Recommend me anime with cute girls and space battles in one package

>>128814

Gunbuster
Diebuster
Houkago no Pleiades?
Space Patrol Luluco (Airing, not finished yet)
Gurren Lagann
Knights of Sidonia (If you don't mind the 3D)
Dangaioh (The original, but maybe the new one would fit this, too, haven't watched it.)
A lot of the Gundam franchise

For others I missed, check these recommendations. Not all of them have fights in space though.
http://myanimelist.net/anime/949/Top_wo_Nerae_Gunbuster/userrecs

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gal force

oh well

Oh no

I haven't seen it yet so I'm not sure how many space battles are in it, but Mouretsu Pirates: might be what you're looking for.
Uchuu Senkan Yamato 2199 also has some qt3.14s although you've probably already seen it given your image.
Also the various macross'

AKB0048

>>128828
Oh man. I haven't seen that in 20 years.