Group #50304463 — subgroups

Subgroups — C₇×C₁₃×D₁₅⋊D₇ #50304463

Order 38220.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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×C₇×C₁₃×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×C₁₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₁₃×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₅×C₁₃×D₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇×C₁₃×D₇	—	5	1	no	maximal, Hall
7	C₇×C₁₃×D₃₅	D₃	1	1	yes	characteristic, complemented
8	C₇²×D₅×C₁₃	—	3	1	no	—
9	C₅×C₇×C₁₃×D₇	—	3	1	no	—
10	C₁₃×D₁₅⋊D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
11	D₃×C₇×D₅×C₁₃	—	7	1	no	maximal
12	C₇×C₁₃×D₂₁	D₅	1	1	yes	characteristic, complemented
13	D₃×C₇²×C₁₃	—	5	1	no	—
14	C₃×C₇×C₁₃×D₇	—	5	1	no	—
15	C₅×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₅⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₇×C₁₃×D₁₅	—	2	3	no	—
18	C₇×C₁₃×D₁₅	D₇	1	1	yes	characteristic, complemented
19	C₇×C₁₃×D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
20	C₅×C₁₃×D₂₁	C₂×C₇	1	1	yes	characteristic, complemented
21	C₅×D₃×C₇×C₁₃	—	7	1	no	—
22	C₃×C₁₃×D₃₅	C₂×C₇	1	1	yes	characteristic, complemented
23	C₃×C₇×D₅×C₁₃	—	7	1	no	—
24	C₂×C₇×C₁₃×D₇	—	15	1	no	Hall
25	C₃×C₇²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×D₅×C₁₃	—	21	1	no	—
27	D₅×C₁₃×D₇	—	3	1	no	—
28	C₇²×D₁₅	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₅×C₇×D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
30	C₃×C₇×D₃₅	C₂×C₁₃	1	1	yes	characteristic, complemented
31	C₃×C₅×C₇×C₁₃	—	2	3	no	—
32	C₃×C₅×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
33	C₃×C₅×C₇×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented
34	C₂×C₇²×C₁₃	—	15	1	no	—
35	C₇×C₁₃×D₇	—	3	1	no	—
36	C₇×C₁₃×D₇	—	5	1	no	—
37	C₂×D₃×C₇×C₁₃	—	35	1	no	—
38	D₃×C₁₃×D₇	—	5	1	no	—
39	C₇×D₅×D₇	—	3	1	no	Hall
40	C₂×C₅×C₇×C₁₃	—	21	1	no	—
41	C₁₃×D₃₅	D₃×C₇	1	1	yes	characteristic, complemented
42	C₇×D₅×C₁₃	—	3	1	no	—
43	C₇×D₅×C₁₃	—	3	1	no	—
44	C₇×D₅×C₁₃	—	6	3	no	—
45	C₇×D₅×C₁₃	—	7	1	no	—
46	C₅×C₁₃×D₇	—	3	1	no	—
47	D₃×D₅×C₁₃	—	7	1	no	Hall
48	C₃×C₅×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
49	C₇²×C₁₃	D₃×D₅	1	1	yes	characteristic, complemented, Hall
