Subgroups — #34095358

Order 20052.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₆₇₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅₅₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₁₆₇₁	—	6	2	no	—
4	#14555805	—	9	1	no	maximal, Hall
5	C₃×C₅₅₇	—	2	2	no	—
6	D₅₅₇	—	9	1	no	—
7	C₅₅₇	#157	1	1	yes	characteristic, complemented, Sylow
8	#157	—	557	1	no	maximal, Hall
9	C₃⋊D₃	—	557	1	no	—
10	C₃²	#14555805	1	1	yes	characteristic, complemented, Sylow
11	D₃	—	3342	2	no	—
12	C₄	—	5013	1	no	Sylow
13	C₃	—	2	2	no	—
14	C₂	—	5013	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅₅₇	C₄
prime radical, cosocle	C₃⋊D₁₆₇₁	C₂
LCS	G ▷ C₃²×C₅₅₇
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.