Finite Group Databasebeta

← C₅×#16809823 #30680849

Subgroups — C₅×#16809823 #30680849

Order 16775.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₆₁	C₅	1	1	yes	maximal, characteristic, complemented
2	#16809823	C₅	1	5	yes	maximal, direct product factor
3	C₅×C₆₁⋊C₅	—	11	1	no	maximal, Hall
4	C₁₁×C₆₁	C₅²	1	1	yes	characteristic, complemented, Hall
5	C₅×C₆₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented
6	C₆₁⋊C₅	—	11	5	no	—
7	C₅×C₁₁⋊C₅	—	61	1	no	maximal, Hall
8	C₆₁	C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₁	C₆₁⋊C₅	1	1	yes	characteristic, complemented
10	C₁₁⋊C₅	—	61	5	no	—
11	C₅²	—	671	1	no	Sylow
12	C₁₁	C₅×C₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
13	C₅	—	671	5	no	—
14	C₅	#16809823	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₅	#16809823
commutator, cosocle, hypocenter	C₁₁×C₆₁	C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₆₁	C₅
LCS	G ▷ C₁₁×C₆₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₆₁	C₅	semidirect
2. #16809823	C₅	direct (N × H)
4. C₁₁×C₆₁	C₅²	semidirect
5. C₅×C₆₁	C₁₁⋊C₅	semidirect
8. C₆₁	C₅×C₁₁⋊C₅	semidirect
9. C₅×C₁₁	C₆₁⋊C₅	semidirect
12. C₁₁	C₅×C₆₁⋊C₅	semidirect
14. C₅	#16809823	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×C₁₁×C₆₁	5
#16809823	5
C₅×C₆₁⋊C₅	11
C₅×C₁₁⋊C₅	61