Subgroups — C₅×C₁₁×#10596815 #44542073

Order 31900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×D₁₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#10596815	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₁₁×#1181	—	5	1	no	maximal
5	C₁₁×D₁₄₅	C₂×C₅	1	1	yes	characteristic
6	C₅×C₁₁×D₂₉	—	5	1	no	—
7	C₅×#10596815	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₂₉	—	4	1	no	—
9	C₅×C₁₁×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
10	C₅×C₁₁×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	C₅×D₁₄₅	C₂×C₁₁	1	1	yes	characteristic
12	C₁₁×#1181	—	5	1	no	Hall
13	C₅×C₁₁×AGL(1,𝔽₅)	—	29	1	no	maximal, Hall
14	C₅²×C₂₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×D₂₉	—	5	1	no	—
16	#10596815	C₅×C₁₁	1	1	yes	characteristic, direct product factor
17	C₅×#1181	—	5	1	no	—
18	C₅×D₅×C₁₁	—	29	1	no	—
19	C₁₁×C₂₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
20	D₁₄₅	C₂×C₅×C₁₁	1	1	yes	characteristic
21	C₅×D₂₉	—	5	1	no	—
22	C₅²×C₁₁	#1181	1	1	yes	characteristic, complemented, Hall
23	C₁₁×AGL(1,𝔽₅)	—	29	1	no	—
24	C₄×C₅×C₁₁	—	145	1	no	—
25	C₅×C₂₉	—	4	1	no	—
26	C₅×C₂₉	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented
27	C₅×C₂₉	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
28	#1181	—	5	1	no	Hall
29	C₂×C₅×C₁₁	—	145	1	no	—
30	D₅×C₁₁	—	29	1	no	—
31	C₅×AGL(1,𝔽₅)	—	29	1	no	Hall
32	D₂₉	—	5	1	no	—
33	C₅×C₁₁	—	4	1	no	—
34	C₅×C₁₁	C₅×#1181	1	1	yes	characteristic, complemented
35	C₅×C₁₁	#10596815	1	1	yes	characteristic, direct product factor
36	C₅×D₅	—	29	1	no	—
37	C₄×C₁₁	—	145	1	no	Hall
38	C₂₉	C₅×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
39	C₅²	C₁₁×#1181	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₁	—	145	1	no	—
41	AGL(1,𝔽₅)	—	29	1	no	—
42	C₄×C₅	—	145	1	no	—
43	C₁₁	C₅×#10596815	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₅	—	145	1	no	—
45	D₅	—	29	1	no	—
46	C₅	—	4	1	no	—
47	C₅	C₅×C₁₁×#1181	1	1	yes	characteristic, complemented
48	C₅	C₁₁×#10596815	1	1	yes	characteristic, direct product factor
49	C₄	—	145	1	no	Sylow
50	C₂	—	145	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	#10596815
commutator, hypocenter	C₅×C₂₉	C₄×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₉	C₄
prime radical	C₅×C₁₁×D₁₄₅	C₂
cosocle	D₁₄₅	C₂×C₅×C₁₁
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₂₉	C₄	semidirect
3. C₁₁×#10596815	C₅	direct (N × H)
7. C₅×#10596815	C₁₁	direct (N × H)
9. C₅×C₁₁×C₂₉	C₄×C₅	semidirect
10. C₅×C₁₁×C₂₉	AGL(1,𝔽₅)	semidirect
14. C₅²×C₂₉	C₄×C₁₁	semidirect
16. #10596815	C₅×C₁₁	direct (N × H)
19. C₁₁×C₂₉	C₅×AGL(1,𝔽₅)	semidirect
22. C₅²×C₁₁	#1181	semidirect
26. C₅×C₂₉	C₄×C₅×C₁₁	semidirect
27. C₅×C₂₉	C₁₁×AGL(1,𝔽₅)	semidirect
34. C₅×C₁₁	C₅×#1181	semidirect
35. C₅×C₁₁	#10596815	direct (N × H)
38. C₂₉	C₅×C₁₁×AGL(1,𝔽₅)	semidirect
39. C₅²	C₁₁×#1181	semidirect
43. C₁₁	C₅×#10596815	direct (N × H)
47. C₅	C₅×C₁₁×#1181	semidirect
48. C₅	C₁₁×#10596815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×D₁₄₅	2
C₁₁×#10596815	5
C₅×C₁₁×#1181	5
C₅×#10596815	11
C₅×C₁₁×AGL(1,𝔽₅)	29

Subgroups — C5×C11×#10596815 #44542073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×#10596815 #44542073