Subgroups — C₁₁⋊(C₃₁⋊#1043) #46802209

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊(C₃₁⋊AGL(1,𝔽₅))	—	5	6	no	maximal
4	D₅×C₁₁×C₃₁	—	5	6	no	—
5	C₃₁⋊#1043	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	1	6	yes	complemented
7	C₃₁×C₅⋊D₅	D₁₁	1	1	yes	characteristic
8	Dic₃₄₁	—	25	1	no	Hall
9	C₁₁⋊#1043	—	31	1	no	maximal, Hall
10	C₅²×C₃₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₃₁	—	25	1	no	—
12	C₃₁⋊AGL(1,𝔽₅)	—	55	6	no	—
13	C₁₁×C₅⋊D₅	D₃₁	1	1	yes	characteristic
14	C₁₁×C₃₁	#1043	1	1	yes	characteristic, complemented, Hall
15	D₅×C₃₁	—	5	6	no	—
16	C₅²×C₁₁	Dic₃₁	1	1	yes	characteristic, complemented, Hall
17	C₁₁⋊AGL(1,𝔽₅)	—	155	6	no	—
18	C₅×C₃₁	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
19	Dic₃₁	—	275	1	no	Hall
20	D₅×C₁₁	—	5	6	no	—
21	#1043	—	341	1	no	Hall
22	C₂×C₃₁	—	25	1	no	—
23	C₅×C₁₁	C₃₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
24	C₅⋊D₅	D₃₄₁	1	1	yes	characteristic
25	Dic₁₁	—	775	1	no	Hall
26	C₃₁	C₁₁⋊#1043	1	1	yes	characteristic, complemented, Sylow
27	C₅²	Dic₃₄₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	—	25	1	no	—
29	AGL(1,𝔽₅)	—	1705	6	no	—
30	C₁₁	C₃₁⋊#1043	1	1	yes	characteristic, complemented, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₁₁⋊(C₃₁⋊AGL(1,𝔽₅))	1	6	yes	complemented
33	C₄	—	8525	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁×C₃₁	C₄
prime radical, cosocle	C₁₁×C₃₁×C₅⋊D₅	C₂
LCS	G ▷ C₅²×C₁₁×C₃₁
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.