Finite Group Databasebeta

← C₂×C₇×C₁₃₁⋊C₁₃ #37558639

Subgroups — C₂×C₇×C₁₃₁⋊C₁₃ #37558639

Order 23842.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃₁⋊C₁₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃₁⋊C₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₇×C₁₃₁	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃₁⋊C₁₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
5	C₇×C₁₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃₁	C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₁₃	—	131	1	no	maximal, Hall
8	C₁₃₁	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₇×C₁₃	—	131	1	no	Hall
10	C₂×C₁₃	—	131	1	no	Hall
11	C₂×C₇	C₁₃₁⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃	—	131	1	no	Sylow
13	C₇	C₂×C₁₃₁⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₇×C₁₃₁⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	C₁₃₁⋊C₁₃
commutator, cosocle, hypocenter	C₁₃₁	C₂×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃₁	C₁₃
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃₁⋊C₁₃	C₂	direct (N × H)
2. C₂×C₁₃₁⋊C₁₃	C₇	direct (N × H)
3. C₂×C₇×C₁₃₁	C₁₃	semidirect
4. C₁₃₁⋊C₁₃	C₂×C₇	direct (N × H)
5. C₇×C₁₃₁	C₂×C₁₃	semidirect
6. C₂×C₁₃₁	C₇×C₁₃	semidirect
8. C₁₃₁	C₂×C₇×C₁₃	semidirect
11. C₂×C₇	C₁₃₁⋊C₁₃	direct (N × H)
13. C₇	C₂×C₁₃₁⋊C₁₃	direct (N × H)
14. C₂	C₇×C₁₃₁⋊C₁₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×C₁₃₁⋊C₁₃	2
C₂×C₁₃₁⋊C₁₃	7
C₂×C₇×C₁₃₁	13
C₂×C₇×C₁₃	131