Finite Group Databasebeta

← C₇×C₁₃×D₁₃₇ #38735513

Subgroups — C₇×C₁₃×D₁₃₇ #38735513

Order 24934.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×D₁₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₁₃₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₃₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₁₃₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₇×C₁₃	—	137	1	no	maximal, Hall
8	C₁₃₇	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₇×C₁₃	D₁₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	137	1	no	Hall
11	C₂×C₇	—	137	1	no	Hall
12	C₁₃	C₇×D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₁₃×D₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	137	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₁₃₇
commutator, cosocle, hypocenter	C₁₃₇	C₂×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₃₇	C₂
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₁₃₇	C₂	semidirect
2. C₁₃×D₁₃₇	C₇	direct (N × H)
3. C₇×D₁₃₇	C₁₃	direct (N × H)
4. C₁₃×C₁₃₇	C₂×C₇	semidirect
5. C₇×C₁₃₇	C₂×C₁₃	semidirect
6. D₁₃₇	C₇×C₁₃	direct (N × H)
8. C₁₃₇	C₂×C₇×C₁₃	semidirect
9. C₇×C₁₃	D₁₃₇	direct (N × H)
12. C₁₃	C₇×D₁₃₇	direct (N × H)
13. C₇	C₁₃×D₁₃₇	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×C₁₃×C₁₃₇	2
C₁₃×D₁₃₇	7
C₇×D₁₃₇	13
C₂×C₇×C₁₃	137