50	D₃×C₇×D₇	—	5	1	no	Hall
51	C₂×C₃×C₇×C₁₃	—	35	1	no	—
52	C₁₃×D₂₁	C₇×D₅	1	1	yes	characteristic, complemented
53	D₃×C₇×C₁₃	—	5	1	no	—
54	D₃×C₇×C₁₃	—	5	1	no	—
55	D₃×C₇×C₁₃	—	7	1	no	—
56	D₃×C₇×C₁₃	—	10	3	no	—
57	C₃×C₁₃×D₇	—	5	1	no	—
58	C₇×D₃₅	D₃×C₁₃	1	1	yes	characteristic, complemented
59	C₇²×D₅	—	3	1	no	—
60	C₅×C₇×D₇	—	3	1	no	—
61	C₅×C₇×C₁₃	—	2	3	no	—
62	C₅×C₇×C₁₃	D₃×D₇	1	1	yes	characteristic, complemented
63	C₅×C₇×C₁₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented
64	D₁₅⋊D₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor
65	D₃×C₇×D₅	—	7	1	no	—
66	C₁₃×D₁₅	C₇×D₇	1	1	yes	characteristic, complemented
67	C₅×D₃×C₁₃	—	7	1	no	—
68	C₃×D₅×C₁₃	—	7	1	no	—
69	C₂²×C₇×C₁₃	—	105	1	no	—
70	C₂×C₁₃×D₇	—	15	1	no	—
71	C₇×D₂₁	D₅×C₁₃	1	1	yes	characteristic, complemented
72	D₃×C₇²	—	5	1	no	—
73	C₃×C₇×D₇	—	5	1	no	—
74	C₃×C₇×C₁₃	—	2	3	no	—
75	C₃×C₇×C₁₃	D₅×D₇	1	1	yes	characteristic, complemented
76	C₃×C₇×C₁₃	C₂×C₇×D₅	1	1	yes	characteristic, complemented
77	C₂×D₅×C₁₃	—	21	1	no	Hall
78	C₅×C₇²	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
79	C₇×D₁₅	—	2	3	no	—
80	C₇×D₁₅	C₁₃×D₇	1	1	yes	characteristic, complemented
81	C₇×D₁₅	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
82	C₅×D₂₁	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
83	C₅×D₃×C₇	—	7	1	no	—
84	C₃×D₃₅	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
85	C₃×C₇×D₅	—	7	1	no	—
86	C₂×C₇×D₇	—	15	1	no	Hall
87	C₃×C₅×C₁₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
88	C₂×C₇×C₁₃	—	15	1	no	—
89	C₂×C₇×C₁₃	—	15	1	no	—
90	C₂×C₇×C₁₃	—	21	1	no	—
91	C₂×C₇×C₁₃	—	30	3	no	—
92	C₂×C₇×C₁₃	—	35	1	no	—
93	C₁₃×D₇	—	3	1	no	—
94	C₁₃×D₇	—	5	1	no	—
95	C₂×D₃×C₁₃	—	35	1	no	Hall
96	C₃×C₇²	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
97	C₂×C₇×D₅	—	21	1	no	—
98	D₅×D₇	—	3	1	no	—
99	C₂×C₅×C₁₃	—	21	1	no	—
100	D₅×C₁₃	—	3	1	no	—
101	D₅×C₁₃	—	7	1	no	—
102	C₃×C₅×C₇	—	2	3	no	—
103	C₃×C₅×C₇	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented
104	C₃×C₅×C₇	C₂²×C₇×C₁₃	1	1	yes	characteristic, complemented
105	C₂×C₇²	—	15	1	no	—
106	C₇×D₇	—	3	1	no	—
107	C₇×D₇	—	5	1	no	—
108	C₇×C₁₃	—	2	3	no	—
109	C₇×C₁₃	D₃×C₇×D₅	1	1	yes	characteristic, complemented
