Group #49141597 — subgroups

Subgroups — C₅×D₃×C₂₉×D₂₁ #49141597

Order 36540.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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	C₃×C₅×D₃×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×C₂₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₂₉×D₂₁	—	3	1	no	maximal
5	C₅×D₃×D₇×C₂₉	—	3	1	no	maximal
6	C₃²×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×C₂₉×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₂₉×D₂₁	—	3	1	no	—
9	C₅×C₂₉×D₂₁	—	3	1	no	—
10	C₅×C₂₉×D₂₁	—	6	1	no	—
11	C₅×C₂₉×D₂₁	D₃	1	1	yes	characteristic, direct product factor
12	C₅×D₃×C₇×C₂₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₅×D₇×C₂₉	—	3	1	no	—
14	C₂×C₃×C₅×C₇×C₂₉	—	3	1	no	—
15	C₅×D₃²×C₂₉	—	7	1	no	maximal, Hall
16	C₂×C₅×D₇×C₂₉	—	9	1	no	Hall
17	C₂₉×C₃⋊D₂₁	C₂×C₅	1	1	yes	characteristic, complemented
18	C₃×C₂₉×D₂₁	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×D₃×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
20	C₃×C₅×C₇×C₂₉	—	2	1	no	—
21	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
22	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
23	C₅×C₃⋊D₃×C₂₉	—	7	1	no	—
24	C₃×C₅×D₃×C₂₉	—	7	1	no	—
25	C₃×C₅×D₃×C₂₉	D₇	1	1	yes	characteristic, complemented
26	C₂×C₂₉×D₂₁	—	3	1	no	—
27	D₃×D₇×C₂₉	—	3	1	no	—
28	C₅×D₇×C₂₉	—	3	1	no	—
29	C₅×D₇×C₂₉	—	9	1	no	—
30	C₂×C₅×C₇×C₂₉	—	3	1	no	—
31	C₃²×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅×D₃×C₂₉	—	21	1	no	—
33	C₂×C₅×D₃×C₂₉	—	21	1	no	—
34	C₃²×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
35	C₅×D₃×D₂₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₃×C₇×C₂₉	—	3	1	no	—
37	C₂₉×D₂₁	—	3	1	no	—
38	C₂₉×D₂₁	—	3	1	no	—
39	C₂₉×D₂₁	—	6	1	no	—
40	C₂₉×D₂₁	C₅×D₃	1	1	yes	characteristic, direct product factor
41	D₃×C₇×C₂₉	C₅×D₃	1	1	yes	characteristic, complemented
42	C₃×D₇×C₂₉	—	3	1	no	—
43	D₃²×C₂₉	—	7	1	no	Hall
44	C₅×C₇×C₂₉	D₃²	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅×C₂₉	—	3	1	no	—
46	C₂×C₃×C₅×C₂₉	—	21	1	no	—
47	C₅×D₃×C₂₉	—	7	1	no	—
48	C₅×D₃×C₂₉	—	21	1	no	—
49	C₅×D₃×C₂₉	—	21	1	no	—
50	C₅×D₃×C₂₉	—	42	1	no	—
51	C₅×D₃×C₂₉	D₂₁	1	1	yes	characteristic, direct product factor
52	C₂×D₇×C₂₉	—	9	1	no	Hall
53	C₅×C₃⋊D₂₁	C₂×C₂₉	1	1	yes	characteristic, complemented
