Finite Group Databasebeta

← C₂×C₁₃×D₄₅₇ #37557719

Subgroups — C₂×C₁₃×D₄₅₇ #37557719

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	C₁₃×D₄₅₇	C₂	1	2	yes	maximal, direct product factor
3	C₁₃×C₄₅₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₄₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₄₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented
6	D₄₅₇	C₂×C₁₃	1	2	yes	direct product factor
7	C₄₅₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₁₃	—	457	1	no	maximal, Hall
9	C₂×C₁₃	—	457	2	no	—
10	C₂×C₁₃	D₄₅₇	1	1	yes	characteristic, direct product factor
11	C₁₃	C₂×D₄₅₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²	—	457	1	no	Sylow
13	C₂	—	457	2	no	—
14	C₂	C₁₃×D₄₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₄₅₇
commutator, cosocle, hypocenter	C₄₅₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₄₅₇	C₂
LCS	G ▷ C₄₅₇
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₄₅₇	C₂	semidirect
2. C₁₃×D₄₅₇	C₂	direct (N × H)
3. C₁₃×C₄₅₇	C₂²	semidirect
4. C₂×D₄₅₇	C₁₃	direct (N × H)
5. C₂×C₄₅₇	C₂×C₁₃	semidirect
6. D₄₅₇	C₂×C₁₃	direct (N × H)
7. C₄₅₇	C₂²×C₁₃	semidirect
10. C₂×C₁₃	D₄₅₇	direct (N × H)
11. C₁₃	C₂×D₄₅₇	direct (N × H)
14. C₂	C₁₃×D₄₅₇	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
C₁₃×D₄₅₇	2
C₂×D₄₅₇	13
C₂²×C₁₃	457