Group #49141604 — subgroups

Subgroups — D₃×C₇×C₂₉×D₁₅ #49141604

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×C₇×C₂₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₂₉×D₁₅	—	3	1	no	maximal
5	D₃×C₇×D₅×C₂₉	—	3	1	no	maximal
6	C₃²×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃²×C₇×C₂₉	—	5	1	no	maximal, Hall
8	C₇×C₂₉×D₁₅	—	3	1	no	—
9	C₇×C₂₉×D₁₅	—	3	1	no	—
10	C₇×C₂₉×D₁₅	—	6	1	no	—
11	C₇×C₂₉×D₁₅	D₃	1	1	yes	characteristic, direct product factor
12	C₅×D₃×C₇×C₂₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₅×C₂₉	—	3	1	no	—
14	C₂×C₃×C₅×C₇×C₂₉	—	3	1	no	—
15	D₃×C₂₉×D₁₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₇×D₅×C₂₉	—	9	1	no	Hall
17	C₇×C₃⋊D₃×C₂₉	—	5	1	no	—
18	C₃×D₃×C₇×C₂₉	—	5	1	no	—
19	C₃×D₃×C₇×C₂₉	D₅	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	C₂₉×C₃⋊D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
24	C₃×C₂₉×D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
25	C₃×C₅×D₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
26	C₂×D₃×C₇×C₂₉	—	15	1	no	—
27	C₂×D₃×C₇×C₂₉	—	15	1	no	—
28	C₇×D₅×C₂₉	—	3	1	no	—
29	C₇×D₅×C₂₉	—	9	1	no	—
30	C₂×C₅×C₇×C₂₉	—	3	1	no	—
31	C₃²×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₉×D₁₅	—	3	1	no	—
33	D₃×D₅×C₂₉	—	3	1	no	—
34	C₃²×C₅×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
35	D₃×C₇×D₁₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₃×C₇×C₂₉	—	3	1	no	—
37	C₂×C₃×C₇×C₂₉	—	15	1	no	—
38	D₃×C₇×C₂₉	—	5	1	no	—
39	D₃×C₇×C₂₉	—	15	1	no	—
40	D₃×C₇×C₂₉	—	15	1	no	—
41	D₃×C₇×C₂₉	—	30	1	no	—
42	D₃×C₇×C₂₉	D₁₅	1	1	yes	characteristic, direct product factor
43	D₃²×C₂₉	—	5	1	no	Hall
44	C₅×C₇×C₂₉	D₃²	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅×C₂₉	—	3	1	no	—
46	C₂₉×D₁₅	—	3	1	no	—
47	C₂₉×D₁₅	—	3	1	no	—
48	C₂₉×D₁₅	—	6	1	no	—
49	C₂₉×D₁₅	D₃×C₇	1	1	yes	characteristic, direct product factor
50	C₅×D₃×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented
51	C₃×D₅×C₂₉	—	3	1	no	—
52	C₂²×C₇×C₂₉	—	45	1	no	Hall
53	C₇×C₃⋊D₁₅	C₂×C₂₉	1	1	yes	characteristic, complemented
54	C₃×C₇×D₁₅	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	D₃×D₅	1	1	yes	characteristic, complemented
58	C₃×C₇×C₂₉	C₂×D₁₅	1	1	yes	characteristic, complemented
59	C₂×D₅×C₂₉	—	9	1	no	Hall
60	C₃⋊D₃×C₂₉	—	5	1	no	—
61	C₃×D₃×C₂₉	—	5	1	no	—
62	C₃×D₃×C₂₉	C₇×D₅	1	1	yes	characteristic, complemented
63	C₃×C₅×C₂₉	—	2	1	no	—
64	C₃×C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented
65	C₃×C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented
66	C₂×C₇×D₁₅	—	3	1	no	—
67	D₃×C₇×D₅	—	3	1	no	—
68	C₂×C₇×C₂₉	—	3	1	no	—
69	C₂×C₇×C₂₉	—	15	1	no	—
70	C₂×C₇×C₂₉	—	45	1	no	—
71	C₂×D₃×C₂₉	—	15	1	no	—
72	C₂×D₃×C₂₉	—	15	1	no	—
73	C₃²×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
74	C₂×C₅×C₂₉	—	3	1	no	—
75	D₅×C₂₉	—	3	1	no	—
76	D₅×C₂₉	—	9	1	no	—
77	C₃²×C₂₉	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
78	D₃²×C₇	—	5	1	no	Hall
79	C₂×C₃×C₅×C₇	—	3	1	no	—
80	C₇×D₁₅	—	3	1	no	—
81	C₇×D₁₅	—	3	1	no	—
82	C₇×D₁₅	—	6	1	no	—
83	C₇×D₁₅	D₃×C₂₉	1	1	yes	characteristic, direct product factor
84	C₅×D₃×C₇	D₃×C₂₉	1	1	yes	characteristic, complemented
85	C₃×C₇×D₅	—	3	1	no	—
