# Extensions 1→N→G→Q→1 with N=C5×C10 and Q=C4

Direct product G=N×Q with N=C5×C10 and Q=C4
dρLabelID
C10×C20200C10xC20200,37

Semidirect products G=N:Q with N=C5×C10 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C5×C10)⋊1C4 = C10×F5φ: C4/C1C4 ⊆ Aut C5×C10404(C5xC10):1C4200,45
(C5×C10)⋊2C4 = C2×D5.D5φ: C4/C1C4 ⊆ Aut C5×C10404(C5xC10):2C4200,46
(C5×C10)⋊3C4 = C2×C5⋊F5φ: C4/C1C4 ⊆ Aut C5×C1050(C5xC10):3C4200,47
(C5×C10)⋊4C4 = C2×C52⋊C4φ: C4/C1C4 ⊆ Aut C5×C10204+(C5xC10):4C4200,48
(C5×C10)⋊5C4 = C10×Dic5φ: C4/C2C2 ⊆ Aut C5×C1040(C5xC10):5C4200,30
(C5×C10)⋊6C4 = C2×C526C4φ: C4/C2C2 ⊆ Aut C5×C10200(C5xC10):6C4200,35

Non-split extensions G=N.Q with N=C5×C10 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C5×C10).1C4 = C5×C5⋊C8φ: C4/C1C4 ⊆ Aut C5×C10404(C5xC10).1C4200,18
(C5×C10).2C4 = C523C8φ: C4/C1C4 ⊆ Aut C5×C10404(C5xC10).2C4200,19
(C5×C10).3C4 = C524C8φ: C4/C1C4 ⊆ Aut C5×C10200(C5xC10).3C4200,20
(C5×C10).4C4 = C525C8φ: C4/C1C4 ⊆ Aut C5×C10404-(C5xC10).4C4200,21
(C5×C10).5C4 = C5×C52C8φ: C4/C2C2 ⊆ Aut C5×C10402(C5xC10).5C4200,15
(C5×C10).6C4 = C527C8φ: C4/C2C2 ⊆ Aut C5×C10200(C5xC10).6C4200,16

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