Subgroups — C₁₁×C₃₁×#1043 #46802206

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×AGL(1,𝔽₅)×C₃₁	—	5	6	no	maximal
4	D₅×C₁₁×C₃₁	—	5	6	no	—
5	C₃₁×#1043	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	1	6	yes	complemented
7	C₃₁×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
8	C₄×C₁₁×C₃₁	—	25	1	no	Hall
9	C₁₁×#1043	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅²×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₃₁	—	25	1	no	—
12	AGL(1,𝔽₅)×C₃₁	—	5	6	no	—
13	C₁₁×C₅⋊D₅	C₂×C₃₁	1	1	yes	characteristic
14	C₁₁×C₃₁	#1043	1	1	yes	characteristic, direct product factor, Hall
15	D₅×C₃₁	—	5	6	no	—
16	C₅²×C₁₁	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
17	C₁₁×AGL(1,𝔽₅)	—	5	6	no	—
18	C₅×C₃₁	C₁₁×AGL(1,𝔽₅)	1	6	yes	complemented
19	C₄×C₃₁	—	25	1	no	Hall
20	D₅×C₁₁	—	5	6	no	—
21	#1043	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃₁	—	25	1	no	—
23	C₅×C₁₁	AGL(1,𝔽₅)×C₃₁	1	6	yes	complemented
24	C₅⋊D₅	C₂×C₁₁×C₃₁	1	1	yes	characteristic
25	C₄×C₁₁	—	25	1	no	Hall
26	C₃₁	C₁₁×#1043	1	1	yes	characteristic, direct product factor, Sylow
27	C₅²	C₄×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	—	25	1	no	—
29	AGL(1,𝔽₅)	—	5	6	no	—
30	C₁₁	C₃₁×#1043	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₁₁×AGL(1,𝔽₅)×C₃₁	1	6	yes	complemented
33	C₄	—	25	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₃₁	#1043
commutator, hypocenter	C₅²	C₄×C₁₁×C₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₃₁	C₄
prime radical	C₁₁×C₃₁×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₁₁×C₃₁
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₁×C₃₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅²×C₁₁×C₃₁	C₄	semidirect
5. C₃₁×#1043	C₁₁	direct (N × H)
6. C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	semidirect
9. C₁₁×#1043	C₃₁	direct (N × H)
10. C₅²×C₃₁	C₄×C₁₁	semidirect
14. C₁₁×C₃₁	#1043	direct (N × H)
16. C₅²×C₁₁	C₄×C₃₁	semidirect
18. C₅×C₃₁	C₁₁×AGL(1,𝔽₅)	semidirect
21. #1043	C₁₁×C₃₁	direct (N × H)
23. C₅×C₁₁	AGL(1,𝔽₅)×C₃₁	semidirect
26. C₃₁	C₁₁×#1043	direct (N × H)
27. C₅²	C₄×C₁₁×C₃₁	semidirect
30. C₁₁	C₃₁×#1043	direct (N × H)
32. C₅	C₁₁×AGL(1,𝔽₅)×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×C₃₁×C₅⋊D₅	2
C₁₁×AGL(1,𝔽₅)×C₃₁	5
C₃₁×#1043	11
C₁₁×#1043	31

Subgroups — C11×C31×#1043 #46802206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃₁×#1043 #46802206