110	C₇×C₁₃	D₁₅⋊D₇	1	1	yes	characteristic, direct product factor
111	C₂×D₃×C₇	—	35	1	no	—
112	D₃×D₇	—	5	1	no	—
113	C₂×C₃×C₁₃	—	35	1	no	—
114	D₃×C₁₃	—	5	1	no	—
115	D₃×C₁₃	—	7	1	no	—
116	C₂×C₅×C₇	—	21	1	no	—
117	D₃₅	D₃×C₇×C₁₃	1	1	yes	characteristic, complemented
118	C₅×D₇	—	3	1	no	—
119	C₇×D₅	—	3	1	no	—
120	C₇×D₅	—	3	1	no	—
121	C₇×D₅	—	6	3	no	—
122	C₇×D₅	—	7	1	no	—
123	C₅×C₁₃	D₃×C₇×D₇	1	1	yes	characteristic, complemented, Hall
124	D₃×D₅	—	7	1	no	Hall
125	C₂²×C₁₃	—	105	1	no	Hall
126	C₇²	D₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₃×C₇	—	35	1	no	—
128	D₂₁	C₇×D₅×C₁₃	1	1	yes	characteristic, complemented
129	C₃×D₇	—	5	1	no	—
130	D₃×C₇	—	5	1	no	—
131	D₃×C₇	—	5	1	no	—
132	D₃×C₇	—	7	1	no	—
133	D₃×C₇	—	10	3	no	—
134	C₃×C₁₃	C₇×D₅×D₇	1	1	yes	characteristic, complemented, Hall
135	C₅×C₇	—	2	3	no	—
136	C₅×C₇	D₃×C₁₃×D₇	1	1	yes	characteristic, complemented
137	C₅×C₇	C₂×D₃×C₇×C₁₃	1	1	yes	characteristic, complemented
138	D₁₅	C₇×C₁₃×D₇	1	1	yes	characteristic, complemented
139	C₃×D₅	—	7	1	no	—
140	C₅×D₃	—	7	1	no	—
141	C₂²×C₇	—	105	1	no	—
142	C₂×D₇	—	15	1	no	—
143	C₂×C₁₃	—	15	1	no	—
144	C₂×C₁₃	—	21	1	no	—
145	C₂×C₁₃	—	35	1	no	—
146	C₃×C₇	—	2	3	no	—
147	C₃×C₇	D₅×C₁₃×D₇	1	1	yes	characteristic, complemented
148	C₃×C₇	C₂×C₇×D₅×C₁₃	1	1	yes	characteristic, complemented
149	C₂×D₅	—	21	1	no	Hall
150	C₃×C₅	C₂×C₇×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
151	C₂×C₇	—	15	1	no	—
152	C₂×C₇	—	15	1	no	—
153	C₂×C₇	—	21	1	no	—
154	C₂×C₇	—	30	3	no	—
155	C₂×C₇	—	35	1	no	—
156	D₇	—	3	1	no	—
157	D₇	—	5	1	no	—
158	C₁₃	C₇×D₁₅⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
159	C₂×D₃	—	35	1	no	Hall
160	C₂×C₅	—	21	1	no	—
161	D₅	—	3	1	no	—
162	D₅	—	7	1	no	—
163	C₇	—	2	3	no	—
164	C₇	D₃×C₇×D₅×C₁₃	1	1	yes	characteristic, complemented
165	C₇	C₁₃×D₁₅⋊D₇	1	1	yes	characteristic, direct product factor
166	C₂×C₃	—	35	1	no	—
167	D₃	—	5	1	no	—
168	D₃	—	7	1	no	—
169	C₅	D₃×C₇×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
170	C₂²	—	105	1	no	Sylow
171	C₃	C₇×D₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
172	C₂	—	15	1	no	—
173	C₂	—	21	1	no	—
174	C₂	—	35	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₇×C₁₃×D₃₅

