Subgroups — D₇×C₂₉×D₃₅ #43249362

Order 28420.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂₉×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₅⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇²×C₂₉	—	5	1	no	maximal, Hall
6	C₂×C₂₉×D₃₅	—	7	1	no	maximal
7	D₅×D₇×C₂₉	—	7	1	no	maximal
8	C₂₉×C₇⋊D₇	—	5	1	no	—
9	C₇×D₇×C₂₉	—	5	1	no	—
10	C₇×D₇×C₂₉	D₅	1	1	yes	characteristic, complemented
11	C₂₉×D₃₅	—	7	1	no	—
12	C₂₉×D₃₅	—	7	1	no	—
13	C₂₉×D₃₅	—	14	3	no	—
14	C₂₉×D₃₅	D₇	1	1	yes	characteristic, direct product factor
15	C₇×D₅×C₂₉	—	7	1	no	—
16	C₅×D₇×C₂₉	D₇	1	1	yes	characteristic, complemented
17	C₂×C₅×C₇×C₂₉	—	7	1	no	—
18	C₇²×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	C₅×C₇×C₂₉	—	2	3	no	—
20	C₅×C₇×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented
21	C₅×C₇×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented
22	D₇×D₃₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×D₇×C₂₉	—	35	1	no	—
24	C₂×D₇×C₂₉	—	35	1	no	—
25	C₂×D₅×C₂₉	—	49	1	no	Hall
26	C₅⋊(C₇⋊D₇)	C₂×C₂₉	1	1	yes	characteristic, complemented
27	C₇×D₃₅	C₂×C₂₉	1	1	yes	characteristic, complemented
28	C₅×C₇×D₇	C₂×C₂₉	1	1	yes	characteristic, complemented
29	C₂×C₇×C₂₉	—	7	1	no	—
30	C₂×C₇×C₂₉	—	35	1	no	—
31	D₇×C₂₉	—	5	1	no	—
32	D₇×C₂₉	—	35	1	no	—
33	D₇×C₂₉	—	35	1	no	—
34	D₇×C₂₉	—	70	3	no	—
35	D₇×C₂₉	D₃₅	1	1	yes	characteristic, direct product factor
36	C₂×C₅×C₂₉	—	7	1	no	—
37	D₅×C₂₉	—	7	1	no	—
38	D₅×C₂₉	—	49	1	no	—
39	C₅×C₇²	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
40	C₇×C₂₉	—	2	3	no	—
41	C₇×C₂₉	D₅×D₇	1	1	yes	characteristic, complemented
42	C₇×C₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented
43	D₇²	—	5	1	no	Hall
44	C₅×C₂₉	D₇²	1	1	yes	characteristic, complemented, Hall
45	C₂×D₃₅	—	7	1	no	—
46	D₅×D₇	—	7	1	no	—
47	C₂²×C₂₉	—	245	1	no	Hall
48	C₇⋊D₇	—	5	1	no	—
49	C₇×D₇	—	5	1	no	—
50	C₇×D₇	D₅×C₂₉	1	1	yes	characteristic, complemented
51	C₂×C₅×C₇	—	7	1	no	—
52	D₃₅	—	7	1	no	—
53	D₃₅	—	7	1	no	—
54	D₃₅	—	14	3	no	—
55	D₃₅	D₇×C₂₉	1	1	yes	characteristic, direct product factor
56	C₅×D₇	D₇×C₂₉	1	1	yes	characteristic, complemented
57	C₇×D₅	—	7	1	no	—
58	C₂×C₂₉	—	7	1	no	—
59	C₂×C₂₉	—	35	1	no	—
60	C₂×C₂₉	—	245	1	no	—
61	C₇²	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
62	C₅×C₇	—	2	3	no	—
63	C₅×C₇	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented
64	C₅×C₇	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented
65	C₂₉	D₇×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×D₇	—	35	1	no	—
67	C₂×D₇	—	35	1	no	—
68	C₂×D₅	—	49	1	no	Hall
69	C₂×C₇	—	7	1	no	—
70	C₂×C₇	—	35	1	no	—
71	D₇	—	5	1	no	—
72	D₇	—	35	1	no	—
73	D₇	—	35	1	no	—
74	D₇	—	70	3	no	—
75	D₇	C₂₉×D₃₅	1	1	yes	characteristic, direct product factor
76	C₂×C₅	—	7	1	no	—
77	D₅	—	7	1	no	—
78	D₅	—	49	1	no	—
79	C₇	—	2	3	no	—
80	C₇	D₅×D₇×C₂₉	1	1	yes	characteristic, complemented
81	C₇	C₂×C₂₉×D₃₅	1	1	yes	characteristic, complemented
82	C₅	D₇²×C₂₉	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	245	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	35	1	no	—
86	C₂	—	245	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₇×D₃₅
commutator, cosocle, hypocenter	C₅×C₇²	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₂²
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₇×C₂₉	C₂	semidirect
2. C₇×C₂₉×D₃₅	C₂	semidirect
3. C₂₉×C₅⋊(C₇⋊D₇)	C₂	semidirect
4. C₅×C₇²×C₂₉	C₂²	semidirect
10. C₇×D₇×C₂₉	D₅	semidirect
14. C₂₉×D₃₅	D₇	direct (N × H)
16. C₅×D₇×C₂₉	D₇	semidirect
18. C₇²×C₂₉	C₂×D₅	semidirect
20. C₅×C₇×C₂₉	C₂×D₇	semidirect
21. C₅×C₇×C₂₉	C₂×D₇	semidirect
22. D₇×D₃₅	C₂₉	direct (N × H)
26. C₅⋊(C₇⋊D₇)	C₂×C₂₉	semidirect
27. C₇×D₃₅	C₂×C₂₉	semidirect
28. C₅×C₇×D₇	C₂×C₂₉	semidirect
35. D₇×C₂₉	D₃₅	direct (N × H)
39. C₅×C₇²	C₂²×C₂₉	semidirect
41. C₇×C₂₉	D₅×D₇	semidirect
42. C₇×C₂₉	C₂×D₃₅	semidirect
44. C₅×C₂₉	D₇²	semidirect
50. C₇×D₇	D₅×C₂₉	semidirect
55. D₃₅	D₇×C₂₉	direct (N × H)
56. C₅×D₇	D₇×C₂₉	semidirect
61. C₇²	C₂×D₅×C₂₉	semidirect
63. C₅×C₇	C₂×D₇×C₂₉	semidirect
64. C₅×C₇	C₂×D₇×C₂₉	semidirect
65. C₂₉	D₇×D₃₅	direct (N × H)
75. D₇	C₂₉×D₃₅	direct (N × H)
80. C₇	D₅×D₇×C₂₉	semidirect
81. C₇	C₂×C₂₉×D₃₅	semidirect
82. C₅	D₇²×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×D₇×C₂₉	2
C₇×C₂₉×D₃₅	2
C₂₉×C₅⋊(C₇⋊D₇)	2
D₇²×C₂₉	5
C₂×C₂₉×D₃₅	7
D₅×D₇×C₂₉	7
D₇×D₃₅	29

Subgroups — D7×C29×D35 #43249362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₂₉×D₃₅ #43249362