Subgroups — C₂×C₂₉⋊#10587721 #44539895

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉⋊#10587721	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₉×#63271	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₂₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₉×#63271	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₂₀₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₁₃⋊C₃×D₂₉	—	7	1	no	maximal, Hall
8	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×ΓL(1,𝔽₈)⋊D₂₉	—	13	1	no	maximal, Hall
10	C₁₃⋊C₃×D₂₉	—	7	2	no	—
11	C₂×C₂₉×C₁₃⋊C₃	—	7	1	no	—
12	C₂×C₁₃×D₂₉	—	7	1	no	Hall
13	C₂×ΓL(1,𝔽₈)×C₂₉	—	13	1	no	—
14	ΓL(1,𝔽₈)⋊D₂₉	—	13	2	no	—
15	C₂₉×C₁₃⋊C₃	—	7	1	no	Hall
16	C₂×#10587721	—	29	1	no	maximal, Hall
17	C₂×D₂₀₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
19	C₁₃×D₂₉	—	7	2	no	—
20	ΓL(1,𝔽₈)×C₂₉	—	13	1	no	Hall
21	C₂×#63271	D₂₉	1	1	yes	characteristic, complemented
22	#10587721	—	29	2	no	—
23	C₂×C₇×C₂₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
24	D₂₀₃	C₂×C₁₃⋊C₃	1	2	yes	complemented
25	C₁₃×C₂₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃×D₇	—	29	1	no	Hall
27	C₂×C₃×D₂₉	—	91	1	no	Hall
28	#63271	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
29	C₇×C₂₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₃	C₃×D₂₉	1	1	yes	characteristic, complemented
31	C₁₃×D₇	—	29	2	no	—
32	C₂×C₃×C₂₉	—	91	1	no	—
33	C₃×D₂₉	—	91	2	no	—
34	C₂²×C₁₃⋊C₃	—	203	1	no	Hall
35	C₂×D₂₉	—	7	1	no	Hall
36	C₇×C₁₃	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
37	C₃×C₂₉	—	91	1	no	Hall
38	C₂×AGL(1,𝔽₇)	—	377	1	no	Hall
39	C₂×C₁₃⋊C₃	—	7	1	no	—
40	C₂×C₁₃⋊C₃	—	203	2	no	—
41	C₂×C₂₉	#10587721	1	1	yes	characteristic, complemented
42	D₂₉	—	7	2	no	—
43	C₂²×C₁₃	—	203	1	no	Hall
44	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
45	AGL(1,𝔽₇)	—	377	2	no	—
46	C₁₃⋊C₃	—	7	1	no	Hall
47	C₂₉	C₂×#10587721	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₇	—	29	1	no	Hall
49	C₂×C₁₃	—	203	2	no	—
50	C₂×C₁₃	ΓL(1,𝔽₈)⋊D₂₉	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₈)	—	13	1	no	Hall
52	C₂×C₇	C₁₃⋊C₃×D₂₉	1	1	yes	characteristic, complemented
53	D₇	—	29	2	no	—
54	C₁₃	C₂×ΓL(1,𝔽₈)⋊D₂₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	2639	1	no	Hall
56	C₇	C₂×C₁₃⋊C₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	2639	2	no	—
58	C₂×C₃	—	91	1	no	—
59	C₂²	—	203	1	no	Sylow
60	C₃	—	91	1	no	Sylow
61	C₂	—	203	2	no	—
62	C₂	C₂₉⋊#10587721	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₂₉⋊#10587721
commutator, cosocle, hypocenter	C₇×C₁₃×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂₉⋊#10587721	C₂	direct (N × H)
2. C₂×C₂₉×#63271	C₂	semidirect
3. C₂×C₁₃×D₂₀₃	C₃	semidirect
4. C₂₉×#63271	C₂²	semidirect
5. C₁₃×D₂₀₃	C₂×C₃	semidirect
6. C₂×C₇×C₁₃×C₂₉	C₂×C₃	semidirect
8. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
17. C₂×D₂₀₃	C₁₃⋊C₃	semidirect
18. C₂×C₁₃×C₂₉	AGL(1,𝔽₇)	semidirect
21. C₂×#63271	D₂₉	semidirect
23. C₂×C₇×C₂₉	C₂×C₁₃⋊C₃	semidirect
24. D₂₀₃	C₂×C₁₃⋊C₃	semidirect
25. C₁₃×C₂₉	C₂×AGL(1,𝔽₇)	semidirect
28. #63271	C₂×D₂₉	semidirect
29. C₇×C₂₉	C₂²×C₁₃⋊C₃	semidirect
30. C₂×C₇×C₁₃	C₃×D₂₉	semidirect
36. C₇×C₁₃	C₂×C₃×D₂₉	semidirect
41. C₂×C₂₉	#10587721	semidirect
47. C₂₉	C₂×#10587721	semidirect
50. C₂×C₁₃	ΓL(1,𝔽₈)⋊D₂₉	semidirect
52. C₂×C₇	C₁₃⋊C₃×D₂₉	semidirect
54. C₁₃	C₂×ΓL(1,𝔽₈)⋊D₂₉	semidirect
56. C₇	C₂×C₁₃⋊C₃×D₂₉	semidirect
62. C₂	C₂₉⋊#10587721	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⋊#10587721	2
C₂×C₂₉×#63271	2
C₂×C₁₃×D₂₀₃	3
C₂×C₁₃⋊C₃×D₂₉	7
C₂×ΓL(1,𝔽₈)⋊D₂₉	13
C₂×#10587721	29

Subgroups — C2×C29⋊#10587721 #44539895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉⋊#10587721 #44539895