Finite Group Databasebeta

← C₅×C₁₃×D₁₅₇ #35205254

Subgroups — C₅×C₁₃×D₁₅₇ #35205254

Order 20410.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₁₅₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₁₅₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₁₅₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×C₁₃	—	157	1	no	maximal, Hall
9	C₅×C₁₃	D₁₅₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	157	1	no	Hall
11	C₁₃	C₅×D₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	157	1	no	Hall
13	C₅	C₁₃×D₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	157	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₁₅₇
commutator, cosocle, hypocenter	C₁₅₇	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₅₇	C₂
LCS	G ▷ C₁₅₇
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₁₅₇	C₂	semidirect
2. C₁₃×D₁₅₇	C₅	direct (N × H)
3. C₁₃×C₁₅₇	C₂×C₅	semidirect
4. C₅×D₁₅₇	C₁₃	direct (N × H)
5. C₅×C₁₅₇	C₂×C₁₃	semidirect
6. D₁₅₇	C₅×C₁₃	direct (N × H)
7. C₁₅₇	C₂×C₅×C₁₃	semidirect
9. C₅×C₁₃	D₁₅₇	direct (N × H)
11. C₁₃	C₅×D₁₅₇	direct (N × H)
13. C₅	C₁₃×D₁₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₁₅₇	2
C₁₃×D₁₅₇	5
C₅×D₁₅₇	13
C₂×C₅×C₁₃	157