Subgroups — #37587604

Order 24492.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133646	C₂	1	1	yes	maximal, characteristic
2	#261×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20259405	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₅₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₅₇⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₅₇⋊C₃	—	13	1	no	—
8	C₄×C₁₅₇	—	13	1	no	Hall
9	C₁₅₇⋊C₃	—	13	1	no	Hall
10	C₂×C₁₅₇	—	13	1	no	—
11	C₁₅₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
12	AGL(1,𝔽₁₃)	—	157	1	no	maximal, Hall
13	D₁₃⋊C₃	—	157	1	no	—
14	#261	C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₁₃⋊C₃	—	157	1	no	Hall
16	D₁₃	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic
17	C₁₃	C₄×C₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2041	1	no	Hall
19	C₂×C₃	—	2041	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	—	2041	1	no	Sylow
22	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₅₇	C₃×C₄
prime radical	#27133646	C₂
cosocle	D₁₃×C₁₅₇	C₂×C₃
LCS	G ▷ C₁₃×C₁₅₇
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.