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The Parliament shall, subject to this Constitution, have power to make laws for the peace, order, and good government of the Commonwealth with respect to:
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(xix) naturalization and aliens;
… (Sec. 51)

A subject of the Queen, resident in any State, shall not be subject in any other State to any disability or discrimination which would not be equally applicable to him if he were a subject of the Queen resident in such other State. (Sec. 117)

The Parliament shall, subject to this Constitution, have power to make laws for the peace, order, and good government of the Commonwealth with respect to:
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(xxi) marriage;
(xxii) divorce and matrimonial causes; and in relation thereto, parental rights, and the custody and guardianship of infants;
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(xxiiiA) the provision of maternity allowances, widows’ pensions, child endowment, ... and family allowances;
… (Sec. 51)

The Parliament shall, subject to this Constitution, have power to make laws for the peace, order, and good government of the Commonwealth with respect to:
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xxiii. invalid and old-age pensions;
xxiiiA. the provision of maternity allowances, widows' pensions, child endowment, unemployment, pharmaceutical, sickness and hospital benefits, medical and dental services (but not so as to authorize any form of civil conscription), benefits to students and family allowances;
… (Sec. 51)

This Act, and all laws made by the Parliament of the Commonwealth under the Constitution, shall be binding on the courts, judges, and people of every State and of every part of the Commonwealth, notwithstanding anything in the laws of any State; and the laws of the Commonwealth shall be in force on all British ships, the Queen’s ships of war excepted, whose first port of clearance and whose port of destination are in the Commonwealth. (Covering Clause 5)

In all matters:
(i) arising under any treaty;
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the High Court shall have original jurisdiction. (Sec. 75)

The Parliament may make laws conferring original jurisdiction on the High Court in any matter:
(i) arising under this Constitution, or involving its interpretation;
… (Sec. 76)

No adult person who has or acquires a right to vote at elections for the more numerous House of the Parliament of a State shall, while the right continues, be prevented by any law of the Commonwealth from voting at elections for either House of the Parliament of the Commonwealth. (Sec. 41)

Until the Parliament otherwise provides, the qualification of electors of members of the House of Representatives shall be in each State that which is prescribed by the law of the State as the qualification of electors of the more numerous House of Parliament of the State; but in the choosing of members each elector shall vote only once. (Sec. 30)

The qualification of electors of senators shall be in each State that which is prescribed by this Constitution, or by the Parliament, as the qualification for electors of members of the House of Representatives; but in the choosing of senators each elector shall vote only once. (Sec. 8)