Finite Group Databasebeta

← C₃×C₁₃×D₂₅₇ #34095306

Subgroups — C₃×C₁₃×D₂₅₇ #34095306

Order 20046.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₂₅₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₂₅₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂₅₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₁₃	—	257	1	no	maximal, Hall
9	C₃×C₁₃	D₂₅₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	257	1	no	Hall
11	C₁₃	C₃×D₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	257	1	no	Hall
13	C₃	C₁₃×D₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	257	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₂₅₇
commutator, cosocle, hypocenter	C₂₅₇	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₂₅₇	C₂
LCS	G ▷ C₂₅₇
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₂₅₇	C₂	semidirect
2. C₁₃×D₂₅₇	C₃	direct (N × H)
3. C₁₃×C₂₅₇	C₂×C₃	semidirect
4. C₃×D₂₅₇	C₁₃	direct (N × H)
5. C₃×C₂₅₇	C₂×C₁₃	semidirect
6. D₂₅₇	C₃×C₁₃	direct (N × H)
7. C₂₅₇	C₂×C₃×C₁₃	semidirect
9. C₃×C₁₃	D₂₅₇	direct (N × H)
11. C₁₃	C₃×D₂₅₇	direct (N × H)
13. C₃	C₁₃×D₂₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃×C₂₅₇	2
C₁₃×D₂₅₇	3
C₃×D₂₅₇	13
C₂×C₃×C₁₃	257