Subgroups — C₁₃×AGL(1,𝔽₇)×D₂₉ #44539814

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₃	AGL(1,𝔽₇)×D₂₉
commutator, cosocle, hypocenter	C₇×C₂₉	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₂²×C₃
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×ΓL(1,𝔽₈)⋊D₂₉	C₂	semidirect
2. C₁₃×C₂₉×AGL(1,𝔽₇)	C₂	semidirect
3. C₁₃×ΓL(1,𝔽₈)×D₂₉	C₂	semidirect
4. C₁₃×D₇×D₂₉	C₃	semidirect
5. C₁₃×ΓL(1,𝔽₈)×C₂₉	C₂²	semidirect
6. C₁₃×D₂₀₃	C₂×C₃	semidirect
7. C₁₃×D₇×C₂₉	C₂×C₃	semidirect
8. C₇×C₁₃×D₂₉	C₂×C₃	semidirect
10. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
11. AGL(1,𝔽₇)×D₂₉	C₁₃	direct (N × H)
16. ΓL(1,𝔽₈)⋊D₂₉	C₂×C₁₃	semidirect
17. C₂₉×AGL(1,𝔽₇)	C₂×C₁₃	semidirect
18. ΓL(1,𝔽₈)×D₂₉	C₂×C₁₃	semidirect
21. D₇×D₂₉	C₃×C₁₃	semidirect
24. C₁₃×D₂₉	AGL(1,𝔽₇)	direct (N × H)
25. ΓL(1,𝔽₈)×C₂₉	C₂²×C₁₃	semidirect
28. C₁₃×AGL(1,𝔽₇)	D₂₉	direct (N × H)
29. D₂₀₃	C₂×C₃×C₁₃	semidirect
30. C₇×D₂₉	C₂×C₃×C₁₃	semidirect
31. D₇×C₂₉	C₂×C₃×C₁₃	semidirect
32. C₁₃×C₂₉	C₂×AGL(1,𝔽₇)	semidirect
35. C₁₃×ΓL(1,𝔽₈)	C₂×D₂₉	semidirect
36. C₇×C₂₉	C₂²×C₃×C₁₃	semidirect
39. C₁₃×D₇	C₃×D₂₉	semidirect
45. C₇×C₁₃	C₂×C₃×D₂₉	semidirect
53. D₂₉	C₁₃×AGL(1,𝔽₇)	direct (N × H)
57. AGL(1,𝔽₇)	C₁₃×D₂₉	direct (N × H)
59. C₂₉	C₂×C₁₃×AGL(1,𝔽₇)	semidirect
64. ΓL(1,𝔽₈)	C₂×C₁₃×D₂₉	semidirect
67. D₇	C₃×C₁₃×D₂₉	semidirect
68. C₁₃	AGL(1,𝔽₇)×D₂₉	direct (N × H)
70. C₇	C₂×C₃×C₁₃×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×ΓL(1,𝔽₈)⋊D₂₉	2
C₁₃×C₂₉×AGL(1,𝔽₇)	2
C₁₃×ΓL(1,𝔽₈)×D₂₉	2
C₁₃×D₇×D₂₉	3
C₂×C₃×C₁₃×D₂₉	7
AGL(1,𝔽₇)×D₂₉	13
C₂×C₁₃×AGL(1,𝔽₇)	29

Subgroups — C13×AGL(1,𝔽7)×D29 #44539814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×AGL(1,𝔽₇)×D₂₉ #44539814