Group #49141297 — subgroups

Subgroups — D₉×C₂₉×D₃₅ #49141297

Order 36540.

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₃₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₂₉×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₂₉×D₃₅	—	3	1	no	maximal
5	C₅×C₇×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₇×D₉×C₂₉	—	5	1	no	maximal, Hall
7	C₂₉×D₁₀₅	—	3	1	no	—
8	C₅×D₃×C₇×C₂₉	—	3	1	no	—
9	C₃×C₂₉×D₃₅	D₃	1	1	yes	characteristic
10	D₅×D₉×C₂₉	—	7	1	no	maximal, Hall
11	C₂×C₂₉×D₃₅	—	9	1	no	Hall
12	C₂₉×D₆₃	—	5	1	no	—
13	C₇×D₉×C₂₉	D₅	1	1	yes	characteristic, complemented
14	C₉×D₇×C₂₉	—	5	1	no	—
15	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic
16	C₂₉×D₄₅	—	7	1	no	—
17	C₅×D₉×C₂₉	D₇	1	1	yes	characteristic, complemented
18	C₉×D₅×C₂₉	—	7	1	no	—
19	D₃×D₇×C₂₉	—	15	1	no	—
20	C₂₉×D₃₅	—	9	1	no	—
21	C₂₉×D₃₅	D₉	1	1	yes	characteristic, direct product factor
22	C₂×C₅×C₇×C₂₉	—	9	1	no	—
23	C₇×C₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
24	D₃×D₅×C₂₉	—	21	1	no	—
25	C₅×C₉×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
26	D₉×D₃₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂₉×D₂₁	—	15	1	no	—
28	D₃×C₇×C₂₉	—	3	1	no	—
29	C₃×D₇×C₂₉	—	5	1	no	—
30	C₂×D₉×C₂₉	—	35	1	no	Hall
31	C₅×C₇×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
32	C₂₉×D₁₅	—	21	1	no	—
33	C₅×D₃×C₂₉	—	3	1	no	—
34	C₃×D₅×C₂₉	—	7	1	no	—
35	C₂×D₇×C₂₉	—	45	1	no	Hall
36	D₃₁₅	C₂×C₂₉	1	1	yes	characteristic, complemented
37	C₅×C₇×D₉	C₂×C₂₉	1	1	yes	characteristic, complemented
38	C₉×D₃₅	C₂×C₂₉	1	1	yes	characteristic, complemented
39	C₃×C₇×C₂₉	D₃×D₅	1	1	yes	characteristic
40	C₂×D₅×C₂₉	—	63	1	no	Hall
41	C₂×C₉×C₂₉	—	35	1	no	—
42	D₉×C₂₉	—	35	1	no	—
43	D₉×C₂₉	D₃₅	1	1	yes	characteristic, direct product factor
44	C₃×C₅×C₂₉	D₃×D₇	1	1	yes	characteristic
45	D₃×D₃₅	—	3	1	no	—
46	C₂×C₇×C₂₉	—	9	1	no	—
47	D₇×C₂₉	—	5	1	no	—
48	D₇×C₂₉	—	45	1	no	—
49	C₂×D₃×C₂₉	—	105	1	no	—
50	C₅×C₇×C₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅×C₂₉	—	9	1	no	—
52	D₅×C₂₉	—	7	1	no	—
53	D₅×C₂₉	—	63	1	no	—
54	C₉×C₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
