem’s Name

7Women have the option to form a zimun by themselves but when they eat with men they are obligated to answer and they fulfill their obligation by listening to the men Rem'a: even though they do not understand lashon kodesh

8An androgynous makes a zimun with other androgynous, and he cannot be included in the zimun of men or women.

9A tum tum never makes a zimun

10A minor that has reached the age of understanding that he is praying to God can be included for the zimun for 3 and 10. Some say that a child cannot be included in a zimun until he reaches the age of thirteen and then he is assumed to be an adult who has produced two hairs. (Rosh and Mordechai Perek Shlosha Sheachlu and Tur) This is the custom and one should not deviate from it. Someone deaf or insane may be included in a zimun if he can concentrate and focus even though the deaf person cannot hear the beracha (Mahril)

11One whom they excommunicated due to a sin is not included in a zimmun.