# Extensions 1→N→G→Q→1 with N=C4 and Q=D52

Direct product G=N×Q with N=C4 and Q=D52
dρLabelID
C4×D52404C4xD5^2400,169

Semidirect products G=N:Q with N=C4 and Q=D52
extensionφ:Q→Aut NdρLabelID
C41D52 = D5×D20φ: D52/C5×D5C2 ⊆ Aut C4404+C4:1D5^2400,170
C42D52 = C20⋊D10φ: D52/C5⋊D5C2 ⊆ Aut C4404C4:2D5^2400,171

Non-split extensions G=N.Q with N=C4 and Q=D52
extensionφ:Q→Aut NdρLabelID
C4.1D52 = C5⋊D40φ: D52/C5×D5C2 ⊆ Aut C4404+C4.1D5^2400,65
C4.2D52 = C523SD16φ: D52/C5×D5C2 ⊆ Aut C4804-C4.2D5^2400,67
C4.3D52 = C524SD16φ: D52/C5×D5C2 ⊆ Aut C4404+C4.3D5^2400,68
C4.4D52 = C523Q16φ: D52/C5×D5C2 ⊆ Aut C4804-C4.4D5^2400,70
C4.5D52 = D5×Dic10φ: D52/C5×D5C2 ⊆ Aut C4804-C4.5D5^2400,163
C4.6D52 = D205D5φ: D52/C5×D5C2 ⊆ Aut C4804-C4.6D5^2400,164
C4.7D52 = Dic105D5φ: D52/C5×D5C2 ⊆ Aut C4404+C4.7D5^2400,168
C4.8D52 = C522D8φ: D52/C5⋊D5C2 ⊆ Aut C4804C4.8D5^2400,64
C4.9D52 = D20.D5φ: D52/C5⋊D5C2 ⊆ Aut C4804C4.9D5^2400,66
C4.10D52 = C522Q16φ: D52/C5⋊D5C2 ⊆ Aut C4804C4.10D5^2400,69
C4.11D52 = D20⋊D5φ: D52/C5⋊D5C2 ⊆ Aut C4404C4.11D5^2400,165
C4.12D52 = Dic10⋊D5φ: D52/C5⋊D5C2 ⊆ Aut C4404C4.12D5^2400,166
C4.13D52 = D5×C52C8central extension (φ=1)804C4.13D5^2400,60
C4.14D52 = C20.29D10central extension (φ=1)404C4.14D5^2400,61
C4.15D52 = C20.30D10central extension (φ=1)804C4.15D5^2400,62
C4.16D52 = C20.31D10central extension (φ=1)404C4.16D5^2400,63
C4.17D52 = D10.9D10central extension (φ=1)404C4.17D5^2400,167

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