Finite Group Databasebeta

← C₂×D₁₃×C₄₅₇ #37557720

Subgroups — C₂×D₁₃×C₄₅₇ #37557720

Order 23764.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×C₄₅₇	C₂	1	2	yes	maximal, direct product factor
3	C₁₃×C₄₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₄₅₇	—	13	1	no	maximal, Hall
5	C₂×C₄₅₇	—	13	2	no	—
6	C₂×C₄₅₇	D₁₃	1	1	yes	characteristic, direct product factor
7	C₄₅₇	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×D₁₃	C₄₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₃	C₂×C₄₅₇	1	1	yes	characteristic, complemented
10	D₁₃	C₂×C₄₅₇	1	2	yes	direct product factor
11	C₁₃	C₂²×C₄₅₇	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	13	1	no	Sylow
13	C₂	—	13	2	no	—
14	C₂	D₁₃×C₄₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₅₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₄₅₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₄₅₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄₅₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₄₅₇	C₂	semidirect
2. D₁₃×C₄₅₇	C₂	direct (N × H)
3. C₁₃×C₄₅₇	C₂²	semidirect
6. C₂×C₄₅₇	D₁₃	direct (N × H)
7. C₄₅₇	C₂×D₁₃	direct (N × H)
8. C₂×D₁₃	C₄₅₇	direct (N × H)
9. C₂×C₁₃	C₂×C₄₅₇	semidirect
10. D₁₃	C₂×C₄₅₇	direct (N × H)
11. C₁₃	C₂²×C₄₅₇	semidirect
14. C₂	D₁₃×C₄₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×C₄₅₇	2
D₁₃×C₄₅₇	2
C₂²×C₄₅₇	13
C₂×D₁₃	457