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Seventh-tier Alvechurch - the lowest ranked side left in the FA Cup - face a trip to League One club Forest Green in the second round of the competition.
Nineteen non-league sides were in the draw, with National League South side Ebbsfleet to host League One Fleetwood, while fellow sixth-tier club King's Lynn take on League Two Stevenage.
Chippenham, who beat Lincoln on Saturday, will visit League One Burton.
The ties will be played between Friday, 25 November and Monday, 28 November, with Premier League and Championship sides entering the competition in the third round.
Seventh-tier Bracknell host former winners Ipswich in the final first-round tie on Monday, with the winners hosting non-league Buxton next.
Full FA Cup second-round draw
Curzon Ashton or Cambridge United v Grimsby Town
Wrexham v Farnborough
Accrington Stanley v Barnet or Chelmsford
Ebbsfleet United v Fleetwood Town
Bracknell Town or Ipswich Town v Buxton
Barnsley v Crewe Alexandra
Forest Green Rovers v Alvechurch
Portsmouth v MK Dons
Shrewsbury Town v Peterborough United or Salford City
Solihull Moors or Hartlepool v Harrogate Town
King's Lynn Town v Stevenage
Charlton Athletic v Stockport County
Bristol Rovers v Boreham Wood
Dagenham & Redbridge v AFC Fylde or Gillingham
Woking or Oxford United v Exeter City
Sheffield Wednesday v Mansfield Town
Weymouth or AFC Wimbledon v Chesterfield
Burton Albion v Chippenham Town
Walsall v Carlisle United
Newport County v Torquay United or Derby County
Watch all of the latest FA Cup highlights and reaction here
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