Finite Group Databasebeta

← C₃⋊(D₅₇₁⋊C₅) #30686180

Subgroups — C₃⋊(D₅₇₁⋊C₅) #30686180

Order 17130.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₇₁⋊C₅	—	3	1	no	maximal, Hall
3	D₁₇₁₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅₇₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₅₇₁	—	3	1	no	Hall
7	C₅₇₁	C₅×D₃	1	1	yes	characteristic, complemented, Sylow
8	C₅×D₃	—	571	1	no	maximal, Hall
9	C₃×C₅	—	571	1	no	Hall
10	C₂×C₅	—	1713	1	no	Hall
11	D₃	—	2855	1	no	Hall
12	C₅	—	571	1	no	Sylow
13	C₃	D₅₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	8565	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅₇₁	C₂×C₅
LCS	G ▷ C₃×C₅₇₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₇₁⋊C₅	C₂	semidirect
3. D₁₇₁₃	C₅	semidirect
4. C₅₇₁⋊C₅	D₃	semidirect
5. C₃×C₅₇₁	C₂×C₅	semidirect
7. C₅₇₁	C₅×D₃	semidirect
13. C₃	D₅₇₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅₇₁⋊C₅	2
D₅₇₁⋊C₅	3
D₁₇₁₃	5
C₅×D₃	571