# Extensions 1→N→G→Q→1 with N=C52 and Q=F5

Direct product G=N×Q with N=C52 and Q=F5
dρLabelID
F5×C52100F5xC5^2500,41

Semidirect products G=N:Q with N=C52 and Q=F5
extensionφ:Q→Aut NdρLabelID
C521F5 = C52⋊C20φ: F5/C1F5 ⊆ Aut C522520+C5^2:1F5500,17
C522F5 = He5⋊C4φ: F5/C1F5 ⊆ Aut C522520+C5^2:2F5500,21
C523F5 = C52⋊F5φ: F5/C1F5 ⊆ Aut C522510+C5^2:3F5500,23
C524F5 = He54C4φ: F5/C1F5 ⊆ Aut C52255C5^2:4F5500,25
C525F5 = C5×C5⋊F5φ: F5/C5C4 ⊆ Aut C52100C5^2:5F5500,43
C526F5 = C5×C52⋊C4φ: F5/C5C4 ⊆ Aut C52204C5^2:6F5500,44
C527F5 = C536C4φ: F5/C5C4 ⊆ Aut C52204C5^2:7F5500,46
C528F5 = C537C4φ: F5/C5C4 ⊆ Aut C52100C5^2:8F5500,47
C529F5 = C538C4φ: F5/C5C4 ⊆ Aut C52125C5^2:9F5500,48
C5210F5 = C539C4φ: F5/C5C4 ⊆ Aut C5250C5^2:10F5500,49
C5211F5 = C5×D5.D5φ: F5/D5C2 ⊆ Aut C52204C5^2:11F5500,42
C5212F5 = C53⋊C4φ: F5/D5C2 ⊆ Aut C52100C5^2:12F5500,45

Non-split extensions G=N.Q with N=C52 and Q=F5
extensionφ:Q→Aut NdρLabelID
C52.F5 = C25⋊C20φ: F5/C1F5 ⊆ Aut C522520+C5^2.F5500,18
C52.2F5 = C5×C25⋊C4φ: F5/C5C4 ⊆ Aut C521004C5^2.2F5500,16
C52.3F5 = D25.D5φ: F5/C5C4 ⊆ Aut C521004C5^2.3F5500,20
C52.4F5 = C25⋊F5φ: F5/C5C4 ⊆ Aut C52125C5^2.4F5500,22
C52.5F5 = C252F5φ: F5/C5C4 ⊆ Aut C52504+C5^2.5F5500,24

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