C₂

yes

maximal, characteristic, complemented

C₅×C₇×C₁₃×D₂₁

C₂

yes

maximal, characteristic, complemented

C₇²×C₁₃×D₁₅

C₂

yes

maximal, characteristic, complemented

C₇×D₅×C₁₃×D₇

—

maximal, Hall

C₃×C₅×C₇²×C₁₃

C₂²

yes

characteristic, complemented, Hall

D₃×C₇×C₁₃×D₇

—

maximal, Hall

C₇×C₁₃×D₃₅

D₃

yes

characteristic, complemented

C₇²×D₅×C₁₃

—

C₅×C₇×C₁₃×D₇

—

C₁₃×D₁₅⋊D₇

C₇

yes

maximal, characteristic, direct product factor

D₃×C₇×D₅×C₁₃

—

maximal

C₇×C₁₃×D₂₁

D₅

yes

characteristic, complemented

D₃×C₇²×C₁₃

—

C₃×C₇×C₁₃×D₇

—

C₅×C₇²×C₁₃

C₂×D₃

yes

characteristic, complemented, Hall

C₇×D₁₅⋊D₇

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₇×C₁₃×D₁₅

—

C₇×C₁₃×D₁₅

D₇

yes

characteristic, complemented

C₇×C₁₃×D₁₅

C₂×C₇

yes

characteristic, complemented

C₅×C₁₃×D₂₁

C₂×C₇

yes

characteristic, complemented

C₅×D₃×C₇×C₁₃

—

C₃×C₁₃×D₃₅

C₂×C₇

yes

characteristic, complemented

C₃×C₇×D₅×C₁₃

—

C₂×C₇×C₁₃×D₇

—

Hall

C₃×C₇²×C₁₃

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₇×D₅×C₁₃

—

D₅×C₁₃×D₇

—

C₇²×D₁₅

C₂×C₁₃

yes

characteristic, complemented

C₅×C₇×D₂₁

C₂×C₁₃

yes

characteristic, complemented

C₃×C₇×D₃₅

C₂×C₁₃

yes

characteristic, complemented

C₃×C₅×C₇×C₁₃

—

C₃×C₅×C₇×C₁₃

C₂×D₇

yes

characteristic, complemented

C₃×C₅×C₇×C₁₃

C₂²×C₇

yes

characteristic, complemented

C₂×C₇²×C₁₃

—

C₇×C₁₃×D₇

—

C₇×C₁₃×D₇

—

C₂×D₃×C₇×C₁₃

—

D₃×C₁₃×D₇

—

C₇×D₅×D₇

—

Hall

C₂×C₅×C₇×C₁₃

—

C₁₃×D₃₅

D₃×C₇

yes

characteristic, complemented

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

—

C₅×C₁₃×D₇

—

D₃×D₅×C₁₃

—

Hall

C₃×C₅×C₇²

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₇²×C₁₃

D₃×D₅

yes

characteristic, complemented, Hall

D₃×C₇×D₇

—

Hall

C₂×C₃×C₇×C₁₃

—

C₁₃×D₂₁

C₇×D₅

yes

characteristic, complemented

D₃×C₇×C₁₃

—

D₃×C₇×C₁₃

—

D₃×C₇×C₁₃

—

D₃×C₇×C₁₃

—

C₃×C₁₃×D₇

—

C₇×D₃₅

D₃×C₁₃

yes

characteristic, complemented

C₇²×D₅

—

C₅×C₇×D₇

—

C₅×C₇×C₁₃

—

C₅×C₇×C₁₃

D₃×D₇

yes

characteristic, complemented

C₅×C₇×C₁₃

C₂×D₃×C₇

yes

characteristic, complemented

D₁₅⋊D₇

C₇×C₁₃

yes

characteristic, direct product factor

D₃×C₇×D₅

—

C₁₃×D₁₅

C₇×D₇

yes

characteristic, complemented

C₅×D₃×C₁₃

—

C₃×D₅×C₁₃

—

C₂²×C₇×C₁₃

—

105

—

C₂×C₁₃×D₇

—

C₇×D₂₁

D₅×C₁₃

yes

characteristic, complemented

D₃×C₇²

—

C₃×C₇×D₇

—

C₃×C₇×C₁₃

—

C₃×C₇×C₁₃

D₅×D₇

yes

characteristic, complemented

C₃×C₇×C₁₃

C₂×C₇×D₅

yes

characteristic, complemented

C₂×D₅×C₁₃

—

Hall

C₅×C₇²

C₂×D₃×C₁₃

yes

characteristic, complemented, Hall

C₇×D₁₅

—

C₇×D₁₅

C₁₃×D₇

yes

characteristic, complemented

C₇×D₁₅