54	C₃×C₅×D₂₁	C₂×C₂₉	1	1	yes	characteristic, complemented
55	C₃×C₅×D₃×C₇	C₂×C₂₉	1	1	yes	characteristic, complemented
56	C₃×C₇×C₂₉	—	2	1	no	—
57	C₃×C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented
58	C₃×C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented
59	C₂²×C₅×C₂₉	—	63	1	no	Hall
60	C₃⋊D₃×C₂₉	—	7	1	no	—
61	C₃×D₃×C₂₉	—	7	1	no	—
62	C₃×D₃×C₂₉	C₅×D₇	1	1	yes	characteristic, complemented
63	C₃×C₅×C₂₉	—	2	1	no	—
64	C₃×C₅×C₂₉	D₃×D₇	1	1	yes	characteristic, complemented
65	C₃×C₅×C₂₉	C₂×D₂₁	1	1	yes	characteristic, complemented
66	C₂×C₅×D₂₁	—	3	1	no	—
67	C₅×D₃×D₇	—	3	1	no	—
68	C₂×C₇×C₂₉	—	3	1	no	—
69	D₇×C₂₉	—	3	1	no	—
70	D₇×C₂₉	—	9	1	no	—
71	C₂×D₃×C₂₉	—	21	1	no	—
72	C₂×D₃×C₂₉	—	21	1	no	—
73	C₃²×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
74	C₂×C₅×C₂₉	—	3	1	no	—
75	C₂×C₅×C₂₉	—	21	1	no	—
76	C₂×C₅×C₂₉	—	63	1	no	—
77	C₃²×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
78	D₃×D₂₁	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
79	C₂×C₃×C₅×C₇	—	3	1	no	—
80	C₅×D₂₁	—	3	1	no	—
81	C₅×D₂₁	—	3	1	no	—
82	C₅×D₂₁	—	6	1	no	—
83	C₅×D₂₁	D₃×C₂₉	1	1	yes	characteristic, direct product factor
84	C₅×D₃×C₇	D₃×C₂₉	1	1	yes	characteristic, complemented
85	C₃×C₅×D₇	—	3	1	no	—
86	C₇×C₂₉	C₅×D₃²	1	1	yes	characteristic, complemented, Hall
87	C₅×D₃²	—	7	1	no	Hall
88	C₂×C₃×C₂₉	—	3	1	no	—
89	C₂×C₃×C₂₉	—	21	1	no	—
90	D₃×C₂₉	—	7	1	no	—
91	D₃×C₂₉	—	21	1	no	—
92	D₃×C₂₉	—	21	1	no	—
93	D₃×C₂₉	—	42	1	no	—
94	D₃×C₂₉	C₅×D₂₁	1	1	yes	characteristic, direct product factor
95	C₅×C₂₉	D₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
96	C₂×C₅×D₇	—	9	1	no	Hall
97	C₃⋊D₂₁	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
98	C₃×D₂₁	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
99	C₃×D₃×C₇	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
100	C₂²×C₂₉	—	63	1	no	Hall
101	C₃×C₅×C₇	—	2	1	no	—
102	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
103	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
104	C₅×C₃⋊D₃	—	7	1	no	—
105	C₃×C₅×D₃	—	7	1	no	—
106	C₃×C₅×D₃	D₇×C₂₉	1	1	yes	characteristic, complemented
107	C₃×C₂₉	—	2	1	no	—
108	C₃×C₂₉	C₅×D₃×D₇	1	1	yes	characteristic, complemented
109	C₃×C₂₉	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented
