Finite Group Databasebeta

← C₁₃×D₁₀₃₇ #41004046

Subgroups — C₁₃×D₁₀₃₇ #41004046

Order 26962.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₃₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×D₆₁	—	17	1	no	maximal, Hall
4	C₁₇×C₆₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₆₁	D₁₇	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₁₇	—	61	1	no	maximal, Hall
7	C₁₃×C₁₇	D₆₁	1	1	yes	characteristic, complemented, Hall
8	D₆₁	—	17	1	no	Hall
9	C₆₁	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
10	D₁₇	—	61	1	no	Hall
11	C₂×C₁₃	—	1037	1	no	Hall
12	C₁₇	C₁₃×D₆₁	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	D₁₀₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	1037	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₁₀₃₇
commutator, cosocle, hypocenter	C₁₇×C₆₁	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₆₁	C₂
LCS	G ▷ C₁₇×C₆₁
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₆₁	C₂	semidirect
2. D₁₀₃₇	C₁₃	direct (N × H)
4. C₁₇×C₆₁	C₂×C₁₃	semidirect
5. C₁₃×C₆₁	D₁₇	semidirect
7. C₁₃×C₁₇	D₆₁	semidirect
9. C₆₁	C₁₃×D₁₇	semidirect
12. C₁₇	C₁₃×D₆₁	semidirect
13. C₁₃	D₁₀₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₇×C₆₁	2
D₁₀₃₇	13
C₁₃×D₆₁	17
C₁₃×D₁₇	61