86	C₇×C₂₉	D₃×D₁₅	1	1	yes	characteristic, direct product factor, Hall
87	D₃×D₁₅	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
88	C₂×C₃×C₂₉	—	3	1	no	—
89	C₂×C₃×C₂₉	—	15	1	no	—
90	D₃×C₂₉	—	5	1	no	—
91	D₃×C₂₉	—	15	1	no	—
92	D₃×C₂₉	—	15	1	no	—
93	D₃×C₂₉	—	30	1	no	—
94	D₃×C₂₉	C₇×D₁₅	1	1	yes	characteristic, direct product factor
95	C₅×C₂₉	D₃²×C₇	1	1	yes	characteristic, complemented, Hall
96	C₂×C₇×D₅	—	9	1	no	Hall
97	C₇×C₃⋊D₃	—	5	1	no	—
98	C₃×D₃×C₇	—	5	1	no	—
99	C₃×D₃×C₇	D₅×C₂₉	1	1	yes	characteristic, complemented
100	C₂²×C₂₉	—	45	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	C₃⋊D₁₅	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
105	C₃×D₁₅	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
106	C₃×C₅×D₃	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
107	C₃×C₂₉	—	2	1	no	—
108	C₃×C₂₉	D₃×C₇×D₅	1	1	yes	characteristic, complemented
109	C₃×C₂₉	C₂×C₇×D₁₅	1	1	yes	characteristic, complemented
110	C₂×D₃×C₇	—	15	1	no	—
111	C₂×D₃×C₇	—	15	1	no	—
112	C₂×C₅×C₇	—	3	1	no	—
113	C₇×D₅	—	3	1	no	—
114	C₇×D₅	—	9	1	no	—
115	C₃²×C₇	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
116	C₂×D₁₅	—	3	1	no	—
117	D₃×D₅	—	3	1	no	—
118	C₂×C₂₉	—	3	1	no	—
119	C₂×C₂₉	—	15	1	no	—
120	C₂×C₂₉	—	45	1	no	—
121	C₃²×C₅	C₂²×C₇×C₂₉	1	1	yes	characteristic, complemented, Hall
122	C₂×C₃×C₇	—	3	1	no	—
123	C₂×C₃×C₇	—	15	1	no	—
124	D₃×C₇	—	5	1	no	—
125	D₃×C₇	—	15	1	no	—
126	D₃×C₇	—	15	1	no	—
127	D₃×C₇	—	30	1	no	—
128	D₃×C₇	C₂₉×D₁₅	1	1	yes	characteristic, direct product factor
129	D₃²	—	5	1	no	Hall
130	C₅×C₇	D₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
131	C₂×C₃×C₅	—	3	1	no	—
132	D₁₅	—	3	1	no	—
133	D₁₅	—	3	1	no	—
134	D₁₅	—	6	1	no	—
135	D₁₅	D₃×C₇×C₂₉	1	1	yes	characteristic, direct product factor
136	C₃×D₅	—	3	1	no	—
137	C₅×D₃	D₃×C₇×C₂₉	1	1	yes	characteristic, complemented
138	C₂₉	D₃×C₇×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
139	C₂²×C₇	—	45	1	no	Hall
140	C₃×C₇	—	2	1	no	—
141	C₃×C₇	D₃×D₅×C₂₉	1	1	yes	characteristic, complemented
142	C₃×C₇	C₂×C₂₉×D₁₅	1	1	yes	characteristic, complemented
143	C₂×D₅	—	9	1	no	Hall
144	C₃⋊D₃	—	5	1	no	—
145	C₃×D₃	—	5	1	no	—
146	C₃×D₃	C₇×D₅×C₂₉	1	1	yes	characteristic, complemented
147	C₃×C₅	—	2	1	no	—
148	C₃×C₅	C₂×D₃×C₇×C₂₉	1	1	yes	characteristic, complemented
149	C₃×C₅	C₂×D₃×C₇×C₂₉	1	1	yes	characteristic, complemented
150	C₂×C₇	—	3	1	no	—
151	C₂×C₇	—	15	1	no	—
152	C₂×C₇	—	45	1	no	—
153	C₂×D₃	—	15	1	no	—
154	C₂×D₃	—	15	1	no	—
155	C₂×C₅	—	3	1	no	—
156	D₅	—	3	1	no	—
157	D₅	—	9	1	no	—
158	C₃²	C₂×C₇×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
159	C₇	D₃×C₂₉×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
160	C₂×C₃	—	3	1	no	—
161	C₂×C₃	—	15	1	no	—
162	D₃	—	5	1	no	—
163	D₃	—	15	1	no	—
164	D₃	—	15	1	no	—
165	D₃	—	30	1	no	—
166	D₃	C₇×C₂₉×D₁₅	1	1	yes	characteristic, direct product factor
167	C₅	D₃²×C₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
168	C₂²	—	45	1	no	Sylow
169	C₃	—	2	1	no	—
170	C₃	D₃×C₇×D₅×C₂₉	1	1	yes	characteristic, complemented
171	C₃	C₂×C₇×C₂₉×D₁₅	1	1	yes	characteristic, complemented
172	C₂	—	3	1	no	—
173	C₂	—	15	1	no	—
174	C₂	—	45	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×D₃×C₇×C₂₉

