Subgroups — C₁₁×C₃₁×#1044 #46802210

Order 34100.

64 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	2	no	maximal
4	D₅×C₁₁×C₃₁	—	5	2	no	—
5	D₅×C₁₁×C₃₁	—	10	2	no	—
6	C₃₁×#1044	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₃₁	—	2	2	no	—
8	C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	1	2	yes	complemented
9	C₃₁×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
10	C₄×C₁₁×C₃₁	—	25	1	no	Hall
11	C₁₁×#1044	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅²×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁×C₃₁	—	25	1	no	—
14	AGL(1,𝔽₅)×C₃₁	—	5	2	no	—
15	C₁₁×C₅⋊D₅	C₂×C₃₁	1	1	yes	characteristic
16	C₁₁×C₃₁	#1044	1	1	yes	characteristic, direct product factor, Hall
17	D₅×C₃₁	—	5	2	no	—
18	D₅×C₃₁	—	10	2	no	—
19	C₅²×C₁₁	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
20	C₁₁×AGL(1,𝔽₅)	—	5	2	no	—
21	C₅×C₃₁	—	2	2	no	—
22	C₅×C₃₁	C₁₁×AGL(1,𝔽₅)	1	2	yes	complemented
23	C₄×C₃₁	—	25	1	no	Hall
24	D₅×C₁₁	—	5	2	no	—
25	D₅×C₁₁	—	10	2	no	—
26	#1044	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃₁	—	25	1	no	—
28	C₅×C₁₁	—	2	2	no	—
29	C₅×C₁₁	AGL(1,𝔽₅)×C₃₁	1	2	yes	complemented
30	C₅⋊D₅	C₂×C₁₁×C₃₁	1	1	yes	characteristic
31	C₄×C₁₁	—	25	1	no	Hall
32	C₃₁	C₁₁×#1044	1	1	yes	characteristic, direct product factor, Sylow
33	C₅²	C₄×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₁	—	25	1	no	—
35	AGL(1,𝔽₅)	—	5	2	no	—
36	C₁₁	C₃₁×#1044	1	1	yes	characteristic, direct product factor, Sylow
37	D₅	—	5	2	no	—
38	D₅	—	10	2	no	—
39	C₅	—	2	2	no	—
40	C₅	C₁₁×AGL(1,𝔽₅)×C₃₁	1	2	yes	complemented
41	C₄	—	25	1	no	Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₃₁	#1044
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
6. C₃₁×#1044	C₁₁	direct (N × H)
8. C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	semidirect
11. C₁₁×#1044	C₃₁	direct (N × H)
12. C₅²×C₃₁	C₄×C₁₁	semidirect
16. C₁₁×C₃₁	#1044	direct (N × H)
19. C₅²×C₁₁	C₄×C₃₁	semidirect
22. C₅×C₃₁	C₁₁×AGL(1,𝔽₅)	semidirect
26. #1044	C₁₁×C₃₁	direct (N × H)
29. C₅×C₁₁	AGL(1,𝔽₅)×C₃₁	semidirect
32. C₃₁	C₁₁×#1044	direct (N × H)
33. C₅²	C₄×C₁₁×C₃₁	semidirect
36. C₁₁	C₃₁×#1044	direct (N × H)
40. 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×#1044	11
C₁₁×#1044	31

Subgroups — C11×C31×#1044 #46802210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃₁×#1044 #46802210