Finite Group Databasebeta

← C₁₃×D₇×C₁₃₁ #37558643

Subgroups — C₁₃×D₇×C₁₃₁ #37558643

Order 23842.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃×C₁₃₁	—	7	1	no	maximal, Hall
3	D₇×C₁₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₁₃₁	D₇	1	1	yes	characteristic, direct product factor, Hall
5	C₇×C₁₃₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃₁	—	7	1	no	Hall
7	C₁₃×D₇	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃₁	C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₇×C₁₃	C₂×C₁₃₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	—	7	1	no	Hall
11	D₇	C₁₃×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃	D₇×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₂×C₁₃×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₃₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₃×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₃×C₁₃₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₁₃₁	C₂	semidirect
3. D₇×C₁₃₁	C₁₃	direct (N × H)
4. C₁₃×C₁₃₁	D₇	direct (N × H)
5. C₇×C₁₃₁	C₂×C₁₃	semidirect
7. C₁₃×D₇	C₁₃₁	direct (N × H)
8. C₁₃₁	C₁₃×D₇	direct (N × H)
9. C₇×C₁₃	C₂×C₁₃₁	semidirect
11. D₇	C₁₃×C₁₃₁	direct (N × H)
12. C₁₃	D₇×C₁₃₁	direct (N × H)
13. C₇	C₂×C₁₃×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₁₃₁	2
C₂×C₁₃×C₁₃₁	7
D₇×C₁₃₁	13
C₁₃×D₇	131