C₂

yes

maximal, characteristic, complemented

C₃×C₇×C₂₉×D₁₅

C₂

yes

maximal, characteristic, complemented

C₇×C₂₉×C₃⋊D₁₅

C₂

yes

maximal, characteristic, complemented

C₂×C₇×C₂₉×D₁₅

—

maximal

D₃×C₇×D₅×C₂₉

—

maximal

C₃²×C₅×C₇×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₃²×C₇×C₂₉

—

maximal, Hall

C₇×C₂₉×D₁₅

—

C₇×C₂₉×D₁₅

—

C₇×C₂₉×D₁₅

—

C₇×C₂₉×D₁₅

D₃

yes

characteristic, direct product factor

C₅×D₃×C₇×C₂₉

D₃

yes

characteristic, complemented

C₃×C₇×D₅×C₂₉

—

C₂×C₃×C₅×C₇×C₂₉

—

D₃×C₂₉×D₁₅

C₇

yes

maximal, characteristic, direct product factor, Hall

C₂×C₇×D₅×C₂₉

—

Hall

C₇×C₃⋊D₃×C₂₉

—

C₃×D₃×C₇×C₂₉

—

C₃×D₃×C₇×C₂₉

D₅

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

C₂₉×C₃⋊D₁₅

C₂×C₇

yes

characteristic, complemented

C₃×C₂₉×D₁₅

C₂×C₇

yes

characteristic, complemented

C₃×C₅×D₃×C₂₉

C₂×C₇

yes

characteristic, complemented

C₂×D₃×C₇×C₂₉

—

C₂×D₃×C₇×C₂₉

—

C₇×D₅×C₂₉

—

C₇×D₅×C₂₉

—

C₂×C₅×C₇×C₂₉

—

C₃²×C₇×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₂₉×D₁₅

—

D₃×D₅×C₂₉

—

C₃²×C₅×C₂₉

C₂²×C₇

yes

characteristic, complemented, Hall

D₃×C₇×D₁₅

C₂₉

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₇×C₂₉

—

C₂×C₃×C₇×C₂₉

—

D₃×C₇×C₂₉

—

D₃×C₇×C₂₉

—

D₃×C₇×C₂₉

—

D₃×C₇×C₂₉

—

D₃×C₇×C₂₉

D₁₅

yes

characteristic, direct product factor

D₃²×C₂₉

—

Hall

C₅×C₇×C₂₉

D₃²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₂₉

—

C₂₉×D₁₅

—

C₂₉×D₁₅

—

C₂₉×D₁₅

—

C₂₉×D₁₅

D₃×C₇

yes

characteristic, direct product factor

C₅×D₃×C₂₉

D₃×C₇

yes

characteristic, complemented

C₃×D₅×C₂₉

—

C₂²×C₇×C₂₉

—

Hall

C₇×C₃⋊D₁₅

C₂×C₂₉

yes

characteristic, complemented

C₃×C₇×D₁₅

C₂×C₂₉

yes

characteristic, complemented

C₃×C₅×D₃×C₇

C₂×C₂₉

yes

characteristic, complemented

C₃×C₇×C₂₉

—

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic, complemented

C₃×C₇×C₂₉

C₂×D₁₅

yes

characteristic, complemented

C₂×D₅×C₂₉

—

Hall

C₃⋊D₃×C₂₉

—

C₃×D₃×C₂₉

—

C₃×D₃×C₂₉

C₇×D₅

yes

characteristic, complemented

C₃×C₅×C₂₉

—

C₃×C₅×C₂₉

C₂×D₃×C₇

yes

characteristic, complemented

C₃×C₅×C₂₉

C₂×D₃×C₇

yes

characteristic, complemented

C₂×C₇×D₁₅

—

D₃×C₇×D₅

—

C₂×C₇×C₂₉

—

C₂×C₇×C₂₉

—

C₂×C₇×C₂₉

—

C₂×D₃×C₂₉

—

C₂×D₃×C₂₉

—

C₃²×C₅×C₇

C₂²×C₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

D₅×C₂₉

—

D₅×C₂₉

—

C₃²×C₂₉

C₂×C₇×D₅

yes

characteristic, complemented, Hall

D₃²×C₇

—

Hall

C₂×C₃×C₅×C₇

—

C₇×D₁₅

—

C₇×D₁₅

—

C₇×D₁₅

—

C₇×D₁₅

D₃×C₂₉

yes

characteristic, direct product factor

C₅×D₃×C₇

D₃×C₂₉

yes

characteristic, complemented

C₃×C₇×D₅

—

C₇×C₂₉

D₃×D₁₅

yes

characteristic, direct product factor, Hall

