Finite Group Databasebeta

← C₅×D₃₁×C₇₉ #37587540

Subgroups — C₅×D₃₁×C₇₉ #37587540

Order 24490.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁×C₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₇₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₇₉	—	31	1	no	maximal, Hall
5	C₅×C₇₉	D₃₁	1	1	yes	characteristic, direct product factor, Hall
6	C₅×D₃₁	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇₉	—	31	1	no	Hall
8	C₅×C₃₁	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
9	C₇₉	C₅×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
10	D₃₁	C₅×C₇₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃₁	C₂×C₅×C₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	31	1	no	Hall
13	C₅	D₃₁×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇₉	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₅×C₇₉
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₇₉	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₇₉	C₂	semidirect
2. D₃₁×C₇₉	C₅	direct (N × H)
3. C₃₁×C₇₉	C₂×C₅	semidirect
5. C₅×C₇₉	D₃₁	direct (N × H)
6. C₅×D₃₁	C₇₉	direct (N × H)
8. C₅×C₃₁	C₂×C₇₉	semidirect
9. C₇₉	C₅×D₃₁	direct (N × H)
10. D₃₁	C₅×C₇₉	direct (N × H)
11. C₃₁	C₂×C₅×C₇₉	semidirect
13. C₅	D₃₁×C₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₃₁×C₇₉	2
D₃₁×C₇₉	5
C₂×C₅×C₇₉	31
C₅×D₃₁	79