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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×C10

Direct product G=N×Q with N=C2×C6 and Q=C2×C10
dρLabelID
C23×C30240C2^3xC30240,208

Semidirect products G=N:Q with N=C2×C6 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(C2×C10) = C5×S3×D4φ: C2×C10/C5 → C22 ⊆ Aut C2×C6604(C2xC6):(C2xC10)240,169
(C2×C6)⋊2(C2×C10) = D4×C30φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6):2(C2xC10)240,186
(C2×C6)⋊3(C2×C10) = C10×C3⋊D4φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6):3(C2xC10)240,174
(C2×C6)⋊4(C2×C10) = S3×C22×C10φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6):4(C2xC10)240,206

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C2×C6).(C2×C10) = C5×D4⋊2S3φ: C2×C10/C5 → C22 ⊆ Aut C2×C61204(C2xC6).(C2xC10)240,170
(C2×C6).2(C2×C10) = C15×C4○D4φ: C2×C10/C10 → C2 ⊆ Aut C2×C61202(C2xC6).2(C2xC10)240,188
(C2×C6).3(C2×C10) = Dic3×C20φ: C2×C10/C10 → C2 ⊆ Aut C2×C6240(C2xC6).3(C2xC10)240,56
(C2×C6).4(C2×C10) = C5×Dic3⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C6240(C2xC6).4(C2xC10)240,57
(C2×C6).5(C2×C10) = C5×C4⋊Dic3φ: C2×C10/C10 → C2 ⊆ Aut C2×C6240(C2xC6).5(C2xC10)240,58
(C2×C6).6(C2×C10) = C5×D6⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6).6(C2xC10)240,59
(C2×C6).7(C2×C10) = C5×C6.D4φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6).7(C2xC10)240,64
(C2×C6).8(C2×C10) = C10×Dic6φ: C2×C10/C10 → C2 ⊆ Aut C2×C6240(C2xC6).8(C2xC10)240,165
(C2×C6).9(C2×C10) = S3×C2×C20φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6).9(C2xC10)240,166
(C2×C6).10(C2×C10) = C10×D12φ: C2×C10/C10 → C2 ⊆ Aut C2×C6120(C2xC6).10(C2xC10)240,167
(C2×C6).11(C2×C10) = C5×C4○D12φ: C2×C10/C10 → C2 ⊆ Aut C2×C61202(C2xC6).11(C2xC10)240,168
(C2×C6).12(C2×C10) = Dic3×C2×C10φ: C2×C10/C10 → C2 ⊆ Aut C2×C6240(C2xC6).12(C2xC10)240,173
(C2×C6).13(C2×C10) = C15×C22⋊C4central extension (φ=1)120(C2xC6).13(C2xC10)240,82
(C2×C6).14(C2×C10) = C15×C4⋊C4central extension (φ=1)240(C2xC6).14(C2xC10)240,83
(C2×C6).15(C2×C10) = Q8×C30central extension (φ=1)240(C2xC6).15(C2xC10)240,187

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