C₂×C₇×C₁₃

yes

characteristic, complemented

C₅×D₂₁

C₂×C₇×C₁₃

yes

characteristic, complemented

C₅×D₃×C₇

—

C₃×D₃₅

C₂×C₇×C₁₃

yes

characteristic, complemented

C₃×C₇×D₅

—

C₂×C₇×D₇

—

Hall

C₃×C₅×C₁₃

C₂×C₇×D₇

yes

characteristic, complemented, Hall

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

—

C₂×D₃×C₁₃

—

Hall

C₃×C₇²

C₂×D₅×C₁₃

yes

characteristic, complemented, Hall

C₂×C₇×D₅

—

D₅×D₇

—

C₂×C₅×C₁₃

—

100

D₅×C₁₃

—

101

D₅×C₁₃

—

102

C₃×C₅×C₇

—

103

C₃×C₅×C₇

C₂×C₁₃×D₇

yes

characteristic, complemented

104

C₃×C₅×C₇

C₂²×C₇×C₁₃

yes

characteristic, complemented

105

C₂×C₇²

—

106

C₇×D₇

—

107

C₇×D₇

—

108

C₇×C₁₃

—

109

C₇×C₁₃

D₃×C₇×D₅

yes

characteristic, complemented

110

C₇×C₁₃

D₁₅⋊D₇

yes

characteristic, direct product factor

111

C₂×D₃×C₇

—

112

D₃×D₇

—

113

C₂×C₃×C₁₃

—

114

D₃×C₁₃

—

115

D₃×C₁₃

—

116

C₂×C₅×C₇

—

117

D₃₅

D₃×C₇×C₁₃

yes

characteristic, complemented

118

C₅×D₇

—

119

C₇×D₅

—

120

C₇×D₅

—

121

C₇×D₅

—

122

C₇×D₅

—

123

C₅×C₁₃

D₃×C₇×D₇

yes

characteristic, complemented, Hall

124

D₃×D₅

—

Hall

125

C₂²×C₁₃

—

105

Hall

126

C₇²

D₃×D₅×C₁₃

yes

characteristic, complemented, Sylow

127

C₂×C₃×C₇

—

128

D₂₁

C₇×D₅×C₁₃

yes

characteristic, complemented

129

C₃×D₇

—

130

D₃×C₇

—

131

D₃×C₇

—

132

D₃×C₇

—

133

D₃×C₇

—

134

C₃×C₁₃

C₇×D₅×D₇

yes

characteristic, complemented, Hall

135

C₅×C₇

—

136

C₅×C₇

D₃×C₁₃×D₇

yes

characteristic, complemented

137

C₅×C₇

C₂×D₃×C₇×C₁₃

yes

characteristic, complemented

138

D₁₅

C₇×C₁₃×D₇

yes

characteristic, complemented

139

C₃×D₅

—

140

C₅×D₃

—

141

C₂²×C₇

—

105

—

142

C₂×D₇

—

143

C₂×C₁₃

—

144

C₂×C₁₃

—

145

C₂×C₁₃

—

146

C₃×C₇

—

147

C₃×C₇

D₅×C₁₃×D₇

yes

characteristic, complemented

148

C₃×C₇

C₂×C₇×D₅×C₁₃

yes

characteristic, complemented

149

C₂×D₅

—

Hall

150

C₃×C₅

C₂×C₇×C₁₃×D₇

yes

characteristic, complemented, Hall

151

C₂×C₇

—

152

C₂×C₇

—

153

C₂×C₇

—

154

C₂×C₇

—

155

C₂×C₇

—

156

D₇

—

157

D₇

—

158

C₁₃

C₇×D₁₅⋊D₇

yes

characteristic, direct product factor, Sylow

159

C₂×D₃

—

Hall

160

C₂×C₅

—

161

D₅

—

162

D₅

—

163

C₇

—

164

C₇

D₃×C₇×D₅×C₁₃

yes

characteristic, complemented

165

C₇

C₁₃×D₁₅⋊D₇

yes

characteristic, direct product factor

166

C₂×C₃

—

167

D₃

—

168

D₃

—

169

C₅

D₃×C₇×C₁₃×D₇

yes

characteristic, complemented, Sylow

170

C₂²

—

105

Sylow

171

C₃

C₇×D₅×C₁₃×D₇

yes

characteristic, complemented, Sylow

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₁₅⋊D₇
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₇×C₁₃

