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Extensions 1→N→G→Q→1 with N=D5×C2×C6 and Q=C4

Direct product G=N×Q with N=D5×C2×C6 and Q=C4
dρLabelID
D5×C22×C12240D5xC2^2xC12480,1136

Semidirect products G=N:Q with N=D5×C2×C6 and Q=C4
extensionφ:Q→Out NdρLabelID
(D5×C2×C6)⋊1C4 = (C2×C6).D20φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6):1C4480,71
(D5×C2×C6)⋊2C4 = C3×C23.1D10φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6):2C4480,84
(D5×C2×C6)⋊3C4 = (C2×C60)⋊C4φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6):3C4480,304
(D5×C2×C6)⋊4C4 = C3×D10.D4φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6):4C4480,279
(D5×C2×C6)⋊5C4 = C2×D10⋊Dic3φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6):5C4480,611
(D5×C2×C6)⋊6C4 = D5×C6.D4φ: C4/C2 → C2 ⊆ Out D5×C2×C6120(D5xC2xC6):6C4480,623
(D5×C2×C6)⋊7C4 = C22×D5×Dic3φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6):7C4480,1112
(D5×C2×C6)⋊8C4 = C3×D5×C22⋊C4φ: C4/C2 → C2 ⊆ Out D5×C2×C6120(D5xC2xC6):8C4480,673
(D5×C2×C6)⋊9C4 = C6×D10⋊C4φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6):9C4480,720
(D5×C2×C6)⋊10C4 = C2×D10.D6φ: C4/C2 → C2 ⊆ Out D5×C2×C6120(D5xC2xC6):10C4480,1072
(D5×C2×C6)⋊11C4 = C23×C3⋊F5φ: C4/C2 → C2 ⊆ Out D5×C2×C6120(D5xC2xC6):11C4480,1206
(D5×C2×C6)⋊12C4 = C6×C22⋊F5φ: C4/C2 → C2 ⊆ Out D5×C2×C6120(D5xC2xC6):12C4480,1059
(D5×C2×C6)⋊13C4 = F5×C22×C6φ: C4/C2 → C2 ⊆ Out D5×C2×C6120(D5xC2xC6):13C4480,1205

Non-split extensions G=N.Q with N=D5×C2×C6 and Q=C4
extensionφ:Q→Out NdρLabelID
(D5×C2×C6).1C4 = C60.28D4φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6).1C4480,34
(D5×C2×C6).2C4 = C3×C20.46D4φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6).2C4480,101
(D5×C2×C6).3C4 = C5⋊(C12.D4)φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6).3C4480,318
(D5×C2×C6).4C4 = C3×C23.F5φ: C4/C1 → C4 ⊆ Out D5×C2×C61204(D5xC2xC6).4C4480,293
(D5×C2×C6).5C4 = C60.93D4φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).5C4480,31
(D5×C2×C6).6C4 = C2×D5×C3⋊C8φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).6C4480,357
(D5×C2×C6).7C4 = D5×C4.Dic3φ: C4/C2 → C2 ⊆ Out D5×C2×C61204(D5xC2xC6).7C4480,358
(D5×C2×C6).8C4 = C2×C20.32D6φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).8C4480,369
(D5×C2×C6).9C4 = C3×D10⋊1C8φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).9C4480,98
(D5×C2×C6).10C4 = C6×C8⋊D5φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).10C4480,693
(D5×C2×C6).11C4 = C3×D5×M4(2)φ: C4/C2 → C2 ⊆ Out D5×C2×C61204(D5xC2xC6).11C4480,699
(D5×C2×C6).12C4 = C30.7M4(2)φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).12C4480,308
(D5×C2×C6).13C4 = C2×C60.C4φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).13C4480,1060
(D5×C2×C6).14C4 = C2×C12.F5φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).14C4480,1061
(D5×C2×C6).15C4 = C60.59(C2×C4)φ: C4/C2 → C2 ⊆ Out D5×C2×C61204(D5xC2xC6).15C4480,1062
(D5×C2×C6).16C4 = C3×D10⋊C8φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).16C4480,283
(D5×C2×C6).17C4 = C6×D5⋊C8φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).17C4480,1047
(D5×C2×C6).18C4 = C6×C4.F5φ: C4/C2 → C2 ⊆ Out D5×C2×C6240(D5xC2xC6).18C4480,1048
(D5×C2×C6).19C4 = C3×D5⋊M4(2)φ: C4/C2 → C2 ⊆ Out D5×C2×C61204(D5xC2xC6).19C4480,1049
(D5×C2×C6).20C4 = D5×C2×C24φ: trivial image240(D5xC2xC6).20C4480,692

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