D₃×D₁₅

C₇×C₂₉

yes

characteristic, direct product factor, Hall

C₂×C₃×C₂₉

—

C₂×C₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

C₇×D₁₅

yes

characteristic, direct product factor

C₅×C₂₉

D₃²×C₇

yes

characteristic, complemented, Hall

C₂×C₇×D₅

—

Hall

C₇×C₃⋊D₃

—

C₃×D₃×C₇

—

C₃×D₃×C₇

D₅×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

C₃⋊D₁₅

C₂×C₇×C₂₉

yes

characteristic, complemented

105

C₃×D₁₅

C₂×C₇×C₂₉

yes

characteristic, complemented

106

C₃×C₅×D₃

C₂×C₇×C₂₉

yes

characteristic, complemented

107

C₃×C₂₉

—

108

C₃×C₂₉

D₃×C₇×D₅

yes

characteristic, complemented

109

C₃×C₂₉

C₂×C₇×D₁₅

yes

characteristic, complemented

110

C₂×D₃×C₇

—

111

C₂×D₃×C₇

—

112

C₂×C₅×C₇

—

113

C₇×D₅

—

114

C₇×D₅

—

115

C₃²×C₇

C₂×D₅×C₂₉

yes

characteristic, complemented, Hall

116

C₂×D₁₅

—

117

D₃×D₅

—

118

C₂×C₂₉

—

119

C₂×C₂₉

—

120

C₂×C₂₉

—

121

C₃²×C₅

C₂²×C₇×C₂₉

yes

characteristic, complemented, Hall

122

C₂×C₃×C₇

—

123

C₂×C₃×C₇

—

124

D₃×C₇

—

125

D₃×C₇

—

126

D₃×C₇

—

127

D₃×C₇

—

128

D₃×C₇

C₂₉×D₁₅

yes

characteristic, direct product factor

129

D₃²

—

Hall

130

C₅×C₇

D₃²×C₂₉

yes

characteristic, complemented, Hall

131

C₂×C₃×C₅

—

132

D₁₅

—

133

D₁₅

—

134

D₁₅

—

135

D₁₅

D₃×C₇×C₂₉

yes

characteristic, direct product factor

136

C₃×D₅

—

137

C₅×D₃

D₃×C₇×C₂₉

yes

characteristic, complemented

138

C₂₉

D₃×C₇×D₁₅

yes

characteristic, direct product factor, Sylow

139

C₂²×C₇

—

Hall

140

C₃×C₇

—

141

C₃×C₇

D₃×D₅×C₂₉

yes

characteristic, complemented

142

C₃×C₇

C₂×C₂₉×D₁₅

yes

characteristic, complemented

143

C₂×D₅

—

Hall

144

C₃⋊D₃

—

145

C₃×D₃

—

146

C₃×D₃

C₇×D₅×C₂₉

yes

characteristic, complemented

147

C₃×C₅

—

148

C₃×C₅

C₂×D₃×C₇×C₂₉

yes

characteristic, complemented

149

C₃×C₅

C₂×D₃×C₇×C₂₉

yes

characteristic, complemented

150

C₂×C₇

—

151

C₂×C₇

—

152

C₂×C₇

—

153

C₂×D₃

—

154

C₂×D₃

—

155

C₂×C₅

—

156

D₅

—

157

D₅

—

158

C₃²

C₂×C₇×D₅×C₂₉

yes

characteristic, complemented, Sylow

159

C₇

D₃×C₂₉×D₁₅

yes

characteristic, direct product factor, Sylow

160

C₂×C₃

—

161

C₂×C₃

—

162

D₃

—

163

D₃

—

164

D₃

—

165

D₃

—

166

D₃

C₇×C₂₉×D₁₅

yes

characteristic, direct product factor

167

C₅

D₃²×C₇×C₂₉

yes

characteristic, complemented, Sylow

168

C₂²

—

Sylow

169

C₃

—

170

C₃

D₃×C₇×D₅×C₂₉

yes

characteristic, complemented

171

C₃

C₂×C₇×C₂₉×D₁₅

yes

characteristic, complemented

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₇×C₂₉	D₃×D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₂₉

