Finite Group Databasebeta

← C₂×C₇₉×C₄₁⋊C₅ #44569251

Subgroups — C₂×C₇₉×C₄₁⋊C₅ #44569251

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, direct product factor, Hall
2	C₂×C₄₁×C₇₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₁×C₇₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₇₉	—	41	1	no	maximal, Hall
5	C₂×C₄₁⋊C₅	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇₉	—	41	1	no	Hall
7	C₄₁⋊C₅	C₂×C₇₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇₉	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₄₁	C₅×C₇₉	1	1	yes	characteristic, complemented, Hall
10	C₇₉	C₂×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
11	C₄₁	C₂×C₅×C₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	41	1	no	Hall
13	C₅	—	41	1	no	Sylow
14	C₂	C₇₉×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₇₉×C₄₁⋊C₅	C₂	direct (N × H)
2. C₂×C₄₁×C₇₉	C₅	semidirect
3. C₄₁×C₇₉	C₂×C₅	semidirect
5. C₂×C₄₁⋊C₅	C₇₉	direct (N × H)
7. C₄₁⋊C₅	C₂×C₇₉	direct (N × H)
8. C₂×C₇₉	C₄₁⋊C₅	direct (N × H)
9. C₂×C₄₁	C₅×C₇₉	semidirect
10. C₇₉	C₂×C₄₁⋊C₅	direct (N × H)
11. C₄₁	C₂×C₅×C₇₉	semidirect
14. C₂	C₇₉×C₄₁⋊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
C₇₉×C₄₁⋊C₅	2
C₂×C₄₁×C₇₉	5
C₂×C₅×C₇₉	41
C₂×C₄₁⋊C₅	79