I can only think of Talking heads
I don’t understand the OP.
WTF? The vast majority of groups have a male lead singer.
Beatles, Zep. Floyd, Doors, etc.
It is extremely common.
@Bijou_Drains; did you mean groups with women in them and no woman is the lead singer? I can fix the title for you.
Oops, sorry.
Many groups also have female backup singers but a male lead. Bob Seger comes to mind.
The Pixies
There’s the Pixies and Velvet Underground — both female members sang but they weren’t the lead. Also Smashing Pumpkins.
I assume the question is about groups that have at least one female member, where that woman is not the lead singer. I will add the White Stripes (if a duo counts as a group). If vocal groups count, there’s also the Platters.
The Pogues are another.
Yes, perhaps the OP is thinking of a group that has a female playing a lead instrument but not a lead singer (or a backup singer). The Talking Heads would be an example.
The Dandy Warhols.
Eagles of Death Metal
Linda LaFlamme of It’s a Beautiful Day. Keyboards only, and they already had a female vocalist (Pattie Santos)
The Honeycombs had Honey Landtree as their drummer. Despite the fact the group was named after her (she was a hairdresser, thus Honey Combs), she did not sing.
For session musicians, there is Carol Kaye.
Decemberists
Gogol Bordello
Gaelic Storm is an Irish music band whose fiddle player is always a woman, and they’ve had a good number of them. As of this post it’s Katie Grennen. Only one ever sang lead, Kathleen Keane sang a few tracks on the 2001 album, Tree.
My Bloody Valentine
Silversun Pickups (often considered Pumpkins/MBV ripoffs)
Yo La Tengo
pre-License to Ill Beastie Boys
If bands can only have one “lead” singer, maybe these Canadian supergroups? My guess is that these guys sing the plurality of the songs, but I haven’t done the math:
Broken Social Scene (Kevin Drew)
The New Pornographers (A.C. Newman)
Gail Ann Dorsey (bass) in Bowie’s band for the Reality Tour
Not a great example due to lack of vocals in general, but Jeff Beck has had some extremely talented female musicians in his touring bands (Tal Wikenfeld, Rhonda Smith, Jennifer Batten)
Velvet Underground
Prince’s various band incarnations.