Subgroups — C₁₁×C₃₁×#1042 #46802186

Order 34100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×AGL(1,𝔽₅)×C₃₁	—	5	1	no	maximal
4	C₁₁×Dic₅×C₃₁	—	5	1	no	maximal
5	D₅×C₁₁×C₃₁	D₅	1	1	yes	characteristic
6	C₂×C₅×C₁₁×C₃₁	—	5	1	no	—
7	C₃₁×#1042	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₃₁	—	4	1	no	—
9	C₅×C₁₁×C₃₁	Dic₅	1	1	yes	characteristic, complemented
10	C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	C₅×D₅×C₃₁	C₂×C₁₁	1	1	yes	characteristic
12	C₄×C₁₁×C₃₁	—	25	1	no	Hall
13	C₁₁×#1042	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅²×C₃₁	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₃₁	—	5	1	no	—
16	AGL(1,𝔽₅)×C₃₁	—	5	1	no	—
17	Dic₅×C₃₁	—	5	1	no	—
18	C₅×D₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic
19	C₁₁×C₃₁	#1042	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₃₁	—	5	1	no	—
21	D₅×C₃₁	D₅×C₁₁	1	1	yes	characteristic
22	C₅²×C₁₁	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
23	C₁₁×AGL(1,𝔽₅)	—	5	1	no	—
24	C₁₁×Dic₅	—	5	1	no	—
25	C₅×C₃₁	—	4	1	no	—
26	C₅×C₃₁	C₁₁×Dic₅	1	1	yes	characteristic, complemented
27	C₅×C₃₁	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
28	C₄×C₃₁	—	25	1	no	Hall
29	C₂×C₅×C₁₁	—	5	1	no	—
30	D₅×C₁₁	D₅×C₃₁	1	1	yes	characteristic
31	#1042	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₃₁	—	5	1	no	—
33	C₅×C₁₁	—	4	1	no	—
34	C₅×C₁₁	Dic₅×C₃₁	1	1	yes	characteristic, complemented
35	C₅×C₁₁	AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented
36	C₅×D₅	C₂×C₁₁×C₃₁	1	1	yes	characteristic
37	C₄×C₁₁	—	25	1	no	Hall
38	C₃₁	C₁₁×#1042	1	1	yes	characteristic, direct product factor, Sylow
39	C₅²	C₄×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₁	—	5	1	no	—
41	AGL(1,𝔽₅)	—	5	1	no	—
42	Dic₅	—	5	1	no	—
43	C₁₁	C₃₁×#1042	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₅	—	5	1	no	—
45	D₅	D₅×C₁₁×C₃₁	1	1	yes	characteristic
46	C₅	—	4	1	no	—
47	C₅	C₁₁×Dic₅×C₃₁	1	1	yes	characteristic, complemented
48	C₅	C₁₁×AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented
49	C₄	—	25	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₃₁	#1042
commutator, hypocenter	C₅²	C₄×C₁₁×C₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₃₁	C₄
prime radical	C₅×D₅×C₁₁×C₃₁	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
7. C₃₁×#1042	C₁₁	direct (N × H)
9. C₅×C₁₁×C₃₁	Dic₅	semidirect
10. C₅×C₁₁×C₃₁	AGL(1,𝔽₅)	semidirect
13. C₁₁×#1042	C₃₁	direct (N × H)
14. C₅²×C₃₁	C₄×C₁₁	semidirect
19. C₁₁×C₃₁	#1042	direct (N × H)
22. C₅²×C₁₁	C₄×C₃₁	semidirect
26. C₅×C₃₁	C₁₁×Dic₅	semidirect
27. C₅×C₃₁	C₁₁×AGL(1,𝔽₅)	semidirect
31. #1042	C₁₁×C₃₁	direct (N × H)
34. C₅×C₁₁	Dic₅×C₃₁	semidirect
35. C₅×C₁₁	AGL(1,𝔽₅)×C₃₁	semidirect
38. C₃₁	C₁₁×#1042	direct (N × H)
39. C₅²	C₄×C₁₁×C₃₁	semidirect
43. C₁₁	C₃₁×#1042	direct (N × H)
47. C₅	C₁₁×Dic₅×C₃₁	semidirect
48. 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
C₅×D₅×C₁₁×C₃₁	2
C₁₁×AGL(1,𝔽₅)×C₃₁	5
C₁₁×Dic₅×C₃₁	5
C₃₁×#1042	11
C₁₁×#1042	31

Subgroups — C11×C31×#1042 #46802186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃₁×#1042 #46802186