55	D₇×D₉	—	5	1	no	Hall
56	D₁₀₅	—	3	1	no	—
57	C₅×D₃×C₇	—	3	1	no	—
58	C₃×D₃₅	D₃×C₂₉	1	1	yes	characteristic
59	C₇×C₂₉	D₅×D₉	1	1	yes	characteristic, complemented, Hall
60	D₅×D₉	—	7	1	no	Hall
61	C₂×C₃×C₂₉	—	35	1	no	—
62	D₃×C₂₉	—	3	1	no	—
63	D₃×C₂₉	—	105	1	no	—
64	C₅×C₂₉	D₇×D₉	1	1	yes	characteristic, complemented, Hall
65	C₂×D₃₅	—	9	1	no	Hall
66	D₆₃	—	5	1	no	—
67	C₉×D₇	—	5	1	no	—
68	C₇×D₉	D₅×C₂₉	1	1	yes	characteristic, complemented
69	C₂²×C₂₉	—	315	1	no	Hall
70	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic
71	D₄₅	—	7	1	no	—
72	C₉×D₅	—	7	1	no	—
73	C₅×D₉	D₇×C₂₉	1	1	yes	characteristic, complemented
74	C₃×C₂₉	D₃×D₃₅	1	1	yes	characteristic
75	D₃×D₇	—	15	1	no	—
76	C₂×C₅×C₇	—	9	1	no	—
77	D₃₅	—	9	1	no	—
78	D₃₅	D₉×C₂₉	1	1	yes	characteristic, direct product factor
79	C₇×C₉	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
80	D₃×D₅	—	21	1	no	—
81	C₂×C₂₉	—	9	1	no	—
82	C₂×C₂₉	—	35	1	no	—
83	C₂×C₂₉	—	315	1	no	—
84	C₅×C₉	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
85	D₂₁	—	15	1	no	—
86	C₃×D₇	—	5	1	no	—
87	D₃×C₇	—	3	1	no	—
88	C₂×D₉	—	35	1	no	Hall
89	C₅×C₇	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Hall
90	D₁₅	—	21	1	no	—
91	C₃×D₅	—	7	1	no	—
92	C₅×D₃	—	3	1	no	—
93	C₂₉	D₉×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×D₇	—	45	1	no	Hall
95	C₃×C₇	D₃×D₅×C₂₉	1	1	yes	characteristic
96	C₂×D₅	—	63	1	no	Hall
97	C₂×C₉	—	35	1	no	—
98	D₉	—	35	1	no	—
99	D₉	C₂₉×D₃₅	1	1	yes	characteristic, direct product factor
100	C₃×C₅	D₃×D₇×C₂₉	1	1	yes	characteristic
101	C₂×C₇	—	9	1	no	—
102	D₇	—	5	1	no	—
103	D₇	—	45	1	no	—
104	C₂×D₃	—	105	1	no	—
105	C₂×C₅	—	9	1	no	—
106	D₅	—	7	1	no	—
107	D₅	—	63	1	no	—
108	C₉	C₂×C₂₉×D₃₅	1	1	yes	characteristic, complemented, Sylow
109	C₇	D₅×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	35	1	no	—
111	D₃	—	3	1	no	—
112	D₃	—	105	1	no	—
113	C₅	D₇×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	315	1	no	Sylow
115	C₃	D₃×C₂₉×D₃₅	1	1	yes	characteristic
116	C₂	—	9	1	no	—
117	C₂	—	35	1	no	—
118	C₂	—	315	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×D₃₁₅

