Finite Group Databasebeta

← C₂×D₁₃₀₁⋊C₅ #39907310

Subgroups — C₂×D₁₃₀₁⋊C₅ #39907310

Order 26020.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃₀₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃₀₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₁₃₀₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₃₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₃₀₁	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₃₀₁	C₂×C₅	1	2	yes	complemented
7	C₁₃₀₁	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₅	—	1301	1	no	maximal, Hall
9	C₂×C₅	—	1301	2	no	—
10	C₂×C₅	—	1301	1	no	—
11	C₅	—	1301	1	no	Sylow
12	C₂²	—	6505	1	no	Sylow
13	C₂	—	6505	2	no	—
14	C₂	D₁₃₀₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₃₀₁⋊C₅
commutator, cosocle, hypocenter	C₁₃₀₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₃₀₁	C₂×C₅
LCS	G ▷ C₁₃₀₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃₀₁⋊C₅	C₂	semidirect
2. D₁₃₀₁⋊C₅	C₂	direct (N × H)
3. C₁₃₀₁⋊C₅	C₂²	semidirect
4. C₂×D₁₃₀₁	C₅	semidirect
5. C₂×C₁₃₀₁	C₂×C₅	semidirect
6. D₁₃₀₁	C₂×C₅	semidirect
7. C₁₃₀₁	C₂²×C₅	semidirect
14. C₂	D₁₃₀₁⋊C₅	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×C₁₃₀₁⋊C₅	2
D₁₃₀₁⋊C₅	2
C₂×D₁₃₀₁	5
C₂²×C₅	1301