Subgroups — #261×C₁₅₁⋊C₃ #37555561

Order 23556.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×C₁₅₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#261×C₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₅₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₅₁	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₅₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₅₁⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₅₁⋊C₃	—	13	1	no	—
8	C₄×C₁₅₁	—	13	1	no	Hall
9	C₁₅₁⋊C₃	#261	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₅₁	—	13	1	no	—
11	C₃×#261	—	151	1	no	maximal, Hall
12	C₁₅₁	C₃×#261	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₁₃	—	151	1	no	—
14	#261	C₁₅₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃	—	151	1	no	Hall
16	D₁₃	C₂×C₁₅₁⋊C₃	1	1	yes	characteristic
17	C₁₃	C₄×C₁₅₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1963	1	no	Hall
19	C₂×C₃	—	1963	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	—	151	1	no	Sylow
22	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₅₁	C₃×C₄
prime radical	D₁₃×C₁₅₁⋊C₃	C₂
cosocle	D₁₃×C₁₅₁	C₂×C₃
LCS	G ▷ C₁₃×C₁₅₁
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.