subgroup

G/H

center, hypercenter

C₇×C₂₉

D₃×D₁₅

commutator, cosocle, hypocenter

C₃²×C₅

C₂²×C₇×C₂₉

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₂₉

C₂²

LCS

G ▷ C₃²×C₅

UCS

C₁ ◁ C₇×C₂₉

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₇×C₂₉	C₂	semidirect
2. C₃×C₇×C₂₉×D₁₅	C₂	semidirect
3. C₇×C₂₉×C₃⋊D₁₅	C₂	semidirect
6. C₃²×C₅×C₇×C₂₉	C₂²	semidirect
11. C₇×C₂₉×D₁₅	D₃	direct (N × H)
12. C₅×D₃×C₇×C₂₉	D₃	semidirect
15. D₃×C₂₉×D₁₅	C₇	direct (N × H)
19. C₃×D₃×C₇×C₂₉	D₅	semidirect
21. C₃×C₅×C₇×C₂₉	C₂×D₃	semidirect
22. C₃×C₅×C₇×C₂₉	C₂×D₃	semidirect
23. C₂₉×C₃⋊D₁₅	C₂×C₇	semidirect
24. C₃×C₂₉×D₁₅	C₂×C₇	semidirect
25. C₃×C₅×D₃×C₂₉	C₂×C₇	semidirect
31. C₃²×C₇×C₂₉	C₂×D₅	semidirect
34. C₃²×C₅×C₂₉	C₂²×C₇	semidirect
35. D₃×C₇×D₁₅	C₂₉	direct (N × H)
42. D₃×C₇×C₂₉	D₁₅	direct (N × H)
44. C₅×C₇×C₂₉	D₃²	semidirect
49. C₂₉×D₁₅	D₃×C₇	direct (N × H)
50. C₅×D₃×C₂₉	D₃×C₇	semidirect
53. C₇×C₃⋊D₁₅	C₂×C₂₉	semidirect
54. C₃×C₇×D₁₅	C₂×C₂₉	semidirect
55. C₃×C₅×D₃×C₇	C₂×C₂₉	semidirect
57. C₃×C₇×C₂₉	D₃×D₅	semidirect
58. C₃×C₇×C₂₉	C₂×D₁₅	semidirect
62. C₃×D₃×C₂₉	C₇×D₅	semidirect
64. C₃×C₅×C₂₉	C₂×D₃×C₇	semidirect
65. C₃×C₅×C₂₉	C₂×D₃×C₇	semidirect
73. C₃²×C₅×C₇	C₂²×C₂₉	semidirect
77. C₃²×C₂₉	C₂×C₇×D₅	semidirect
83. C₇×D₁₅	D₃×C₂₉	direct (N × H)
84. C₅×D₃×C₇	D₃×C₂₉	semidirect
86. C₇×C₂₉	D₃×D₁₅	direct (N × H)
87. D₃×D₁₅	C₇×C₂₉	direct (N × H)
94. D₃×C₂₉	C₇×D₁₅	direct (N × H)
95. C₅×C₂₉	D₃²×C₇	semidirect
99. C₃×D₃×C₇	D₅×C₂₉	semidirect
