Group #50304455 — subgroups

Subgroups — C₇×D₅×C₁₃×D₂₁ #50304455

Order 38220.

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

normal subgroups only

This group has 208 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×C₇²×D₅×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×C₁₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₃×D₁₀₅	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	C₂×C₇×C₁₃×D₂₁	—	5	1	no	maximal, Hall
7	C₇×C₁₃×D₃₅	—	3	1	no	—
8	C₇²×D₅×C₁₃	D₃	1	1	yes	characteristic, complemented
9	C₅×C₇×C₁₃×D₇	—	3	1	no	—
10	D₅×C₁₃×D₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor
11	D₃×C₇×D₅×C₁₃	—	7	1	no	maximal
12	C₇×C₁₃×D₂₁	—	5	1	no	—
13	C₇×C₁₃×D₂₁	D₅	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₇²×C₁₃	—	5	1	no	—
15	C₅×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
16	C₇×D₅×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₁₃×D₁₀₅	C₂×C₇	1	1	yes	characteristic, complemented
18	C₇×C₁₃×D₁₅	—	7	1	no	—
19	C₅×C₁₃×D₂₁	C₂×C₇	1	1	yes	characteristic, complemented
20	C₅×D₃×C₇×C₁₃	—	7	1	no	—
21	C₃×C₇×D₅×C₁₃	—	2	3	no	—
22	C₃×C₇×D₅×C₁₃	D₇	1	1	yes	characteristic, complemented
23	C₃×C₇×D₅×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
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	C₇×D₁₀₅	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₅×C₇×D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
30	C₃×C₇²×D₅	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	—	5	1	no	—
35	C₇×C₁₃×D₇	—	3	1	no	—
36	C₇×C₁₃×D₇	—	15	1	no	—
37	C₂×C₁₃×D₂₁	—	5	1	no	—
38	C₂×D₃×C₇×C₁₃	—	35	1	no	—
39	C₇×D₅×D₇	—	3	1	no	Hall
40	C₂×C₅×C₇×C₁₃	—	21	1	no	—
41	C₁₃×D₃₅	—	3	1	no	—
42	C₇×D₅×C₁₃	—	2	3	no	—
43	C₇×D₅×C₁₃	—	21	1	no	—
44	C₇×D₅×C₁₃	D₃×C₇	1	1	yes	characteristic, complemented
45	C₇×D₅×C₁₃	D₂₁	1	1	yes	characteristic, direct product factor
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	C₂×C₇×D₂₁	—	5	1	no	Hall
51	C₂×C₃×C₇×C₁₃	—	5	1	no	—
52	C₂×C₃×C₇×C₁₃	—	5	1	no	—
53	C₂×C₃×C₇×C₁₃	—	10	3	no	—
54	C₁₃×D₂₁	—	5	1	no	—
55	C₁₃×D₂₁	C₇×D₅	1	1	yes	characteristic, direct product factor
56	D₃×C₇×C₁₃	—	7	1	no	—
57	D₃×C₇×C₁₃	—	35	1	no	—
58	C₇×D₃₅	—	3	1	no	—
59	C₇²×D₅	D₃×C₁₃	1	1	yes	characteristic, complemented
60	C₅×C₇×D₇	—	3	1	no	—
61	C₅×C₇×C₁₃	—	2	3	no	—
62	C₅×C₇×C₁₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented
63	C₅×C₇×C₁₃	C₂×D₂₁	1	1	yes	characteristic, complemented
64	D₅×D₂₁	C₇×C₁₃	1	1	yes	characteristic, direct product factor
65	D₃×C₇×D₅	—	7	1	no	—
66	C₁₃×D₁₅	—	7	1	no	—
67	C₅×D₃×C₁₃	—	7	1	no	—
68	C₃×D₅×C₁₃	C₇×D₇	1	1	yes	characteristic, complemented
69	C₂²×C₇×C₁₃	—	105	1	no	—
70	C₂×C₁₃×D₇	—	15	1	no	—
71	C₂×C₃×C₇²	—	5	1	no	—
72	C₇×D₂₁	—	5	1	no	—
73	C₇×D₂₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor
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	D₁₀₅	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
80	C₇×D₁₅	—	7	1	no	—
81	C₅×D₂₁	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
82	C₅×D₃×C₇	—	7	1	no	—
83	C₃×C₇×D₅	—	2	3	no	—
84	C₃×C₇×D₅	C₁₃×D₇	1	1	yes	characteristic, complemented
85	C₃×C₇×D₅	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
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	—	5	1	no	—
89	C₂×C₇×C₁₃	—	5	1	no	—
90	C₂×C₇×C₁₃	—	10	3	no	—
91	C₂×C₇×C₁₃	—	21	1	no	—
92	C₂×C₇×C₁₃	—	105	1	no	—
93	C₁₃×D₇	—	3	1	no	—
94	C₁₃×D₇	—	15	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	—	21	1	no	—
101	D₅×C₁₃	C₇×D₂₁	1	1	yes	characteristic, direct product factor
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	—	5	1	no	—
106	C₇×D₇	—	3	1	no	—
107	C₇×D₇	—	15	1	no	—
108	C₇×C₁₃	—	2	3	no	—
109	C₇×C₁₃	D₃×C₇×D₅	1	1	yes	characteristic, complemented
110	C₇×C₁₃	D₅×D₂₁	1	1	yes	characteristic, direct product factor
111	C₂×D₂₁	—	5	1	no	—
112	C₂×D₃×C₇	—	35	1	no	—
113	C₂×C₃×C₁₃	—	5	1	no	—
114	D₃×C₁₃	—	7	1	no	—
115	D₃×C₁₃	—	35	1	no	—
116	C₂×C₅×C₇	—	21	1	no	—
117	D₃₅	—	3	1	no	—
118	C₅×D₇	—	3	1	no	—
119	C₇×D₅	—	2	3	no	—
120	C₇×D₅	—	21	1	no	—
121	C₇×D₅	D₃×C₇×C₁₃	1	1	yes	characteristic, complemented
122	C₇×D₅	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
123	C₅×C₁₃	C₂×C₇×D₂₁	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	—	5	1	no	—
128	C₂×C₃×C₇	—	5	1	no	—
129	C₂×C₃×C₇	—	10	3	no	—
130	D₂₁	—	5	1	no	—
131	D₂₁	C₇×D₅×C₁₃	1	1	yes	characteristic, direct product factor
132	D₃×C₇	—	7	1	no	—
133	D₃×C₇	—	35	1	no	—
134	C₃×C₁₃	C₇×D₅×D₇	1	1	yes	characteristic, complemented, Hall
135	C₅×C₇	—	2	3	no	—
136	C₅×C₇	C₂×D₃×C₇×C₁₃	1	1	yes	characteristic, complemented
137	C₅×C₇	C₂×C₁₃×D₂₁	1	1	yes	characteristic, complemented
138	D₁₅	—	7	1	no	—
139	C₃×D₅	C₇×C₁₃×D₇	1	1	yes	characteristic, complemented
140	C₅×D₃	—	7	1	no	—
141	C₂²×C₇	—	105	1	no	—
142	C₂×D₇	—	15	1	no	—
143	C₂×C₁₃	—	5	1	no	—
144	C₂×C₁₃	—	21	1	no	—
145	C₂×C₁₃	—	105	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	—	5	1	no	—
152	C₂×C₇	—	5	1	no	—
153	C₂×C₇	—	10	3	no	—
154	C₂×C₇	—	21	1	no	—
155	C₂×C₇	—	105	1	no	—
156	D₇	—	3	1	no	—
157	D₇	—	15	1	no	—
158	C₁₃	C₇×D₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
159	C₂×D₃	—	35	1	no	Hall
160	C₂×C₅	—	21	1	no	—
161	D₅	—	21	1	no	—
162	D₅	C₇×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
163	C₇	—	2	3	no	—
164	C₇	D₃×C₇×D₅×C₁₃	1	1	yes	characteristic, complemented
165	C₇	D₅×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
166	C₂×C₃	—	5	1	no	—
167	D₃	—	7	1	no	—
168	D₃	—	35	1	no	—
169	C₅	C₂×C₇×C₁₃×D₂₁	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	—	5	1	no	—
173	C₂	—	21	1	no	—
174	C₂	—	105	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₇²×D₅×C₁₃

