We can restrict mail subscription for particular member. To set this kindly follow,

  1. ​Log in from user 

  2. Go to Google Groups.

  3. Near the top left corner, click My Groups.
  4. Find the name of the group > ​Click ​on group​
  5. ​Select Membership and email setting (From upper right setting tab)

  6. Select settings you want to apply

  7. ​And Save

Setting options and how to choose them :

  • Change your name in the group: To the right of your name, click Edit and type your preferred name.
  • Hide or show your photo and a link to your Google profile in group posts:
    • To show your photo and profile, check the box next to "Link to my Google profile and show my photo on posts." 
    • To hide your photo and profile, uncheck the box next to "Link to my Google profile and show my photo on posts."
  • Change your email address in the group: In the middle of the box, click on your email address  and from the drop-down, pick the email you want to use.
  • Choose how frequently you get email from the group: Click the drop-down menu on the line below your email address. You can choose any of the following options.
    • Don't send email updates: You won't get emails, but you can still see posts by logging in to Google Groups and clicking on that group. 
    • Send daily summaries: On days when people post to the group, you'll only get one email that includes every message that was sent.
    • Send combined updates: You'll get one email for every 25 posts to the group.
    • Send me an email for every new message: You'll get an email anytime someone posts to the group.