Finite Group Databasebeta

← C₅×C₃₁×D₇₉ #37587539

Subgroups — C₅×C₃₁×D₇₉ #37587539

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	C₃₁×D₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₇₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₇₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇₉	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×C₃₁	—	79	1	no	maximal, Hall
7	D₇₉	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₃₁	D₇₉	1	1	yes	characteristic, direct product factor, Hall
9	C₇₉	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₃₁	—	79	1	no	Hall
11	C₃₁	C₅×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	79	1	no	Hall
13	C₅	C₃₁×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	79	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₁	D₇₉
commutator, cosocle, hypocenter	C₇₉	C₂×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₇₉	C₂
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₅×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₇₉	C₂	semidirect
2. C₃₁×D₇₉	C₅	direct (N × H)
3. C₃₁×C₇₉	C₂×C₅	semidirect
4. C₅×D₇₉	C₃₁	direct (N × H)
5. C₅×C₇₉	C₂×C₃₁	semidirect
7. D₇₉	C₅×C₃₁	direct (N × H)
8. C₅×C₃₁	D₇₉	direct (N × H)
9. C₇₉	C₂×C₅×C₃₁	semidirect
11. C₃₁	C₅×D₇₉	direct (N × H)
13. C₅	C₃₁×D₇₉	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
C₃₁×D₇₉	5
C₅×D₇₉	31
C₂×C₅×C₃₁	79