Finite Group Databasebeta

← C₅×C₁₉×C₁₂₇ #27130470

Subgroups — C₅×C₁₉×C₁₂₇ #27130470

Order 12065.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₁₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₁₂₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₂₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
4	C₅×C₁₉	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉	C₅×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	C₁₉×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×C₁₂₇	C₅	direct (N × H)
2. C₅×C₁₂₇	C₁₉	direct (N × H)
3. C₁₂₇	C₅×C₁₉	direct (N × H)
4. C₅×C₁₉	C₁₂₇	direct (N × H)
5. C₁₉	C₅×C₁₂₇	direct (N × H)
6. C₅	C₁₉×C₁₂₇	direct (N × H)