Extensions 1→N→G→Q→1 with N=C5×C10 and Q=C22

Direct product G=N×Q with N=C5×C10 and Q=C22
dρLabelID
C2×C102200C2xC10^2200,52

Semidirect products G=N:Q with N=C5×C10 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C5×C10)⋊C22 = C2×D52φ: C22/C1C22 ⊆ Aut C5×C10204+(C5xC10):C2^2200,49
(C5×C10)⋊2C22 = D5×C2×C10φ: C22/C2C2 ⊆ Aut C5×C1040(C5xC10):2C2^2200,50
(C5×C10)⋊3C22 = C22×C5⋊D5φ: C22/C2C2 ⊆ Aut C5×C10100(C5xC10):3C2^2200,51

Non-split extensions G=N.Q with N=C5×C10 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C5×C10).1C22 = D5×Dic5φ: C22/C1C22 ⊆ Aut C5×C10404-(C5xC10).1C2^2200,22
(C5×C10).2C22 = Dic52D5φ: C22/C1C22 ⊆ Aut C5×C10204+(C5xC10).2C2^2200,23
(C5×C10).3C22 = C522D4φ: C22/C1C22 ⊆ Aut C5×C10404-(C5xC10).3C2^2200,24
(C5×C10).4C22 = C5⋊D20φ: C22/C1C22 ⊆ Aut C5×C10204+(C5xC10).4C2^2200,25
(C5×C10).5C22 = C522Q8φ: C22/C1C22 ⊆ Aut C5×C10404-(C5xC10).5C2^2200,26
(C5×C10).6C22 = C5×Dic10φ: C22/C2C2 ⊆ Aut C5×C10402(C5xC10).6C2^2200,27
(C5×C10).7C22 = D5×C20φ: C22/C2C2 ⊆ Aut C5×C10402(C5xC10).7C2^2200,28
(C5×C10).8C22 = C5×D20φ: C22/C2C2 ⊆ Aut C5×C10402(C5xC10).8C2^2200,29
(C5×C10).9C22 = C10×Dic5φ: C22/C2C2 ⊆ Aut C5×C1040(C5xC10).9C2^2200,30
(C5×C10).10C22 = C5×C5⋊D4φ: C22/C2C2 ⊆ Aut C5×C10202(C5xC10).10C2^2200,31
(C5×C10).11C22 = C524Q8φ: C22/C2C2 ⊆ Aut C5×C10200(C5xC10).11C2^2200,32
(C5×C10).12C22 = C4×C5⋊D5φ: C22/C2C2 ⊆ Aut C5×C10100(C5xC10).12C2^2200,33
(C5×C10).13C22 = C20⋊D5φ: C22/C2C2 ⊆ Aut C5×C10100(C5xC10).13C2^2200,34
(C5×C10).14C22 = C2×C526C4φ: C22/C2C2 ⊆ Aut C5×C10200(C5xC10).14C2^2200,35
(C5×C10).15C22 = C527D4φ: C22/C2C2 ⊆ Aut C5×C10100(C5xC10).15C2^2200,36
(C5×C10).16C22 = D4×C52central extension (φ=1)100(C5xC10).16C2^2200,38
(C5×C10).17C22 = Q8×C52central extension (φ=1)200(C5xC10).17C2^2200,39

׿
×
𝔽