Nested ifelse referring to elements in vector

I'm trying to use nested ifelse passing a list of elements in two vectors. Specifically, I would like to achieve the following goal:

set.seed(101)
df <- data.frame("Var1" = sample(c("A", "B", "C", "D", "E", "F"),  size=100, replace = TRUE))

# Group A or B
AB <- c("A", "B")

# Group C or D
CD <- c("C", "D")

df$group <- ifelse(df$Var1 == AB, "AB Group",
                   ifelse(df$Var1 == CD, "CD Group", NA)) # If not AB or CD -> NA

While I have:

> head(df)
    Var1   group
1    A   AB Group
2    A     <NA>
3    F     <NA>
4    A     <NA>
5    B     <NA>
6    E     <NA>
>