Finite Group Databasebeta

← C₂×D₉₅₅₇ #50304635

Subgroups — C₂×D₉₅₅₇ #50304635

Order 38228.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₅₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉₅₅₇	C₂	1	2	yes	maximal, direct product factor
3	C₁₉×C₅₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅₀₃	—	19	1	no	maximal, Hall
5	C₂×C₅₀₃	D₁₉	1	1	yes	characteristic, complemented
6	D₅₀₃	—	19	2	no	—
7	C₅₀₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₁₉	—	503	1	no	maximal, Hall
9	C₂×C₁₉	D₅₀₃	1	1	yes	characteristic, complemented
10	D₁₉	—	503	2	no	—
11	C₁₉	C₂×D₅₀₃	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	9557	1	no	Sylow
13	C₂	—	9557	2	no	—
14	C₂	D₉₅₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉₅₅₇
commutator, cosocle, hypocenter	C₁₉×C₅₀₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₅₀₃	C₂
LCS	G ▷ C₁₉×C₅₀₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₅₀₃	C₂	semidirect
2. D₉₅₅₇	C₂	direct (N × H)
3. C₁₉×C₅₀₃	C₂²	semidirect
5. C₂×C₅₀₃	D₁₉	semidirect
7. C₅₀₃	C₂×D₁₉	semidirect
9. C₂×C₁₉	D₅₀₃	semidirect
11. C₁₉	C₂×D₅₀₃	semidirect
14. C₂	D₉₅₅₇	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×C₁₉×C₅₀₃	2
D₉₅₅₇	2
C₂×D₅₀₃	19
C₂×D₁₉	503