# Extensions 1→N→G→Q→1 with N=C5×C3⋊S3 and Q=C22

Direct product G=N×Q with N=C5×C3⋊S3 and Q=C22
dρLabelID
C3⋊S3×C2×C10180C3:S3xC2xC10360,160

Semidirect products G=N:Q with N=C5×C3⋊S3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C5×C3⋊S3)⋊C22 = S32×D5φ: C22/C1C22 ⊆ Out C5×C3⋊S3308+(C5xC3:S3):C2^2360,137
(C5×C3⋊S3)⋊2C22 = C2×D5×C3⋊S3φ: C22/C2C2 ⊆ Out C5×C3⋊S390(C5xC3:S3):2C2^2360,152
(C5×C3⋊S3)⋊3C22 = C2×D15⋊S3φ: C22/C2C2 ⊆ Out C5×C3⋊S3604(C5xC3:S3):3C2^2360,155
(C5×C3⋊S3)⋊4C22 = S32×C10φ: C22/C2C2 ⊆ Out C5×C3⋊S3604(C5xC3:S3):4C2^2360,153

Non-split extensions G=N.Q with N=C5×C3⋊S3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C5×C3⋊S3).1C22 = D5×C32⋊C4φ: C22/C1C22 ⊆ Out C5×C3⋊S3308+(C5xC3:S3).1C2^2360,130
(C5×C3⋊S3).2C22 = S32⋊D5φ: C22/C1C22 ⊆ Out C5×C3⋊S3304(C5xC3:S3).2C2^2360,133
(C5×C3⋊S3).3C22 = C32⋊D20φ: C22/C1C22 ⊆ Out C5×C3⋊S3308+(C5xC3:S3).3C2^2360,134
(C5×C3⋊S3).4C22 = C5×S3≀C2φ: C22/C1C22 ⊆ Out C5×C3⋊S3304(C5xC3:S3).4C2^2360,132
(C5×C3⋊S3).5C22 = C5×PSU3(𝔽2)φ: C22/C1C22 ⊆ Out C5×C3⋊S3458(C5xC3:S3).5C2^2360,135
(C5×C3⋊S3).6C22 = C32⋊Dic10φ: C22/C1C22 ⊆ Out C5×C3⋊S3458(C5xC3:S3).6C2^2360,136
(C5×C3⋊S3).7C22 = C10×C32⋊C4φ: C22/C2C2 ⊆ Out C5×C3⋊S3604(C5xC3:S3).7C2^2360,148
(C5×C3⋊S3).8C22 = C2×C32⋊Dic5φ: C22/C2C2 ⊆ Out C5×C3⋊S3604(C5xC3:S3).8C2^2360,149

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