The original intent of the 13th Amendment was to prohibit chattel slavery, as existed in the South prior to the Civil War. Keep in mind that the Union commenced the first Federal military draft in 1863, and that President Lincoln and the Republicans, who supported and passed legislation to effect said draft also supported this amendment. However, the limitation of the Federal government to certain, specified powers by the 9th and 10th Amendments would appear to preclude a Federal draft. The Constitution authorizes the Federal government the authority to raise armies and provide for a navy. However, that authority cannot be construed to include a military draft.
Nonetheless, none of these amendments preclude State governments from establishing conscription. The English common law concepts that underlie the establishment of militias place all able-bodied males within certain age ranges (like 18 to 50) as members of the unorganized militia. These men are, under the common law, eligible to be called up by State governments to repel invasions or to suppress insurrections.
"The Constitution authorizes the Federal government the authority to raise armies and provide for a navy. However, that authority cannot be construed to include a military draft.
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Apparently, that authority exists, since we have had a draft in place or on standby since the Civil War. Those who say it is unconsitutional to have a draft are arguing against what is well-established. I have not researched whether the draft has been before the SCOTUS, but I'd guess it has.