Finite Group Databasebeta

← C₇×C₁₃×C₇₁⋊C₅ #44568151

Subgroups — C₇×C₁₃×C₇₁⋊C₅ #44568151

Order 32305.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₇₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₇₁⋊C₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₇₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₇₁	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₅×C₇×C₁₃	—	71	1	no	maximal, Hall
7	C₇₁⋊C₅	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₃	C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₇₁	C₅×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
10	C₅×C₁₃	—	71	1	no	Hall
11	C₅×C₇	—	71	1	no	Hall
12	C₁₃	C₇×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₁₃×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
14	C₅	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₃	C₇₁⋊C₅
commutator, cosocle, hypocenter	C₇₁	C₅×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₇₁	C₅
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₇₁	C₅	semidirect
2. C₁₃×C₇₁⋊C₅	C₇	direct (N × H)
3. C₇×C₇₁⋊C₅	C₁₃	direct (N × H)
4. C₁₃×C₇₁	C₅×C₇	semidirect
5. C₇×C₇₁	C₅×C₁₃	semidirect
7. C₇₁⋊C₅	C₇×C₁₃	direct (N × H)
8. C₇×C₁₃	C₇₁⋊C₅	direct (N × H)
9. C₇₁	C₅×C₇×C₁₃	semidirect
12. C₁₃	C₇×C₇₁⋊C₅	direct (N × H)
13. C₇	C₁₃×C₇₁⋊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
C₇×C₁₃×C₇₁	5
C₁₃×C₇₁⋊C₅	7
C₇×C₇₁⋊C₅	13
C₅×C₇×C₁₃	71