Finite Group Databasebeta

← C₇₉⋊(D₄₁⋊C₅) #44569261

Subgroups — C₇₉⋊(D₄₁⋊C₅) #44569261

Order 32390.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₁×C₇₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₇₉	—	41	1	no	maximal, Hall
5	D₄₁⋊C₅	—	79	1	no	maximal, Hall
6	C₅×C₇₉	—	41	1	no	Hall
7	C₄₁⋊C₅	D₇₉	1	1	yes	characteristic, complemented, Hall
8	D₇₉	—	41	1	no	Hall
9	D₄₁	—	79	1	no	Hall
10	C₇₉	D₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
11	C₄₁	C₅×D₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3239	1	no	Hall
13	C₅	—	41	1	no	Sylow
14	C₂	—	3239	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₁×C₇₉	C₂×C₅
LCS	G ▷ C₄₁×C₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇₉×C₄₁⋊C₅	C₂	semidirect
2. D₃₂₃₉	C₅	semidirect
3. C₄₁×C₇₉	C₂×C₅	semidirect
7. C₄₁⋊C₅	D₇₉	semidirect
10. C₇₉	D₄₁⋊C₅	semidirect
11. C₄₁	C₅×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×C₄₁⋊C₅	2
D₃₂₃₉	5
C₅×D₇₉	41
D₄₁⋊C₅	79