Finite Group Databasebeta

← C₁₇×C₃₁×D₂₉ #44479882

Subgroups — C₁₇×C₃₁×D₂₉ #44479882

Order 30566.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₇×C₃₁	—	29	1	no	maximal, Hall
4	C₁₇×D₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₉×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₃₁	D₂₉	1	1	yes	characteristic, direct product factor, Hall
7	C₁₇×C₂₉	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃₁	—	29	1	no	Hall
9	D₂₉	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₇	—	29	1	no	Hall
11	C₃₁	C₁₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂₉	C₂×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
13	C₁₇	C₃₁×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₃₁	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₁₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₇×C₂₉×C₃₁	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₁₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₂₉×C₃₁	C₂	semidirect
2. C₃₁×D₂₉	C₁₇	direct (N × H)
4. C₁₇×D₂₉	C₃₁	direct (N × H)
5. C₂₉×C₃₁	C₂×C₁₇	semidirect
6. C₁₇×C₃₁	D₂₉	direct (N × H)
7. C₁₇×C₂₉	C₂×C₃₁	semidirect
9. D₂₉	C₁₇×C₃₁	direct (N × H)
11. C₃₁	C₁₇×D₂₉	direct (N × H)
12. C₂₉	C₂×C₁₇×C₃₁	semidirect
13. C₁₇	C₃₁×D₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₂₉×C₃₁	2
C₃₁×D₂₉	17
C₂×C₁₇×C₃₁	29
C₁₇×D₂₉	31