102. C₃×C₅×C₇	C₂×D₃×C₂₉	semidirect
103. C₃×C₅×C₇	C₂×D₃×C₂₉	semidirect
104. C₃⋊D₁₅	C₂×C₇×C₂₉	semidirect
105. C₃×D₁₅	C₂×C₇×C₂₉	semidirect
106. C₃×C₅×D₃	C₂×C₇×C₂₉	semidirect
108. C₃×C₂₉	D₃×C₇×D₅	semidirect
109. C₃×C₂₉	C₂×C₇×D₁₅	semidirect
115. C₃²×C₇	C₂×D₅×C₂₉	semidirect
121. C₃²×C₅	C₂²×C₇×C₂₉	semidirect
128. D₃×C₇	C₂₉×D₁₅	direct (N × H)
130. C₅×C₇	D₃²×C₂₉	semidirect
135. D₁₅	D₃×C₇×C₂₉	direct (N × H)
137. C₅×D₃	D₃×C₇×C₂₉	semidirect
138. C₂₉	D₃×C₇×D₁₅	direct (N × H)
141. C₃×C₇	D₃×D₅×C₂₉	semidirect
142. C₃×C₇	C₂×C₂₉×D₁₅	semidirect
146. C₃×D₃	C₇×D₅×C₂₉	semidirect
148. C₃×C₅	C₂×D₃×C₇×C₂₉	semidirect
149. C₃×C₅	C₂×D₃×C₇×C₂₉	semidirect
158. C₃²	C₂×C₇×D₅×C₂₉	semidirect
159. C₇	D₃×C₂₉×D₁₅	direct (N × H)
166. D₃	C₇×C₂₉×D₁₅	direct (N × H)
167. C₅	D₃²×C₇×C₂₉	semidirect
170. C₃	D₃×C₇×D₅×C₂₉	semidirect
171. C₃	C₂×C₇×C₂₉×D₁₅	semidirect

H ≅ G/N

type

1. C₃×C₅×D₃×C₇×C₂₉

C₂

semidirect

2. C₃×C₇×C₂₉×D₁₅

C₂

semidirect

3. C₇×C₂₉×C₃⋊D₁₅

C₂

semidirect

6. C₃²×C₅×C₇×C₂₉

C₂²

semidirect

11. C₇×C₂₉×D₁₅

D₃

direct (N × H)

12. C₅×D₃×C₇×C₂₉

D₃

semidirect

15. D₃×C₂₉×D₁₅

C₇

direct (N × H)

19. C₃×D₃×C₇×C₂₉

D₅

semidirect

21. C₃×C₅×C₇×C₂₉

C₂×D₃

semidirect

22. C₃×C₅×C₇×C₂₉

C₂×D₃

semidirect

23. C₂₉×C₃⋊D₁₅

C₂×C₇

semidirect

24. C₃×C₂₉×D₁₅

C₂×C₇

semidirect

25. C₃×C₅×D₃×C₂₉

C₂×C₇

semidirect

31. C₃²×C₇×C₂₉

C₂×D₅

semidirect

34. C₃²×C₅×C₂₉

C₂²×C₇

semidirect

35. D₃×C₇×D₁₅

C₂₉

direct (N × H)

42. D₃×C₇×C₂₉

D₁₅

direct (N × H)