110	C₂×D₂₁	—	3	1	no	—
111	D₃×D₇	—	3	1	no	—
112	C₂×C₅×C₇	—	3	1	no	—
113	C₅×D₇	—	3	1	no	—
114	C₅×D₇	—	9	1	no	—
115	C₃²×C₇	C₂²×C₅×C₂₉	1	1	yes	characteristic, complemented, Hall
116	C₂×C₅×D₃	—	21	1	no	—
117	C₂×C₅×D₃	—	21	1	no	—
118	C₂×C₂₉	—	3	1	no	—
119	C₂×C₂₉	—	21	1	no	—
120	C₂×C₂₉	—	63	1	no	—
121	C₃²×C₅	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
122	C₂×C₃×C₇	—	3	1	no	—
123	D₂₁	—	3	1	no	—
124	D₂₁	—	3	1	no	—
125	D₂₁	—	6	1	no	—
126	D₂₁	C₅×D₃×C₂₉	1	1	yes	characteristic, direct product factor
127	C₃×D₇	—	3	1	no	—
128	D₃×C₇	C₅×D₃×C₂₉	1	1	yes	characteristic, complemented
129	D₃²	—	7	1	no	Hall
130	C₅×C₇	D₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
131	C₂×C₃×C₅	—	3	1	no	—
132	C₂×C₃×C₅	—	21	1	no	—
133	C₅×D₃	—	7	1	no	—
134	C₅×D₃	—	21	1	no	—
135	C₅×D₃	—	21	1	no	—
136	C₅×D₃	—	42	1	no	—
137	C₅×D₃	C₂₉×D₂₁	1	1	yes	characteristic, direct product factor
138	C₂₉	C₅×D₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
139	C₂×D₇	—	9	1	no	Hall
140	C₃×C₇	—	2	1	no	—
141	C₃×C₇	C₂×C₅×D₃×C₂₉	1	1	yes	characteristic, complemented
142	C₃×C₇	C₂×C₅×D₃×C₂₉	1	1	yes	characteristic, complemented
143	C₂²×C₅	—	63	1	no	Hall
144	C₃⋊D₃	—	7	1	no	—
145	C₃×D₃	—	7	1	no	—
146	C₃×D₃	C₅×D₇×C₂₉	1	1	yes	characteristic, complemented
147	C₃×C₅	—	2	1	no	—
148	C₃×C₅	D₃×D₇×C₂₉	1	1	yes	characteristic, complemented
149	C₃×C₅	C₂×C₂₉×D₂₁	1	1	yes	characteristic, complemented
150	C₂×C₇	—	3	1	no	—
151	D₇	—	3	1	no	—
152	D₇	—	9	1	no	—
153	C₂×D₃	—	21	1	no	—
154	C₂×D₃	—	21	1	no	—
155	C₂×C₅	—	3	1	no	—
156	C₂×C₅	—	21	1	no	—
157	C₂×C₅	—	63	1	no	—
158	C₃²	C₂×C₅×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
159	C₇	C₅×D₃²×C₂₉	1	1	yes	characteristic, complemented, Sylow
160	C₂×C₃	—	3	1	no	—
161	C₂×C₃	—	21	1	no	—
162	D₃	—	7	1	no	—
163	D₃	—	21	1	no	—
164	D₃	—	21	1	no	—
165	D₃	—	42	1	no	—
166	D₃	C₅×C₂₉×D₂₁	1	1	yes	characteristic, direct product factor
167	C₅	D₃×C₂₉×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²	—	63	1	no	Sylow
169	C₃	—	2	1	no	—
170	C₃	C₅×D₃×D₇×C₂₉	1	1	yes	characteristic, complemented
171	C₃	C₂×C₅×C₂₉×D₂₁	1	1	yes	characteristic, complemented
172	C₂	—	3	1	no	—
173	C₂	—	21	1	no	—
174	C₂	—	63	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×D₃×C₇×C₂₉

