Subgroups — C₉⋊(C₁₃₁⋊AGL(1,𝔽₅)) #37556050

Order 23580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₃₁⋊AGL(1,𝔽₅))	—	3	1	no	maximal
3	C₅×C₉×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₁₇₉	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₃₁	D₃	1	1	yes	characteristic
6	C₁₃₁⋊AGL(1,𝔽₅)	—	9	1	no	Hall
7	C₂×C₉×C₁₃₁	—	5	1	no	—
8	C₃×C₅×C₁₃₁	Dic₃	1	1	yes	characteristic
9	Dic₃₉₃	—	15	1	no	—
10	D₅×C₁₃₁	D₉	1	1	yes	characteristic
11	C₉×C₁₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₃₁	—	5	1	no	—
13	C₅×C₁₃₁	Dic₉	1	1	yes	characteristic, complemented, Hall
14	Dic₁₃₁	—	45	1	no	Hall
15	C₃×C₁₃₁	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
16	C₂×C₁₃₁	—	5	1	no	—
17	C₉⋊AGL(1,𝔽₅)	—	131	1	no	maximal, Hall
18	C₁₃₁	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	C₉×D₅	D₁₃₁	1	1	yes	characteristic
20	ΓL(1,𝔽₁₆)	—	393	1	no	—
21	C₅×C₉	Dic₁₃₁	1	1	yes	characteristic, complemented, Hall
22	Dic₉	—	655	1	no	Hall
23	C₃×D₅	D₃₉₃	1	1	yes	characteristic
24	AGL(1,𝔽₅)	—	1179	1	no	Hall
25	C₂×C₉	—	5	1	no	—
26	C₃×C₅	Dic₃₉₃	1	1	yes	characteristic
27	Dic₃	—	1965	1	no	—
28	D₅	D₁₁₇₉	1	1	yes	characteristic
29	C₉	C₁₃₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	1	no	—
31	C₅	Dic₁₁₇₉	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	5895	1	no	Sylow
33	C₃	C₃⋊(C₁₃₁⋊AGL(1,𝔽₅))	1	1	yes	characteristic
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₉×C₁₃₁	C₄
Frattini	C₃	C₃⋊(C₁₃₁⋊AGL(1,𝔽₅))
socle	C₃×C₅×C₁₃₁	Dic₃
prime radical	C₃×D₅×C₁₃₁	D₃
cosocle	C₉×D₅×C₁₃₁	C₂
LCS	G ▷ C₅×C₉×C₁₃₁
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.