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Mar 24, 2021 at 15:52 comment added Neil Strickland That's certainly the right idea; I'm not sure exactly what technical assumptions you need to support it. It should work for $K(n)$-local even periodic $H_\infty$ ring spectra. If $E$ is even periodic and $p$-complete then in many cases it is a retract of $\prod_nL_{K(n)}E$. I don't remember what is the maximum generality in which that is known. Using that fact, one should be able to generalise the statement about special subgroups.
Mar 24, 2021 at 15:41 comment added kiran Thanks, is the claim you're making that any (or many?) formal group coming from a ring spectrum that admits an H-infinity complex orientation has only "special" subgroups? Because the reason I actually posted this question is that I had convinced myself that something like that is true!
Mar 23, 2021 at 18:34 history answered Neil Strickland CC BY-SA 4.0