C₂

yes

maximal, characteristic, complemented

C₃×C₅×C₂₉×D₂₁

C₂

yes

maximal, characteristic, complemented

C₅×C₂₉×C₃⋊D₂₁

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₂₉×D₂₁

—

maximal

C₅×D₃×D₇×C₂₉

—

maximal

C₃²×C₅×C₇×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₃×C₂₉×D₂₁

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₂₉×D₂₁

—

C₅×C₂₉×D₂₁

—

C₅×C₂₉×D₂₁

—

C₅×C₂₉×D₂₁

D₃

yes

characteristic, direct product factor

C₅×D₃×C₇×C₂₉

D₃

yes

characteristic, complemented

C₃×C₅×D₇×C₂₉

—

C₂×C₃×C₅×C₇×C₂₉

—

C₅×D₃²×C₂₉

—

maximal, Hall

C₂×C₅×D₇×C₂₉

—

Hall

C₂₉×C₃⋊D₂₁

C₂×C₅

yes

characteristic, complemented

C₃×C₂₉×D₂₁

C₂×C₅

yes

characteristic, complemented

C₃×D₃×C₇×C₂₉

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₇×C₂₉

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic, complemented

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic, complemented

C₅×C₃⋊D₃×C₂₉

—

C₃×C₅×D₃×C₂₉

—

C₃×C₅×D₃×C₂₉

D₇

yes

characteristic, complemented

C₂×C₂₉×D₂₁

—

D₃×D₇×C₂₉

—

C₅×D₇×C₂₉

—

C₅×D₇×C₂₉

—

C₂×C₅×C₇×C₂₉

—

C₃²×C₇×C₂₉

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₂₉

—

C₂×C₅×D₃×C₂₉

—

C₃²×C₅×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

C₅×D₃×D₂₁

C₂₉

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₇×C₂₉

—

C₂₉×D₂₁

—

C₂₉×D₂₁

—

C₂₉×D₂₁

—

C₂₉×D₂₁

C₅×D₃

yes

characteristic, direct product factor

D₃×C₇×C₂₉

C₅×D₃

yes

characteristic, complemented

C₃×D₇×C₂₉

—

D₃²×C₂₉

—

Hall

C₅×C₇×C₂₉

D₃²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₂₉

—

C₂×C₃×C₅×C₂₉

—

C₅×D₃×C₂₉

—

C₅×D₃×C₂₉

—

C₅×D₃×C₂₉

—

C₅×D₃×C₂₉

—

C₅×D₃×C₂₉

D₂₁

yes

characteristic, direct product factor

C₂×D₇×C₂₉

—

Hall

C₅×C₃⋊D₂₁

C₂×C₂₉

yes

characteristic, complemented

C₃×C₅×D₂₁

C₂×C₂₉

yes

characteristic, complemented

C₃×C₅×D₃×C₇

C₂×C₂₉

yes

characteristic, complemented

C₃×C₇×C₂₉

—

C₃×C₇×C₂₉

C₂×C₅×D₃

yes

characteristic, complemented

C₃×C₇×C₂₉

C₂×C₅×D₃

yes

characteristic, complemented

C₂²×C₅×C₂₉

—

Hall

C₃⋊D₃×C₂₉

—

C₃×D₃×C₂₉

—

C₃×D₃×C₂₉

C₅×D₇

yes

characteristic, complemented

C₃×C₅×C₂₉

—

C₃×C₅×C₂₉

D₃×D₇

yes

characteristic, complemented

C₃×C₅×C₂₉

C₂×D₂₁

yes

characteristic, complemented

C₂×C₅×D₂₁

—

C₅×D₃×D₇

—

C₂×C₇×C₂₉

—

D₇×C₂₉

—

D₇×C₂₉

—

C₂×D₃×C₂₉

—

C₂×D₃×C₂₉

—

C₃²×C₅×C₇

C₂²×C₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

C₂×C₅×C₂₉

—

C₂×C₅×C₂₉

—

C₃²×C₂₉

C₂×C₅×D₇

yes

characteristic, complemented, Hall

D₃×D₂₁

C₅×C₂₉

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅×C₇

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₂₁

D₃×C₂₉

yes

characteristic, direct product factor

C₅×D₃×C₇

D₃×C₂₉

yes

characteristic, complemented

C₃×C₅×D₇

—

C₇×C₂₉

C₅×D₃²