subgroup

G/H

center, hypercenter

C₇×C₁₃

D₁₅⋊D₇

commutator, cosocle, hypocenter

C₃×C₅×C₇

C₂²×C₇×C₁₃

Frattini

C₁

Fitting, socle

C₃×C₅×C₇²×C₁₃

C₂²

LCS

G ▷ C₃×C₅×C₇

UCS

C₁ ◁ C₇×C₁₃

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×D₃₅	C₂	semidirect
2. C₅×C₇×C₁₃×D₂₁	C₂	semidirect
3. C₇²×C₁₃×D₁₅	C₂	semidirect
5. C₃×C₅×C₇²×C₁₃	C₂²	semidirect
7. C₇×C₁₃×D₃₅	D₃	semidirect
10. C₁₃×D₁₅⋊D₇	C₇	direct (N × H)
12. C₇×C₁₃×D₂₁	D₅	semidirect
15. C₅×C₇²×C₁₃	C₂×D₃	semidirect
16. C₇×D₁₅⋊D₇	C₁₃	direct (N × H)
18. C₇×C₁₃×D₁₅	D₇	semidirect
19. C₇×C₁₃×D₁₅	C₂×C₇	semidirect
20. C₅×C₁₃×D₂₁	C₂×C₇	semidirect
22. C₃×C₁₃×D₃₅	C₂×C₇	semidirect
25. C₃×C₇²×C₁₃	C₂×D₅	semidirect
28. C₇²×D₁₅	C₂×C₁₃	semidirect
29. C₅×C₇×D₂₁	C₂×C₁₃	semidirect
30. C₃×C₇×D₃₅	C₂×C₁₃	semidirect
32. C₃×C₅×C₇×C₁₃	C₂×D₇	semidirect
33. C₃×C₅×C₇×C₁₃	C₂²×C₇	semidirect
41. C₁₃×D₃₅	D₃×C₇	semidirect
48. C₃×C₅×C₇²	C₂²×C₁₃	semidirect
49. C₇²×C₁₃	D₃×D₅	semidirect
52. C₁₃×D₂₁	C₇×D₅	semidirect
58. C₇×D₃₅	D₃×C₁₃	semidirect
62. C₅×C₇×C₁₃	D₃×D₇	semidirect
63. C₅×C₇×C₁₃	C₂×D₃×C₇	semidirect
64. D₁₅⋊D₇	C₇×C₁₃	direct (N × H)
66. C₁₃×D₁₅	C₇×D₇	semidirect
71. C₇×D₂₁	D₅×C₁₃	semidirect
75. C₃×C₇×C₁₃	D₅×D₇	semidirect
76. C₃×C₇×C₁₃	C₂×C₇×D₅	semidirect
78. C₅×C₇²	C₂×D₃×C₁₃	semidirect
80. C₇×D₁₅	C₁₃×D₇	semidirect
81. C₇×D₁₅	C₂×C₇×C₁₃	semidirect
82. C₅×D₂₁	C₂×C₇×C₁₃	semidirect
84. C₃×D₃₅	C₂×C₇×C₁₃	semidirect
87. C₃×C₅×C₁₃	C₂×C₇×D₇	semidirect
96. C₃×C₇²	C₂×D₅×C₁₃	semidirect
103. C₃×C₅×C₇	C₂×C₁₃×D₇	semidirect
104. C₃×C₅×C₇	C₂²×C₇×C₁₃	semidirect
109. C₇×C₁₃	D₃×C₇×D₅	semidirect
110. C₇×C₁₃	D₁₅⋊D₇	direct (N × H)
117. D₃₅	D₃×C₇×C₁₃	semidirect
123. C₅×C₁₃	D₃×C₇×D₇	semidirect
126. C₇²	D₃×D₅×C₁₃	semidirect
128. D₂₁	C₇×D₅×C₁₃	semidirect
134. C₃×C₁₃	C₇×D₅×D₇	semidirect
136. C₅×C₇	D₃×C₁₃×D₇	semidirect
137. C₅×C₇	C₂×D₃×C₇×C₁₃	semidirect
138. D₁₅	C₇×C₁₃×D₇	semidirect
147. C₃×C₇	D₅×C₁₃×D₇	semidirect
148. C₃×C₇	C₂×C₇×D₅×C₁₃	semidirect
150. C₃×C₅	C₂×C₇×C₁₃×D₇	semidirect
158. C₁₃	C₇×D₁₅⋊D₇	direct (N × H)
164. C₇	D₃×C₇×D₅×C₁₃	semidirect
165. C₇	C₁₃×D₁₅⋊D₇	direct (N × H)
169. C₅	D₃×C₇×C₁₃×D₇	semidirect
171. C₃	C₇×D₅×C₁₃×D₇	semidirect

H ≅ G/N

type

1. C₃×C₇×C₁₃×D₃₅

C₂

semidirect

2. C₅×C₇×C₁₃×D₂₁

C₂

semidirect

3. C₇²×C₁₃×D₁₅

C₂

semidirect

5. C₃×C₅×C₇²×C₁₃

C₂²

semidirect

7. C₇×C₁₃×D₃₅

D₃

semidirect

10. C₁₃×D₁₅⋊D₇

C₇

direct (N × H)

12. C₇×C₁₃×D₂₁

D₅

semidirect

15. C₅×C₇²×C₁₃

C₂×D₃

semidirect

16. C₇×D₁₅⋊D₇

C₁₃

direct (N × H)

