You can sort emails in your Inbox using Sort Gmail Inbox extension which can be installed from Chrome Web Store.
chrome extension

Emails can sorted to three different domains of your Gmail as follows:

  • Received emails
    • Unread
    • Contacts – Not Replied
    • These contacts who emailed you and you did not reply to them. If you select a particular contact the following options are available:
      chrome extension

      • Ignore / Mark it as done
      • Save emails to PDF
      • Export emails to Google Sheets
      • Setup text & SMS alerts for this contact
    • Contacts
    • Companies
    • Attachments
    • By Date
  • Sent emails
    • Unread
    • Contacts
    • Contacts – Not Replied
    • These contacts you sent an email to and you are awaiting a reply from them.

    • Companies
    • Attachments
    • By Date
  • All emails
    • Unread
    • Contacts
    • Companies
    • Attachments
    • By Date