yes

characteristic, complemented, Hall

C₅×D₃²

—

Hall

C₂×C₃×C₂₉

—

C₂×C₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

C₅×D₂₁

yes

characteristic, direct product factor

C₅×C₂₉

D₃×D₂₁

yes

characteristic, direct product factor, Hall

C₂×C₅×D₇

—

Hall

C₃⋊D₂₁

C₂×C₅×C₂₉

yes

characteristic, complemented

C₃×D₂₁

C₂×C₅×C₂₉

yes

characteristic, complemented

C₃×D₃×C₇

C₂×C₅×C₂₉

yes

characteristic, complemented

100

C₂²×C₂₉

—

Hall

101

C₃×C₅×C₇

—

102

C₃×C₅×C₇

C₂×D₃×C₂₉

yes

characteristic, complemented

103

C₃×C₅×C₇

C₂×D₃×C₂₉

yes

characteristic, complemented

104

C₅×C₃⋊D₃

—

105

C₃×C₅×D₃

—

106

C₃×C₅×D₃

D₇×C₂₉

yes

characteristic, complemented

107

C₃×C₂₉

—

108

C₃×C₂₉

C₅×D₃×D₇

yes

characteristic, complemented

109

C₃×C₂₉

C₂×C₅×D₂₁

yes

characteristic, complemented

110

C₂×D₂₁

—

111

D₃×D₇

—

112

C₂×C₅×C₇

—

113

C₅×D₇

—

114

C₅×D₇

—

115

C₃²×C₇

C₂²×C₅×C₂₉

yes

characteristic, complemented, Hall

116

C₂×C₅×D₃

—

117

C₂×C₅×D₃

—

118

C₂×C₂₉

—

119

C₂×C₂₉

—

120

C₂×C₂₉

—

121

C₃²×C₅

C₂×D₇×C₂₉

yes

characteristic, complemented, Hall

122

C₂×C₃×C₇

—

123

D₂₁

—

124

D₂₁

—

125

D₂₁

—

126

D₂₁

C₅×D₃×C₂₉

yes

characteristic, direct product factor

127

C₃×D₇

—

128

D₃×C₇

C₅×D₃×C₂₉

yes

characteristic, complemented

129

D₃²

—

Hall

130

C₅×C₇

D₃²×C₂₉

yes

characteristic, complemented, Hall

131

C₂×C₃×C₅

—

132

C₂×C₃×C₅

—

133

C₅×D₃

—

134

C₅×D₃

—

135

C₅×D₃

—

136

C₅×D₃

—

137

C₅×D₃

C₂₉×D₂₁

yes

characteristic, direct product factor

138

C₂₉

C₅×D₃×D₂₁

yes

characteristic, direct product factor, Sylow

139

C₂×D₇

—

Hall

140

C₃×C₇

—

141

C₃×C₇

C₂×C₅×D₃×C₂₉

yes

characteristic, complemented

142

C₃×C₇

C₂×C₅×D₃×C₂₉

yes

characteristic, complemented

143

C₂²×C₅

—

Hall

144

C₃⋊D₃

—

145

C₃×D₃

—

146

C₃×D₃

C₅×D₇×C₂₉

yes

characteristic, complemented

147

C₃×C₅

—

148

C₃×C₅

D₃×D₇×C₂₉

yes

characteristic, complemented

149

C₃×C₅

C₂×C₂₉×D₂₁

yes

characteristic, complemented

150

C₂×C₇

—

151

D₇

—

152

D₇

—

153

C₂×D₃

—

154

C₂×D₃

—

155

C₂×C₅

—

156

C₂×C₅

—

157

C₂×C₅

—

158

C₃²

C₂×C₅×D₇×C₂₉

yes

characteristic, complemented, Sylow

159

C₇

C₅×D₃²×C₂₉

yes

characteristic, complemented, Sylow

160

C₂×C₃

—

161

C₂×C₃

—

162

D₃

—

163

D₃

—

164

D₃

—

165

D₃

—

166

D₃

C₅×C₂₉×D₂₁

yes

characteristic, direct product factor

167

C₅

D₃×C₂₉×D₂₁

yes

characteristic, direct product factor, Sylow

168

C₂²

—

Sylow

169

C₃

—

170

C₃

C₅×D₃×D₇×C₂₉

yes

characteristic, complemented

171

C₃

C₂×C₅×C₂₉×D₂₁

yes

characteristic, complemented

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₃×D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₂₉