18. C₇×C₁₃×D₁₅

D₇

semidirect

19. C₇×C₁₃×D₁₅

C₂×C₇

semidirect

20. C₅×C₁₃×D₂₁

C₂×C₇

semidirect

22. C₃×C₁₃×D₃₅

C₂×C₇

semidirect

25. C₃×C₇²×C₁₃

C₂×D₅

semidirect

28. C₇²×D₁₅

C₂×C₁₃

semidirect

29. C₅×C₇×D₂₁

C₂×C₁₃

semidirect

30. C₃×C₇×D₃₅

C₂×C₁₃

semidirect

32. C₃×C₅×C₇×C₁₃

C₂×D₇

semidirect

33. C₃×C₅×C₇×C₁₃

C₂²×C₇

semidirect

41. C₁₃×D₃₅

D₃×C₇

semidirect

48. C₃×C₅×C₇²

C₂²×C₁₃

semidirect

49. C₇²×C₁₃

D₃×D₅

semidirect

52. C₁₃×D₂₁

C₇×D₅

semidirect

58. C₇×D₃₅

D₃×C₁₃

semidirect

62. C₅×C₇×C₁₃

D₃×D₇

semidirect

63. C₅×C₇×C₁₃

C₂×D₃×C₇

semidirect

64. D₁₅⋊D₇

C₇×C₁₃

direct (N × H)

66. C₁₃×D₁₅

C₇×D₇

semidirect

71. C₇×D₂₁

D₅×C₁₃

semidirect

75. C₃×C₇×C₁₃

D₅×D₇

semidirect

76. C₃×C₇×C₁₃

C₂×C₇×D₅

semidirect

78. C₅×C₇²

C₂×D₃×C₁₃

semidirect

80. C₇×D₁₅

C₁₃×D₇

semidirect

81. C₇×D₁₅

C₂×C₇×C₁₃

semidirect

82. C₅×D₂₁

C₂×C₇×C₁₃

semidirect

84. C₃×D₃₅

C₂×C₇×C₁₃

semidirect

87. C₃×C₅×C₁₃

C₂×C₇×D₇

semidirect

96. C₃×C₇²

C₂×D₅×C₁₃

semidirect

103. C₃×C₅×C₇

C₂×C₁₃×D₇

semidirect

104. C₃×C₅×C₇

C₂²×C₇×C₁₃

semidirect

109. C₇×C₁₃

D₃×C₇×D₅

semidirect

110. C₇×C₁₃

D₁₅⋊D₇

direct (N × H)

117. D₃₅

D₃×C₇×C₁₃

semidirect

123. C₅×C₁₃

D₃×C₇×D₇

semidirect

126. C₇²

D₃×D₅×C₁₃

semidirect

128. D₂₁

C₇×D₅×C₁₃

semidirect

134. C₃×C₁₃

C₇×D₅×D₇

semidirect

136. C₅×C₇

D₃×C₁₃×D₇

semidirect

137. C₅×C₇

C₂×D₃×C₇×C₁₃

semidirect

138. D₁₅

C₇×C₁₃×D₇

semidirect

147. C₃×C₇

D₅×C₁₃×D₇

semidirect

148. C₃×C₇

C₂×C₇×D₅×C₁₃

semidirect

150. C₃×C₅

C₂×C₇×C₁₃×D₇

semidirect

158. C₁₃

C₇×D₁₅⋊D₇

direct (N × H)

164. C₇

D₃×C₇×D₅×C₁₃

semidirect

165. C₇

C₁₃×D₁₅⋊D₇

direct (N × H)

169. C₅

D₃×C₇×C₁₃×D₇

semidirect

171. C₃

C₇×D₅×C₁₃×D₇

semidirect

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

subgroup	index
C₃×C₇×C₁₃×D₃₅	2
C₅×C₇×C₁₃×D₂₁	2
C₇²×C₁₃×D₁₅	2
C₇×D₅×C₁₃×D₇	3
D₃×C₇×C₁₃×D₇	5
C₁₃×D₁₅⋊D₇	7
D₃×C₇×D₅×C₁₃	7
C₇×D₁₅⋊D₇	13

subgroup

index

C₃×C₇×C₁₃×D₃₅

C₅×C₇×C₁₃×D₂₁

C₇²×C₁₃×D₁₅

C₇×D₅×C₁₃×D₇

D₃×C₇×C₁₃×D₇

C₁₃×D₁₅⋊D₇

D₃×C₇×D₅×C₁₃

C₇×D₁₅⋊D₇

Subgroups — C₇×C₁₃×D₁₅⋊D₇ #50304463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C7×C13×D15⋊D7 #50304463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃×D₁₅⋊D₇ #50304463