# Extensions 1→N→G→Q→1 with N=C5×C20 and Q=C4

Direct product G=N×Q with N=C5×C20 and Q=C4
dρLabelID
C202400C20^2400,108

Semidirect products G=N:Q with N=C5×C20 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C5×C20)⋊1C4 = C205F5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20):1C4400,145
(C5×C20)⋊2C4 = C5×C4⋊F5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20):2C4400,138
(C5×C20)⋊3C4 = C20⋊F5φ: C4/C1C4 ⊆ Aut C5×C20100(C5xC20):3C4400,152
(C5×C20)⋊4C4 = C202F5φ: C4/C1C4 ⊆ Aut C5×C20404(C5xC20):4C4400,159
(C5×C20)⋊5C4 = C20×F5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20):5C4400,137
(C5×C20)⋊6C4 = C4×D5.D5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20):6C4400,144
(C5×C20)⋊7C4 = C4×C5⋊F5φ: C4/C1C4 ⊆ Aut C5×C20100(C5xC20):7C4400,151
(C5×C20)⋊8C4 = C4×C52⋊C4φ: C4/C1C4 ⊆ Aut C5×C20404(C5xC20):8C4400,158
(C5×C20)⋊9C4 = C203Dic5φ: C4/C2C2 ⊆ Aut C5×C20400(C5xC20):9C4400,101
(C5×C20)⋊10C4 = C5×C4⋊Dic5φ: C4/C2C2 ⊆ Aut C5×C2080(C5xC20):10C4400,85
(C5×C20)⋊11C4 = Dic5×C20φ: C4/C2C2 ⊆ Aut C5×C2080(C5xC20):11C4400,83
(C5×C20)⋊12C4 = C4×C526C4φ: C4/C2C2 ⊆ Aut C5×C20400(C5xC20):12C4400,99
(C5×C20)⋊13C4 = C4⋊C4×C52φ: C4/C2C2 ⊆ Aut C5×C20400(C5xC20):13C4400,110

Non-split extensions G=N.Q with N=C5×C20 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C5×C20).1C4 = C20.12F5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).1C4400,143
(C5×C20).2C4 = C5×C4.F5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).2C4400,136
(C5×C20).3C4 = C527M4(2)φ: C4/C1C4 ⊆ Aut C5×C20200(C5xC20).3C4400,150
(C5×C20).4C4 = C528M4(2)φ: C4/C1C4 ⊆ Aut C5×C20404(C5xC20).4C4400,157
(C5×C20).5C4 = C5×C5⋊C16φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).5C4400,56
(C5×C20).6C4 = C523C16φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).6C4400,57
(C5×C20).7C4 = C524C16φ: C4/C1C4 ⊆ Aut C5×C20400(C5xC20).7C4400,58
(C5×C20).8C4 = C525C16φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).8C4400,59
(C5×C20).9C4 = C5×D5⋊C8φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).9C4400,135
(C5×C20).10C4 = C20.14F5φ: C4/C1C4 ⊆ Aut C5×C20804(C5xC20).10C4400,142
(C5×C20).11C4 = C20.F5φ: C4/C1C4 ⊆ Aut C5×C20200(C5xC20).11C4400,149
(C5×C20).12C4 = C20.11F5φ: C4/C1C4 ⊆ Aut C5×C20404(C5xC20).12C4400,156
(C5×C20).13C4 = C20.59D10φ: C4/C2C2 ⊆ Aut C5×C20200(C5xC20).13C4400,98
(C5×C20).14C4 = C5×C4.Dic5φ: C4/C2C2 ⊆ Aut C5×C20402(C5xC20).14C4400,82
(C5×C20).15C4 = C5×C52C16φ: C4/C2C2 ⊆ Aut C5×C20802(C5xC20).15C4400,49
(C5×C20).16C4 = C527C16φ: C4/C2C2 ⊆ Aut C5×C20400(C5xC20).16C4400,50
(C5×C20).17C4 = C10×C52C8φ: C4/C2C2 ⊆ Aut C5×C2080(C5xC20).17C4400,81
(C5×C20).18C4 = C2×C527C8φ: C4/C2C2 ⊆ Aut C5×C20400(C5xC20).18C4400,97
(C5×C20).19C4 = M4(2)×C52φ: C4/C2C2 ⊆ Aut C5×C20200(C5xC20).19C4400,112

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