subgroup

G/H

center, hypercenter

C₅×C₂₉

D₃×D₂₁

commutator, cosocle, hypocenter

C₃²×C₇

C₂²×C₅×C₂₉

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₂₉

C₂²

LCS

G ▷ C₃²×C₇

UCS

C₁ ◁ C₅×C₂₉

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₇×C₂₉	C₂	semidirect
2. C₃×C₅×C₂₉×D₂₁	C₂	semidirect
3. C₅×C₂₉×C₃⋊D₂₁	C₂	semidirect
6. C₃²×C₅×C₇×C₂₉	C₂²	semidirect
7. D₃×C₂₉×D₂₁	C₅	direct (N × H)
11. C₅×C₂₉×D₂₁	D₃	direct (N × H)
12. C₅×D₃×C₇×C₂₉	D₃	semidirect
17. C₂₉×C₃⋊D₂₁	C₂×C₅	semidirect
18. C₃×C₂₉×D₂₁	C₂×C₅	semidirect
19. C₃×D₃×C₇×C₂₉	C₂×C₅	semidirect
21. C₃×C₅×C₇×C₂₉	C₂×D₃	semidirect
22. C₃×C₅×C₇×C₂₉	C₂×D₃	semidirect
25. C₃×C₅×D₃×C₂₉	D₇	semidirect
31. C₃²×C₇×C₂₉	C₂²×C₅	semidirect
34. C₃²×C₅×C₂₉	C₂×D₇	semidirect
35. C₅×D₃×D₂₁	C₂₉	direct (N × H)
40. C₂₉×D₂₁	C₅×D₃	direct (N × H)
41. D₃×C₇×C₂₉	C₅×D₃	semidirect
44. C₅×C₇×C₂₉	D₃²	semidirect
51. C₅×D₃×C₂₉	D₂₁	direct (N × H)
53. C₅×C₃⋊D₂₁	C₂×C₂₉	semidirect
54. C₃×C₅×D₂₁	C₂×C₂₉	semidirect
55. C₃×C₅×D₃×C₇	C₂×C₂₉	semidirect
57. C₃×C₇×C₂₉	C₂×C₅×D₃	semidirect
58. C₃×C₇×C₂₉	C₂×C₅×D₃	semidirect
62. C₃×D₃×C₂₉	C₅×D₇	semidirect
64. C₃×C₅×C₂₉	D₃×D₇	semidirect
65. C₃×C₅×C₂₉	C₂×D₂₁	semidirect
73. C₃²×C₅×C₇	C₂²×C₂₉	semidirect
77. C₃²×C₂₉	C₂×C₅×D₇	semidirect
78. D₃×D₂₁	C₅×C₂₉	direct (N × H)
83. C₅×D₂₁	D₃×C₂₉	direct (N × H)
84. C₅×D₃×C₇	D₃×C₂₉	semidirect
86. C₇×C₂₉	C₅×D₃²	semidirect
94. D₃×C₂₉	C₅×D₂₁	direct (N × H)
95. C₅×C₂₉	D₃×D₂₁	direct (N × H)
97. C₃⋊D₂₁	C₂×C₅×C₂₉	semidirect
98. C₃×D₂₁	C₂×C₅×C₂₉	semidirect
99. C₃×D₃×C₇	C₂×C₅×C₂₉	semidirect
102. C₃×C₅×C₇	C₂×D₃×C₂₉	semidirect
103. C₃×C₅×C₇	C₂×D₃×C₂₉	semidirect
106. C₃×C₅×D₃	D₇×C₂₉	semidirect
108. C₃×C₂₉	C₅×D₃×D₇	semidirect
109. C₃×C₂₉	C₂×C₅×D₂₁	semidirect
115. C₃²×C₇	C₂²×C₅×C₂₉	semidirect
121. C₃²×C₅	C₂×D₇×C₂₉	semidirect
126. D₂₁	C₅×D₃×C₂₉	direct (N × H)
128. D₃×C₇	C₅×D₃×C₂₉	semidirect
130. C₅×C₇	D₃²×C₂₉	semidirect
137. C₅×D₃	C₂₉×D₂₁	direct (N × H)
138. C₂₉	C₅×D₃×D₂₁	direct (N × H)
141. C₃×C₇	C₂×C₅×D₃×C₂₉	semidirect
142. C₃×C₇	C₂×C₅×D₃×C₂₉	semidirect
146. C₃×D₃	C₅×D₇×C₂₉	semidirect
148. C₃×C₅	D₃×D₇×C₂₉	semidirect
149. C₃×C₅	C₂×C₂₉×D₂₁	semidirect
158. C₃²	C₂×C₅×D₇×C₂₉	semidirect
159. C₇	C₅×D₃²×C₂₉	semidirect
166. D₃	C₅×C₂₉×D₂₁	direct (N × H)
167. C₅	D₃×C₂₉×D₂₁	direct (N × H)
170. C₃	C₅×D₃×D₇×C₂₉	semidirect
171. C₃	C₂×C₅×C₂₉×D₂₁	semidirect

H ≅ G/N

type

1. C₃×C₅×D₃×C₇×C₂₉

C₂

semidirect

2. C₃×C₅×C₂₉×D₂₁

C₂

semidirect

3. C₅×C₂₉×C₃⋊D₂₁

C₂

semidirect

6. C₃²×C₅×C₇×C₂₉

C₂²

semidirect

7. D₃×C₂₉×D₂₁

C₅

direct (N × H)

11. C₅×C₂₉×D₂₁

D₃

direct (N × H)

12. C₅×D₃×C₇×C₂₉

D₃

semidirect

17. C₂₉×C₃⋊D₂₁

C₂×C₅

semidirect

18. C₃×C₂₉×D₂₁

C₂×C₅

semidirect

19. C₃×D₃×C₇×C₂₉

C₂×C₅

semidirect

21. C₃×C₅×C₇×C₂₉

C₂×D₃

semidirect

22. C₃×C₅×C₇×C₂₉

C₂×D₃

semidirect

25. C₃×C₅×D₃×C₂₉

D₇

semidirect

31. C₃²×C₇×C₂₉

C₂²×C₅

semidirect

34. C₃²×C₅×C₂₉

C₂×D₇

semidirect

35. C₅×D₃×D₂₁

C₂₉

direct (N × H)

40. C₂₉×D₂₁

C₅×D₃

direct (N × H)