C₂

yes

maximal, characteristic, complemented

C₅×C₇×D₉×C₂₉

C₂

yes

maximal, characteristic, complemented

C₉×C₂₉×D₃₅

C₂

yes

maximal, characteristic, complemented

D₃×C₂₉×D₃₅

—

maximal

C₅×C₇×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₇×D₉×C₂₉

—

maximal, Hall

C₂₉×D₁₀₅

—

C₅×D₃×C₇×C₂₉

—

C₃×C₂₉×D₃₅

D₃

yes

characteristic

D₅×D₉×C₂₉

—

maximal, Hall

C₂×C₂₉×D₃₅

—

Hall

C₂₉×D₆₃

—

C₇×D₉×C₂₉

D₅

yes

characteristic, complemented

C₉×D₇×C₂₉

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic

C₂₉×D₄₅

—

C₅×D₉×C₂₉

D₇

yes

characteristic, complemented

C₉×D₅×C₂₉

—

D₃×D₇×C₂₉

—

C₂₉×D₃₅

—

C₂₉×D₃₅

D₉

yes

characteristic, direct product factor

C₂×C₅×C₇×C₂₉

—

C₇×C₉×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

D₃×D₅×C₂₉

—

C₅×C₉×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

D₉×D₃₅

C₂₉

yes

maximal, characteristic, direct product factor, Hall

C₂₉×D₂₁

—

D₃×C₇×C₂₉

—

C₃×D₇×C₂₉

—

C₂×D₉×C₂₉

—

Hall

C₅×C₇×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

C₂₉×D₁₅

—

C₅×D₃×C₂₉

—

C₃×D₅×C₂₉

—

C₂×D₇×C₂₉

—

Hall

D₃₁₅

C₂×C₂₉

yes

characteristic, complemented

C₅×C₇×D₉

C₂×C₂₉

yes

characteristic, complemented

C₉×D₃₅

C₂×C₂₉

yes

characteristic, complemented

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic

C₂×D₅×C₂₉

—

Hall

C₂×C₉×C₂₉

—

D₉×C₂₉

—

D₉×C₂₉

D₃₅

yes

characteristic, direct product factor

C₃×C₅×C₂₉

D₃×D₇

yes

characteristic

D₃×D₃₅

—

C₂×C₇×C₂₉

—

D₇×C₂₉

—

D₇×C₂₉

—

C₂×D₃×C₂₉

—

105

—

C₅×C₇×C₉

C₂²×C₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

D₅×C₂₉

—

D₅×C₂₉

—

C₉×C₂₉

C₂×D₃₅

yes

characteristic, complemented, Hall

D₇×D₉

—

Hall

D₁₀₅

—

C₅×D₃×C₇

—

C₃×D₃₅

D₃×C₂₉

yes

characteristic

C₇×C₂₉

D₅×D₉

yes

characteristic, complemented, Hall

D₅×D₉

—

Hall

C₂×C₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

105

—

C₅×C₂₉

D₇×D₉

yes

characteristic, complemented, Hall

C₂×D₃₅

—

Hall

D₆₃

—

C₉×D₇

—

C₇×D₉

D₅×C₂₉

yes

characteristic, complemented

C₂²×C₂₉

—

315

Hall

C₃×C₅×C₇

C₂×D₃×C₂₉

yes

characteristic

D₄₅

—

C₉×D₅

—

C₅×D₉

D₇×C₂₉

yes

characteristic, complemented

C₃×C₂₉

D₃×D₃₅

yes

characteristic

D₃×D₇

—

C₂×C₅×C₇

—

D₃₅

—

D₃₅

D₉×C₂₉

yes

characteristic, direct product factor

C₇×C₉

C₂×D₅×C₂₉

yes

characteristic, complemented, Hall

D₃×D₅

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

315

—

C₅×C₉

C₂×D₇×C₂₉

yes

characteristic, complemented, Hall

D₂₁

—

C₃×D₇

—

D₃×C₇

—

C₂×D₉

—

Hall

C₅×C₇

C₂×D₉×C₂₉

yes

characteristic, complemented, Hall

D₁₅

—

C₃×D₅

—

C₅×D₃

—

C₂₉

D₉×D₃₅

yes

characteristic, direct product factor, Sylow

C₂×D₇

—

Hall

C₃×C₇

D₃×D₅×C₂₉

yes

characteristic

C₂×D₅

—

Hall

C₂×C₉

—

D₉

—

D₉

C₂₉×D₃₅

yes

characteristic, direct product factor

100

C₃×C₅

D₃×D₇×C₂₉

yes

characteristic

101

C₂×C₇

—

102

D₇

—

103

D₇

—

104

C₂×D₃

—

105

—

105

C₂×C₅

—

106

D₅

—

107

D₅

—

108

C₉

C₂×C₂₉×D₃₅

yes

characteristic, complemented, Sylow

109

C₇

D₅×D₉×C₂₉

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

112

D₃

—

105

—

113

C₅

D₇×D₉×C₂₉

yes

characteristic, complemented, Sylow

114

C₂²

—

315

Sylow

115

C₃

D₃×C₂₉×D₃₅

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

—

315

—

	subgroup	G/H
center, hypercenter	C₂₉	D₉×D₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₂₉
Frattini	C₃	D₃×C₂₉×D₃₅
Fitting	C₅×C₇×C₉×C₂₉	C₂²
socle	C₃×C₅×C₇×C₂₉	C₂×D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₂₉

