Finite Group Databasebeta

Subgroups — #44540180

Order 31700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₃₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₃₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#20263603	—	5	6	no	maximal
4	C₅×D₃₁₇	D₅	1	6	yes	—
5	C₅×C₃₁₇	Dic₅	1	6	yes	complemented
6	#11929639	—	25	1	no	Hall
7	D₃₁₇	C₅⋊D₅	1	1	yes	characteristic
8	C₃₁₇	#1039	1	1	yes	characteristic, complemented, Sylow
9	#1039	—	317	1	no	maximal, Hall
10	C₂×C₅²	—	317	1	no	—
11	C₅²	#11929639	1	1	yes	characteristic, complemented, Sylow
12	Dic₅	—	1585	6	no	—
13	C₂×C₅	—	317	6	no	—
14	C₅	#20263603	1	6	yes	complemented
15	C₄	—	7925	1	no	Sylow
16	C₂	—	317	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₃₁₇	C₄
prime radical, cosocle	C₅²×D₃₁₇	C₂
LCS	G ▷ C₅²×C₃₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₃₁₇	C₄	semidirect
5. C₅×C₃₁₇	Dic₅	semidirect
8. C₃₁₇	#1039	semidirect
11. C₅²	#11929639	semidirect
14. C₅	#20263603	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₃₁₇	2
#20263603	5
#1039	317