Finite Group Databasebeta

← C₅₉⋊(D₄₁⋊C₅) #37564067

Subgroups — C₅₉⋊(D₄₁⋊C₅) #37564067

Order 24190.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₄₁₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₁×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₅₉	—	41	1	no	maximal, Hall
5	D₄₁⋊C₅	—	59	1	no	maximal, Hall
6	C₅×C₅₉	—	41	1	no	Hall
7	C₄₁⋊C₅	D₅₉	1	1	yes	characteristic, complemented, Hall
8	D₅₉	—	205	1	no	Hall
9	D₄₁	—	59	1	no	Hall
10	C₅₉	D₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
11	C₄₁	C₅×D₅₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	2419	1	no	Hall
13	C₅	—	41	1	no	Sylow
14	C₂	—	12095	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₁×C₅₉	C₂×C₅
LCS	G ▷ C₄₁×C₅₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅₉×C₄₁⋊C₅	C₂	semidirect
2. D₂₄₁₉	C₅	semidirect
3. C₄₁×C₅₉	C₂×C₅	semidirect
7. C₄₁⋊C₅	D₅₉	semidirect
10. C₅₉	D₄₁⋊C₅	semidirect
11. C₄₁	C₅×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×C₄₁⋊C₅	2
D₂₄₁₉	5
C₅×D₅₉	41
D₄₁⋊C₅	59