Extensions 1→N→G→Q→1 with N=C2xC4 and Q=C52

Direct product G=NxQ with N=C2xC4 and Q=C52
dρLabelID
C2xC4xC52416C2xC4xC52416,175

Semidirect products G=N:Q with N=C2xC4 and Q=C52
extensionφ:Q→Aut NdρLabelID
(C2xC4):C52 = C13xC23:C4φ: C52/C13C4 ⊆ Aut C2xC41044(C2xC4):C52416,49
(C2xC4):2C52 = C13xC2.C42φ: C52/C26C2 ⊆ Aut C2xC4416(C2xC4):2C52416,45
(C2xC4):3C52 = C4:C4xC26φ: C52/C26C2 ⊆ Aut C2xC4416(C2xC4):3C52416,177
(C2xC4):4C52 = C13xC42:C2φ: C52/C26C2 ⊆ Aut C2xC4208(C2xC4):4C52416,178

Non-split extensions G=N.Q with N=C2xC4 and Q=C52
extensionφ:Q→Aut NdρLabelID
(C2xC4).C52 = C13xC4.10D4φ: C52/C13C4 ⊆ Aut C2xC42084(C2xC4).C52416,51
(C2xC4).2C52 = C13xC8:C4φ: C52/C26C2 ⊆ Aut C2xC4416(C2xC4).2C52416,47
(C2xC4).3C52 = C13xC22:C8φ: C52/C26C2 ⊆ Aut C2xC4208(C2xC4).3C52416,48
(C2xC4).4C52 = C13xC4:C8φ: C52/C26C2 ⊆ Aut C2xC4416(C2xC4).4C52416,55
(C2xC4).5C52 = C13xM5(2)φ: C52/C26C2 ⊆ Aut C2xC42082(C2xC4).5C52416,60
(C2xC4).6C52 = M4(2)xC26φ: C52/C26C2 ⊆ Aut C2xC4208(C2xC4).6C52416,191

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