Finite Group Databasebeta

← C₁₇×D₃₅₅ #27130508

Subgroups — C₁₇×D₃₅₅ #27130508

Order 12070.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₇₁	—	5	1	no	maximal, Hall
3	C₁₇×C₇₁	D₅	1	1	yes	characteristic, complemented, Hall
4	D₃₅₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
6	D₅×C₁₇	—	71	1	no	maximal, Hall
7	D₇₁	—	5	1	no	Hall
8	C₅×C₁₇	D₇₁	1	1	yes	characteristic, complemented, Hall
9	C₇₁	D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₇	—	355	1	no	Hall
11	C₁₇	D₃₅₅	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	—	71	1	no	Hall
13	C₅	C₁₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	355	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₃₅₅
commutator, cosocle, hypocenter	C₅×C₇₁	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₇₁	C₂
LCS	G ▷ C₅×C₇₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₇₁	C₂	semidirect
3. C₁₇×C₇₁	D₅	semidirect
4. D₃₅₅	C₁₇	direct (N × H)
5. C₅×C₇₁	C₂×C₁₇	semidirect
8. C₅×C₁₇	D₇₁	semidirect
9. C₇₁	D₅×C₁₇	semidirect
11. C₁₇	D₃₅₅	direct (N × H)
13. C₅	C₁₇×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₇×C₇₁	2
C₁₇×D₇₁	5
D₃₅₅	17
D₅×C₁₇	71