subgroup

G/H

center, hypercenter

C₂₉

D₉×D₃₅

commutator, cosocle, hypocenter

C₅×C₇×C₉

C₂²×C₂₉

Frattini

C₃

D₃×C₂₉×D₃₅

Fitting

C₅×C₇×C₉×C₂₉

C₂²

socle

C₃×C₅×C₇×C₂₉

C₂×D₃

LCS

G ▷ C₅×C₇×C₉

UCS

C₁ ◁ C₂₉

N	H ≅ G/N	type
1. C₂₉×D₃₁₅	C₂	semidirect
2. C₅×C₇×D₉×C₂₉	C₂	semidirect
3. C₉×C₂₉×D₃₅	C₂	semidirect
5. C₅×C₇×C₉×C₂₉	C₂²	semidirect
13. C₇×D₉×C₂₉	D₅	semidirect
17. C₅×D₉×C₂₉	D₇	semidirect
21. C₂₉×D₃₅	D₉	direct (N × H)
23. C₇×C₉×C₂₉	C₂×D₅	semidirect
25. C₅×C₉×C₂₉	C₂×D₇	semidirect
26. D₉×D₃₅	C₂₉	direct (N × H)
31. C₅×C₇×C₂₉	C₂×D₉	semidirect
36. D₃₁₅	C₂×C₂₉	semidirect
37. C₅×C₇×D₉	C₂×C₂₉	semidirect
38. C₉×D₃₅	C₂×C₂₉	semidirect
43. D₉×C₂₉	D₃₅	direct (N × H)
50. C₅×C₇×C₉	C₂²×C₂₉	semidirect
54. C₉×C₂₉	C₂×D₃₅	semidirect
59. C₇×C₂₉	D₅×D₉	semidirect
64. C₅×C₂₉	D₇×D₉	semidirect
68. C₇×D₉	D₅×C₂₉	semidirect
73. C₅×D₉	D₇×C₂₉	semidirect
78. D₃₅	D₉×C₂₉	direct (N × H)
79. C₇×C₉	C₂×D₅×C₂₉	semidirect
84. C₅×C₉	C₂×D₇×C₂₉	semidirect
89. C₅×C₇	C₂×D₉×C₂₉	semidirect
93. C₂₉	D₉×D₃₅	direct (N × H)
99. D₉	C₂₉×D₃₅	direct (N × H)
108. C₉	C₂×C₂₉×D₃₅	semidirect
109. C₇	D₅×D₉×C₂₉	semidirect
113. C₅	D₇×D₉×C₂₉	semidirect

H ≅ G/N

type

1. C₂₉×D₃₁₅

C₂

semidirect

2. C₅×C₇×D₉×C₂₉

C₂

semidirect

3. C₉×C₂₉×D₃₅

C₂

semidirect

5. C₅×C₇×C₉×C₂₉

C₂²

semidirect

13. C₇×D₉×C₂₉

D₅

semidirect

17. C₅×D₉×C₂₉

D₇

semidirect

21. C₂₉×D₃₅

D₉

direct (N × H)

23. C₇×C₉×C₂₉

C₂×D₅

semidirect

25. C₅×C₉×C₂₉

C₂×D₇

semidirect

26. D₉×D₃₅

C₂₉

direct (N × H)

31. C₅×C₇×C₂₉

C₂×D₉

semidirect

36. D₃₁₅

C₂×C₂₉

semidirect

37. C₅×C₇×D₉

C₂×C₂₉

semidirect

38. C₉×D₃₅

C₂×C₂₉

semidirect

43. D₉×C₂₉

D₃₅

direct (N × H)

50. C₅×C₇×C₉

C₂²×C₂₉

semidirect

54. C₉×C₂₉

C₂×D₃₅

semidirect

59. C₇×C₂₉

D₅×D₉

semidirect

64. C₅×C₂₉

D₇×D₉

semidirect

68. C₇×D₉

D₅×C₂₉

semidirect

73. C₅×D₉

D₇×C₂₉

semidirect

78. D₃₅

D₉×C₂₉

direct (N × H)

79. C₇×C₉

C₂×D₅×C₂₉

semidirect

84. C₅×C₉

C₂×D₇×C₂₉

semidirect

89. C₅×C₇

C₂×D₉×C₂₉

semidirect

93. C₂₉

D₉×D₃₅

direct (N × H)

99. D₉

C₂₉×D₃₅

direct (N × H)

108. C₉

C₂×C₂₉×D₃₅

semidirect

109. C₇

D₅×D₉×C₂₉

semidirect

113. C₅

D₇×D₉×C₂₉

semidirect

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

subgroup	index
C₂₉×D₃₁₅	2
C₅×C₇×D₉×C₂₉	2
C₉×C₂₉×D₃₅	2
D₃×C₂₉×D₃₅	3
D₇×D₉×C₂₉	5
D₅×D₉×C₂₉	7
D₉×D₃₅	29

subgroup

index

C₂₉×D₃₁₅

C₅×C₇×D₉×C₂₉

C₉×C₂₉×D₃₅

D₃×C₂₉×D₃₅

D₇×D₉×C₂₉

D₅×D₉×C₂₉

D₉×D₃₅

Subgroups — D₉×C₂₉×D₃₅ #49141297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D9×C29×D35 #49141297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₂₉×D₃₅ #49141297