# Extensions 1→N→G→Q→1 with N=C5×SL2(𝔽3) and Q=C22

Direct product G=N×Q with N=C5×SL2(𝔽3) and Q=C22
dρLabelID
C2×C10×SL2(𝔽3)160C2xC10xSL(2,3)480,1128

Semidirect products G=N:Q with N=C5×SL2(𝔽3) and Q=C22
extensionφ:Q→Out NdρLabelID
(C5×SL2(𝔽3))⋊1C22 = GL2(𝔽3)⋊D5φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)804+(C5xSL(2,3)):1C2^2480,970
(C5×SL2(𝔽3))⋊2C22 = D5×GL2(𝔽3)φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)404(C5xSL(2,3)):2C2^2480,974
(C5×SL2(𝔽3))⋊3C22 = C2×Q8⋊D15φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)80(C5xSL(2,3)):3C2^2480,1028
(C5×SL2(𝔽3))⋊4C22 = C20.3S4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804+(C5xSL(2,3)):4C2^2480,1032
(C5×SL2(𝔽3))⋊5C22 = C2×Dic5.A4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)160(C5xSL(2,3)):5C2^2480,1038
(C5×SL2(𝔽3))⋊6C22 = C2×D5×SL2(𝔽3)φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)80(C5xSL(2,3)):6C2^2480,1039
(C5×SL2(𝔽3))⋊7C22 = Dic10.A4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)1204+(C5xSL(2,3)):7C2^2480,1041
(C5×SL2(𝔽3))⋊8C22 = D5×C4.A4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)):8C2^2480,1042
(C5×SL2(𝔽3))⋊9C22 = C10×GL2(𝔽3)φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)80(C5xSL(2,3)):9C2^2480,1017
(C5×SL2(𝔽3))⋊10C22 = C5×C4.3S4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)):10C2^2480,1021
(C5×SL2(𝔽3))⋊11C22 = C10×C4.A4φ: trivial image160(C5xSL(2,3)):11C2^2480,1130
(C5×SL2(𝔽3))⋊12C22 = C5×Q8.A4φ: trivial image1204(C5xSL(2,3)):12C2^2480,1131

Non-split extensions G=N.Q with N=C5×SL2(𝔽3) and Q=C22
extensionφ:Q→Out NdρLabelID
(C5×SL2(𝔽3)).1C22 = CSU2(𝔽3)⋊D5φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)1604(C5xSL(2,3)).1C2^2480,967
(C5×SL2(𝔽3)).2C22 = Dic5.6S4φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)).2C2^2480,968
(C5×SL2(𝔽3)).3C22 = Dic5.7S4φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)804+(C5xSL(2,3)).3C2^2480,969
(C5×SL2(𝔽3)).4C22 = D5×CSU2(𝔽3)φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)804-(C5xSL(2,3)).4C2^2480,971
(C5×SL2(𝔽3)).5C22 = D10.1S4φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)804-(C5xSL(2,3)).5C2^2480,972
(C5×SL2(𝔽3)).6C22 = D10.2S4φ: C22/C1C22 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)).6C2^2480,973
(C5×SL2(𝔽3)).7C22 = C2×Q8.D15φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)160(C5xSL(2,3)).7C2^2480,1027
(C5×SL2(𝔽3)).8C22 = Q8.D30φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)).8C2^2480,1029
(C5×SL2(𝔽3)).9C22 = C20.2S4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)1604-(C5xSL(2,3)).9C2^2480,1030
(C5×SL2(𝔽3)).10C22 = C20.6S4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)).10C2^2480,1031
(C5×SL2(𝔽3)).11C22 = SL2(𝔽3).11D10φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)).11C2^2480,1040
(C5×SL2(𝔽3)).12C22 = D20.A4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804-(C5xSL(2,3)).12C2^2480,1043
(C5×SL2(𝔽3)).13C22 = C10×CSU2(𝔽3)φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)160(C5xSL(2,3)).13C2^2480,1016
(C5×SL2(𝔽3)).14C22 = C5×Q8.D6φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)804(C5xSL(2,3)).14C2^2480,1018
(C5×SL2(𝔽3)).15C22 = C5×C4.S4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)1604(C5xSL(2,3)).15C2^2480,1019
(C5×SL2(𝔽3)).16C22 = C5×C4.6S4φ: C22/C2C2 ⊆ Out C5×SL2(𝔽3)802(C5xSL(2,3)).16C2^2480,1020
(C5×SL2(𝔽3)).17C22 = C5×D4.A4φ: trivial image804(C5xSL(2,3)).17C2^2480,1132

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