41. D₃×C₇×C₂₉

C₅×D₃

semidirect

44. C₅×C₇×C₂₉

D₃²

semidirect

51. C₅×D₃×C₂₉

D₂₁

direct (N × H)

53. C₅×C₃⋊D₂₁

C₂×C₂₉

semidirect

54. C₃×C₅×D₂₁

C₂×C₂₉

semidirect

55. C₃×C₅×D₃×C₇

C₂×C₂₉

semidirect

57. C₃×C₇×C₂₉

C₂×C₅×D₃

semidirect

58. C₃×C₇×C₂₉

C₂×C₅×D₃

semidirect

62. C₃×D₃×C₂₉

C₅×D₇

semidirect

64. C₃×C₅×C₂₉

D₃×D₇

semidirect

65. C₃×C₅×C₂₉

C₂×D₂₁

semidirect

73. C₃²×C₅×C₇

C₂²×C₂₉

semidirect

77. C₃²×C₂₉

C₂×C₅×D₇

semidirect

78. D₃×D₂₁

C₅×C₂₉

direct (N × H)

83. C₅×D₂₁

D₃×C₂₉

direct (N × H)

84. C₅×D₃×C₇

D₃×C₂₉

semidirect

86. C₇×C₂₉

C₅×D₃²

semidirect

94. D₃×C₂₉

C₅×D₂₁

direct (N × H)

95. C₅×C₂₉

D₃×D₂₁

direct (N × H)

97. C₃⋊D₂₁

C₂×C₅×C₂₉

semidirect

98. C₃×D₂₁

C₂×C₅×C₂₉

semidirect

99. C₃×D₃×C₇

C₂×C₅×C₂₉

semidirect

102. C₃×C₅×C₇

C₂×D₃×C₂₉

semidirect

103. C₃×C₅×C₇

C₂×D₃×C₂₉

semidirect

106. C₃×C₅×D₃

D₇×C₂₉

semidirect

108. C₃×C₂₉

C₅×D₃×D₇

semidirect

109. C₃×C₂₉

C₂×C₅×D₂₁

semidirect

115. C₃²×C₇

C₂²×C₅×C₂₉

semidirect

121. C₃²×C₅

C₂×D₇×C₂₉

semidirect

126. D₂₁

C₅×D₃×C₂₉

direct (N × H)

128. D₃×C₇

C₅×D₃×C₂₉

semidirect

130. C₅×C₇

D₃²×C₂₉

semidirect

137. C₅×D₃

C₂₉×D₂₁

direct (N × H)

138. C₂₉

C₅×D₃×D₂₁

direct (N × H)

141. C₃×C₇

C₂×C₅×D₃×C₂₉

semidirect

142. C₃×C₇

C₂×C₅×D₃×C₂₉

semidirect

146. C₃×D₃

C₅×D₇×C₂₉

semidirect

148. C₃×C₅

D₃×D₇×C₂₉

semidirect

149. C₃×C₅

C₂×C₂₉×D₂₁

semidirect

158. C₃²

C₂×C₅×D₇×C₂₉

semidirect

159. C₇

C₅×D₃²×C₂₉

semidirect

166. D₃

C₅×C₂₉×D₂₁

direct (N × H)

167. C₅

D₃×C₂₉×D₂₁

direct (N × H)

170. C₃

C₅×D₃×D₇×C₂₉

semidirect

171. C₃

C₂×C₅×C₂₉×D₂₁

semidirect

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

subgroup	index
C₃×C₅×D₃×C₇×C₂₉	2
C₃×C₅×C₂₉×D₂₁	2
C₅×C₂₉×C₃⋊D₂₁	2
C₂×C₅×C₂₉×D₂₁	3
C₅×D₃×D₇×C₂₉	3
D₃×C₂₉×D₂₁	5
C₅×D₃²×C₂₉	7
C₅×D₃×D₂₁	29

subgroup

index

C₃×C₅×D₃×C₇×C₂₉

C₃×C₅×C₂₉×D₂₁

C₅×C₂₉×C₃⋊D₂₁

C₂×C₅×C₂₉×D₂₁

C₅×D₃×D₇×C₂₉

D₃×C₂₉×D₂₁

C₅×D₃²×C₂₉

C₅×D₃×D₂₁

Subgroups — C₅×D₃×C₂₉×D₂₁ #49141597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D3×C29×D21 #49141597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₂₉×D₂₁ #49141597