Aviendha, Egwene and Elayne know each other far better than they know Min. Aviendha thinks as much in TGS - she likes Min, but doesn't really know her, and thinks that Min can be silly, at times.

What I think is important to note is that these three share more in common with Rand than Min ever could:
1) All are channelers
2) They all share some aspect of blood lineage or cultural history (Elayne and Aviendha actually resemble Rand, as has remarked on a few times during the series)
3) They all have strengths that rival Rands'
4) All three are leaders

Thus, if need be, these three seem like a trinity that would confront and oppose Rand if necessary, making it seem like the Pattern made sure there were women who would look out for the greater good of various populations yet still have an interpersonal connection among each other and the Dragon Reborn. IE: They are all potential Latra Posae Decume-like characters, with Elayne and Egwene actually opposing Rand publicly for the sake of their communities.