44. C₅×C₇×C₂₉

D₃²

semidirect

49. C₂₉×D₁₅

D₃×C₇

direct (N × H)

50. C₅×D₃×C₂₉

D₃×C₇

semidirect

53. C₇×C₃⋊D₁₅

C₂×C₂₉

semidirect

54. C₃×C₇×D₁₅

C₂×C₂₉

semidirect

55. C₃×C₅×D₃×C₇

C₂×C₂₉

semidirect

57. C₃×C₇×C₂₉

D₃×D₅

semidirect

58. C₃×C₇×C₂₉

C₂×D₁₅

semidirect

62. C₃×D₃×C₂₉

C₇×D₅

semidirect

64. C₃×C₅×C₂₉

C₂×D₃×C₇

semidirect

65. C₃×C₅×C₂₉

C₂×D₃×C₇

semidirect

73. C₃²×C₅×C₇

C₂²×C₂₉

semidirect

77. C₃²×C₂₉

C₂×C₇×D₅

semidirect

83. C₇×D₁₅

D₃×C₂₉

direct (N × H)

84. C₅×D₃×C₇

D₃×C₂₉

semidirect

86. C₇×C₂₉

D₃×D₁₅

direct (N × H)

87. D₃×D₁₅

C₇×C₂₉

direct (N × H)

94. D₃×C₂₉

C₇×D₁₅

direct (N × H)

95. C₅×C₂₉

D₃²×C₇

semidirect

99. C₃×D₃×C₇

D₅×C₂₉

semidirect

102. C₃×C₅×C₇

C₂×D₃×C₂₉

semidirect

103. C₃×C₅×C₇

C₂×D₃×C₂₉

semidirect

104. C₃⋊D₁₅

C₂×C₇×C₂₉

semidirect

105. C₃×D₁₅

C₂×C₇×C₂₉

semidirect

106. C₃×C₅×D₃

C₂×C₇×C₂₉

semidirect

108. C₃×C₂₉

D₃×C₇×D₅

semidirect

109. C₃×C₂₉

C₂×C₇×D₁₅

semidirect

115. C₃²×C₇

C₂×D₅×C₂₉

semidirect

121. C₃²×C₅

C₂²×C₇×C₂₉

semidirect

128. D₃×C₇

C₂₉×D₁₅

direct (N × H)

130. C₅×C₇

D₃²×C₂₉

semidirect

135. D₁₅

D₃×C₇×C₂₉

direct (N × H)

137. C₅×D₃

D₃×C₇×C₂₉

semidirect

138. C₂₉

D₃×C₇×D₁₅

direct (N × H)

141. C₃×C₇

D₃×D₅×C₂₉

semidirect

142. C₃×C₇

C₂×C₂₉×D₁₅

semidirect

146. C₃×D₃

C₇×D₅×C₂₉

semidirect

148. C₃×C₅

C₂×D₃×C₇×C₂₉

semidirect

149. C₃×C₅

C₂×D₃×C₇×C₂₉

semidirect

158. C₃²

C₂×C₇×D₅×C₂₉

semidirect

159. C₇

D₃×C₂₉×D₁₅

direct (N × H)

166. D₃

C₇×C₂₉×D₁₅

direct (N × H)

167. C₅

D₃²×C₇×C₂₉

semidirect

170. C₃

D₃×C₇×D₅×C₂₉

semidirect

171. C₃

C₂×C₇×C₂₉×D₁₅

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×C₇×C₂₉×D₁₅	2
C₇×C₂₉×C₃⋊D₁₅	2
C₂×C₇×C₂₉×D₁₅	3
D₃×C₇×D₅×C₂₉	3
D₃²×C₇×C₂₉	5
D₃×C₂₉×D₁₅	7
D₃×C₇×D₁₅	29

subgroup

index

C₃×C₅×D₃×C₇×C₂₉

C₃×C₇×C₂₉×D₁₅

C₇×C₂₉×C₃⋊D₁₅

C₂×C₇×C₂₉×D₁₅

D₃×C₇×D₅×C₂₉

D₃²×C₇×C₂₉

D₃×C₂₉×D₁₅

D₃×C₇×D₁₅

Subgroups — D₃×C₇×C₂₉×D₁₅ #49141604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×C7×C29×D15 #49141604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×C₂₉×D₁₅ #49141604