# Extensions 1→N→G→Q→1 with N=C5×C10 and Q=D5

Direct product G=N×Q with N=C5×C10 and Q=D5
dρLabelID
D5×C5×C10100D5xC5xC10500,53

Semidirect products G=N:Q with N=C5×C10 and Q=D5
extensionφ:Q→Aut NdρLabelID
(C5×C10)⋊1D5 = C2×C52⋊C10φ: D5/C1D5 ⊆ Aut C5×C105010+(C5xC10):1D5500,30
(C5×C10)⋊2D5 = C2×He5⋊C2φ: D5/C1D5 ⊆ Aut C5×C10505(C5xC10):2D5500,33
(C5×C10)⋊3D5 = C10×C5⋊D5φ: D5/C5C2 ⊆ Aut C5×C10100(C5xC10):3D5500,54
(C5×C10)⋊4D5 = C2×C53⋊C2φ: D5/C5C2 ⊆ Aut C5×C10250(C5xC10):4D5500,55

Non-split extensions G=N.Q with N=C5×C10 and Q=D5
extensionφ:Q→Aut NdρLabelID
(C5×C10).1D5 = He55C4φ: D5/C1D5 ⊆ Aut C5×C1010010-(C5xC10).1D5500,8
(C5×C10).2D5 = C50.C10φ: D5/C1D5 ⊆ Aut C5×C1010010-(C5xC10).2D5500,9
(C5×C10).3D5 = He56C4φ: D5/C1D5 ⊆ Aut C5×C101005(C5xC10).3D5500,11
(C5×C10).4D5 = C2×C25⋊C10φ: D5/C1D5 ⊆ Aut C5×C105010+(C5xC10).4D5500,31
(C5×C10).5D5 = C5×Dic25φ: D5/C5C2 ⊆ Aut C5×C101002(C5xC10).5D5500,6
(C5×C10).6D5 = C50.D5φ: D5/C5C2 ⊆ Aut C5×C10500(C5xC10).6D5500,10
(C5×C10).7D5 = C10×D25φ: D5/C5C2 ⊆ Aut C5×C101002(C5xC10).7D5500,28
(C5×C10).8D5 = C2×C25⋊D5φ: D5/C5C2 ⊆ Aut C5×C10250(C5xC10).8D5500,32
(C5×C10).9D5 = C5×C526C4φ: D5/C5C2 ⊆ Aut C5×C10100(C5xC10).9D5500,38
(C5×C10).10D5 = C5312C4φ: D5/C5C2 ⊆ Aut C5×C10500(C5xC10).10D5500,39
(C5×C10).11D5 = Dic5×C52central extension (φ=1)100(C5xC10).11D5500,37

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