Finite Group Databasebeta

← C₇×C₁₁×C₁₃₉ #24924171

Subgroups — C₇×C₁₁×C₁₃₉ #24924171

Order 10703.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₇×C₁₃₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃₉	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
4	C₇×C₁₁	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁	C₇×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₇	C₁₁×C₁₃₉	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. C₁₁×C₁₃₉	C₇	direct (N × H)
2. C₇×C₁₃₉	C₁₁	direct (N × H)
3. C₁₃₉	C₇×C₁₁	direct (N × H)
4. C₇×C₁₁	C₁₃₉	direct (N × H)
5. C₁₁	C₇×C₁₃₉	direct (N × H)
6. C₇	C₁₁×C₁₃₉	direct (N × H)