συν-

• ξυν- (xun-) — old Attic
• συ- (su-) — before ζ (z) and before σ (s) plus consonant
• συγ- (sug-) — before the velar consonants γ, κ, ξ, χ (g, k, x, kh)
• συλ- (sul-) — before λ (l)
• συμ- (sum-) — before the labial consonants β, μ, π, φ (b, m, p, ph)
• συρ- (sur-) — before ρ (r)
• συσ- (sus-) — before σ (s) plus vowel

Prefix version of the preposition σύν (sún, “with”).

σῠν- • (sun-)

1. with, together, co-, syn-
2. indicates completeness

• “σύν”, in Liddell & Scott (1940) A Greek–English Lexicon, Oxford: Clarendon Press

• συν- or σύν- before vowels, dental consontants and [n]
• συ-, σύ- (sy-, sý-) before sibilants [s] (+consonant) and [z] and colloquially before [v, γ, δ, f, x, θ, ks, ps]
• συγ-, σύγ- (syg-, sýg-) before the consonants κ, γ, χ (k, g, ch) pronounced /siŋ/
• συλ-, σύλ- (syl-, sýl-) before [l] λ (l) pronounced /sil/ (only one [l])
• συμ-, σύμ- (sym-, sým-) before the labial consonants [p, v, f, m] π, β, φ, μ (p, v, f, m)
• συρ-, σύρ- (syr-, sýr-) before [r] ρ (r)
• συσ-, σύσ- (sys-, sýs-) often before [s] σ (s)

From Ancient Greek σῠν- from preposition σύν (sún, “with”).

• IPA^(key): /sin/

συν- • (syn-)

1. with, together, co-, syn-

   ‎συν- (syn-) + ‎αγωνίζομαι (agonízomai, “strive”) → ‎συναγωνίζομαι (synagonízomai, “compete”)

2. indicates completeness
3. indicates similarity

and

• "συν-", in Λεξικό της κοινής νεοελληνικής [Dictionary of Standard Modern Greek], Triantafyllidis Foundation, 1998 at the Centre for the Greek language