Finite Group Databasebeta

← C₂²×C₅₇₁⋊C₅ #26037656

Subgroups — C₂²×C₅₇₁⋊C₅ #26037656

Order 11420.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₇₁⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₅₇₁⋊C₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₅₇₁	C₂×C₅	1	3	yes	complemented
5	C₅₇₁	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
6	C₂²×C₅	—	571	1	no	maximal, Hall
7	C₂×C₅	—	571	3	no	—
8	C₅	—	571	1	no	Sylow
9	C₂²	C₅₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₂×C₅₇₁⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₅₇₁⋊C₅
commutator, cosocle, hypocenter	C₅₇₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅₇₁	C₅
LCS	G ▷ C₅₇₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₇₁⋊C₅	C₂	direct (N × H)
2. C₅₇₁⋊C₅	C₂²	direct (N × H)
3. C₂²×C₅₇₁	C₅	semidirect
4. C₂×C₅₇₁	C₂×C₅	semidirect
5. C₅₇₁	C₂²×C₅	semidirect
9. C₂²	C₅₇₁⋊C₅	direct (N × H)
10. C₂	C₂×C₅₇₁⋊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×C₅₇₁⋊C₅	2
C₂²×C₅₇₁	5
C₂²×C₅	571