You are welcome to dig further, but to get you started, the following text is from a commonly used Internet summary overview resource (acknowledged below):
According to the IRS Publication 557†, in the Organization Reference Chart section, the following is an exact list of 501(c) American tax-exempt organization types and their corresponding descriptions.[1]
501(c)(1) — Corporations Organized Under Act of Congress (including Federal Credit Unions)
501(c)(2) — Title Holding Corporation for Exempt Organization[2]
501(c)(3) — Religious, Educational, Charitable, Scientific, Literary, Testing for Public Safety, to Foster National or International Amateur Sports Competition, or Prevention of Cruelty to Children or Animals Organizations
501(c)(4) — Civic Leagues, Social Welfare Organizations, and Local Associations of Employees
501(c)(5) — Labor, Agricultural, and Horticultural Organizations
501(c)(6) — Business Leagues, Chambers of Commerce, Real Estate Boards, etc.
501(c)(7) — Social and Recreational Clubs
501(c)(8) — Fraternal Beneficiary Societies and Associations
501(c)(9) — Voluntary Employee Beneficiary Associations
501(c)(10) — Domestic Fraternal Societies and Associations
501(c)(11) — Teachers' Retirement Fund Associations
501(c)(12) — Benevolent Life Insurance Associations, Mutual Ditch or Irrigation Companies, Mutual or Cooperative Telephone Companies, etc.
501(c)(13) — Cemetery Companies
501(c)(14) — State-Chartered Credit Unions, Mutual Reserve Funds
501(c)(15) — Mutual Insurance Companies or Associations
501(c)(16) — Cooperative Organizations to Finance Crop Operations
501(c)(17) — Supplemental Unemployment Benefit Trusts
501(c)(18) — Employee Funded Pension Trust (created before June 25, 1959)
501(c)(19) — Post or Organization of Past or Present Members of the Armed Forces
501(c)(20) — Group Legal Services Plan Organizations
501(c)(21) — Black lung Benefit Trusts
501(c)(22) — Withdrawal Liability Payment Fund
501(c)(23) — Veterans Organization (created before 1880)
501(c)(24) — Section 4049 ERISA Trusts
501(c)(25) — Title Holding Corporations or Trusts with Multiple Parents
501(c)(26) — State-Sponsored Organization Providing Health Coverage for High-Risk Individuals
501(c)(27) — State-Sponsored Workers' Compensation Reinsurance Organization
501(c)(28) — National Railroad Retirement Investment Trust
501(c)(29) — Qualified Nonprofit Health Insurance Issuers (Created in section 1322(h)(1) of the Affordable Care Act)[3]
† 501(c)(20) and 501(c)(24) organization types receive scant mention in IRS Publication 557 and are not included in its Organization Reference Chart. 501(c)(20) organizations are no longer tax-exempt under Section 501(c)(20) after June 30, 1992, but they may request to become exempt under Section 501(c)(9) effective July 1, 1992.[4] 501(c)(24) organizations are described as Section 4049 ERISA Trusts; Section 4049 of ERISA has been repealed.[5] Under Section 511, a 501(c) organization is subject to tax on its "unrelated business income", whether or not the organization actually makes a profit, but not including selling donated merchandise or other business or trade carried on by volunteers, or certain bingo games.[6] Disposal of donated goods valued over $2,500, or acceptance of goods worth over $5,000 may also trigger special filing and record-keeping requirements. Foregoing compiled by Wikipedia from IRS publications.