Subgroups — C₂²⋊C₉×C₁₃₁⋊C₅ #37556040

Order 23580.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₃₁⋊C₅	—	4	1	no	maximal, Hall
3	C₂²⋊C₉×C₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃×C₁₃₁⋊C₅	—	3	1	no	—
5	C₂²×C₁₃₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃₁⋊C₅	A₄	1	1	yes	characteristic
7	C₂²×C₃×C₁₃₁	C₃×C₅	1	1	yes	characteristic
8	C₂×C₁₃₁⋊C₅	—	3	1	no	—
9	C₉×C₁₃₁	—	4	1	no	Hall
10	C₂×C₃×C₁₃₁	—	3	1	no	—
11	C₁₃₁⋊C₅	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₃₁	C₅×A₄	1	1	yes	characteristic
14	C₂×C₁₃₁	—	3	1	no	—
15	C₅×C₂²⋊C₉	—	131	1	no	maximal, Hall
16	C₁₃₁	C₅×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃×C₅	—	131	1	no	—
18	C₅×C₉	—	524	1	no	Hall
19	C₂²⋊C₉	C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₅	—	393	1	no	—
21	C₂²×C₅	—	131	1	no	Hall
22	C₃×C₅	—	131	1	no	—
23	C₂²×C₃	C₃×C₁₃₁⋊C₅	1	1	yes	characteristic
24	C₂×C₅	—	393	1	no	—
25	C₉	—	4	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	C₅	—	131	1	no	Sylow
28	C₂²	C₉×C₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
29	C₃	A₄×C₁₃₁⋊C₅	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	A₄×C₁₃₁⋊C₅
commutator, hypocenter	C₂²×C₁₃₁	C₅×C₉
Fitting, socle, cosocle	C₂²×C₃×C₁₃₁	C₃×C₅
prime radical	C₂²×C₃×C₁₃₁⋊C₅	C₃
LCS	G ▷ C₂²×C₁₃₁
UCS	C₁ ◁ C₃

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.