Subgroups — #35208708

Order 20740.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₁₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#16861895	—	5	1	no	maximal, Hall
4	D₁₀₃₇	—	5	1	no	—
5	#11927413	—	17	1	no	maximal, Hall
6	C₁₇×C₆₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₃₀₅	—	17	1	no	—
8	#66776	—	61	1	no	maximal, Hall
9	C₅×C₆₁	#595	1	1	yes	characteristic, complemented, Hall
10	#6923	—	85	1	no	Hall
11	D₈₅	—	61	1	no	—
12	D₆₁	—	85	1	no	—
13	C₅×C₁₇	#6923	1	1	yes	characteristic, complemented, Hall
14	#595	—	305	1	no	Hall
15	C₆₁	#66776	1	1	yes	characteristic, complemented, Sylow
16	D₁₇	—	305	1	no	—
17	AGL(1,𝔽₅)	—	1037	1	no	Hall
18	C₁₇	#11927413	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	1037	1	no	—
20	C₅	#16861895	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5185	1	no	Sylow
22	C₂	—	5185	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₆₁	C₄
prime radical, cosocle	D₅₁₈₅	C₂
LCS	G ▷ C₅×C₁₇×C₆₁
UCS	C₁

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

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