Subgroups — C₂×C₂₉×#10587720 #44539892

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#10587720	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₉×#63270	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₇×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₉×#63270	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₇×C₂₉	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₂₉×C₁₃⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₂₉×AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
10	C₂×C₂₉×C₁₃⋊C₃	—	7	2	no	—
11	C₂×C₂₉×C₁₃⋊C₃	—	7	1	no	—
12	C₂²×C₁₃×C₂₉	—	7	1	no	Hall
13	C₂×ΓL(1,𝔽₈)×C₂₉	—	13	1	no	—
14	C₂₉×AGL(1,𝔽₇)	—	13	2	no	—
15	C₂₉×C₁₃⋊C₃	—	7	1	no	Hall
16	C₂×#10587720	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×D₇×C₂₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃×C₂₉	—	7	2	no	—
19	C₂×C₁₃×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	ΓL(1,𝔽₈)×C₂₉	—	13	1	no	Hall
21	C₂×#63270	C₂×C₂₉	1	1	yes	characteristic, complemented
22	#10587720	C₂×C₂₉	1	2	yes	direct product factor
23	C₂×C₇×C₂₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
24	D₇×C₂₉	C₂×C₁₃⋊C₃	1	2	yes	complemented
25	C₁₃×C₂₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃×D₇	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₂₉	—	91	1	no	Hall
28	#63270	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
29	C₇×C₂₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₃	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
31	C₁₃×D₇	C₂×C₃×C₂₉	1	2	yes	complemented
32	C₂×C₃×C₂₉	—	91	2	no	—
33	C₂×C₃×C₂₉	—	91	1	no	—
34	C₂²×C₁₃⋊C₃	—	7	1	no	Hall
35	C₂²×C₂₉	—	7	1	no	Hall
36	C₇×C₁₃	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
37	C₃×C₂₉	—	91	1	no	Hall
38	C₂×AGL(1,𝔽₇)	—	13	1	no	Hall
39	C₂×C₁₃⋊C₃	—	7	2	no	—
40	C₂×C₁₃⋊C₃	—	7	1	no	—
41	C₂×C₂₉	—	7	2	no	—
42	C₂×C₂₉	#10587720	1	1	yes	characteristic, direct product factor
43	C₂²×C₁₃	—	7	1	no	Hall
44	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
45	AGL(1,𝔽₇)	—	13	2	no	—
46	C₁₃⋊C₃	—	7	1	no	Hall
47	C₂₉	C₂×#10587720	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₇	C₂₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₁₃	—	7	2	no	—
50	C₂×C₁₃	C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	13	1	no	Hall
52	C₂×C₇	C₂×C₂₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented
53	D₇	C₂×C₂₉×C₁₃⋊C₃	1	2	yes	complemented
54	C₁₃	C₂×C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	91	1	no	Hall
56	C₇	C₂²×C₂₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	91	2	no	—
58	C₂×C₃	—	91	1	no	—
59	C₂²	—	7	1	no	Sylow
60	C₃	—	91	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	C₂₉×#10587720	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉	#10587720
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×#10587720	C₂	direct (N × H)
2. C₂×C₂₉×#63270	C₂	semidirect
3. C₂×C₁₃×D₇×C₂₉	C₃	semidirect
4. C₂₉×#63270	C₂²	semidirect
5. C₁₃×D₇×C₂₉	C₂×C₃	semidirect
6. C₂×C₇×C₁₃×C₂₉	C₂×C₃	semidirect
8. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
16. C₂×#10587720	C₂₉	direct (N × H)
17. C₂×D₇×C₂₉	C₁₃⋊C₃	semidirect
19. C₂×C₁₃×C₂₉	AGL(1,𝔽₇)	semidirect
21. C₂×#63270	C₂×C₂₉	semidirect
22. #10587720	C₂×C₂₉	direct (N × H)
23. C₂×C₇×C₂₉	C₂×C₁₃⋊C₃	semidirect
24. D₇×C₂₉	C₂×C₁₃⋊C₃	semidirect
25. C₁₃×C₂₉	C₂×AGL(1,𝔽₇)	semidirect
26. C₂×C₁₃×D₇	C₃×C₂₉	semidirect
28. #63270	C₂²×C₂₉	semidirect
29. C₇×C₂₉	C₂²×C₁₃⋊C₃	semidirect
30. C₂×C₇×C₁₃	C₂×C₃×C₂₉	semidirect
31. C₁₃×D₇	C₂×C₃×C₂₉	semidirect
36. C₇×C₁₃	C₂²×C₃×C₂₉	semidirect
42. C₂×C₂₉	#10587720	direct (N × H)
47. C₂₉	C₂×#10587720	direct (N × H)
48. C₂×D₇	C₂₉×C₁₃⋊C₃	semidirect
50. C₂×C₁₃	C₂₉×AGL(1,𝔽₇)	semidirect
52. C₂×C₇	C₂×C₂₉×C₁₃⋊C₃	semidirect
53. D₇	C₂×C₂₉×C₁₃⋊C₃	semidirect
54. C₁₃	C₂×C₂₉×AGL(1,𝔽₇)	semidirect
56. C₇	C₂²×C₂₉×C₁₃⋊C₃	semidirect
62. C₂	C₂₉×#10587720	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#10587720	2
C₂×C₂₉×#63270	2
C₂×C₁₃×D₇×C₂₉	3
C₂²×C₂₉×C₁₃⋊C₃	7
C₂×C₂₉×AGL(1,𝔽₇)	13
C₂×#10587720	29

Subgroups — C2×C29×#10587720 #44539892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#10587720 #44539892