a. Both parents must naturalize, or if only one parent naturalizes, the other parent must be either a U.S. citizen at the time of the child’s birth and remain a U.S. citizen,22 or be deceased, or the parents must be legally separated 23 and the naturalizing parent must have legal custody.24
b. In the case of a child who was illegitimate at birth, the child must not be legitimated, and it must be the mother who naturalizes. If the child is legitimated, s/he can derive only if both parents naturalize, or the non-naturalizing parent is dead.25
c. Parent or parents must have been naturalized prior to the child’s 18th birthday;26
d. Child must have been lawfully admitted for permanent residence before the 18th birthday;27
e. Child must be unmarried;28
f. Adopted child may derive citizenship if the child is residing in the U.S. at the time of the adoptive parent(s)’s naturalization,29 is In the legal custody of the adoptive parent(s), is a lawful permanent resident and adoption occurred before s/he turned 18.30 Stepchild cannot derive citizenship.
http://www.cuny.edu/about/resources/...Chart_C-09.pdf