C₂

yes

maximal, characteristic, complemented

C₅×C₇×C₁₃×D₂₁

C₂

yes

maximal, characteristic, complemented

C₇×C₁₃×D₁₀₅

C₂

yes

maximal, characteristic, complemented

C₇×D₅×C₁₃×D₇

—

maximal, Hall

C₃×C₅×C₇²×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₇×C₁₃×D₂₁

—

maximal, Hall

C₇×C₁₃×D₃₅

—

C₇²×D₅×C₁₃

D₃

yes

characteristic, complemented

C₅×C₇×C₁₃×D₇

—

D₅×C₁₃×D₂₁

C₇

yes

maximal, characteristic, direct product factor

D₃×C₇×D₅×C₁₃

—

maximal

C₇×C₁₃×D₂₁

—

C₇×C₁₃×D₂₁

D₅

yes

characteristic, direct product factor

C₂×C₃×C₇²×C₁₃

—

C₅×C₇²×C₁₃

C₂×D₃

yes

characteristic, complemented, Hall

C₇×D₅×D₂₁

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₁₃×D₁₀₅

C₂×C₇

yes

characteristic, complemented

C₇×C₁₃×D₁₅

—

C₅×C₁₃×D₂₁

C₂×C₇

yes

characteristic, complemented

C₅×D₃×C₇×C₁₃

—

C₃×C₇×D₅×C₁₃

—

C₃×C₇×D₅×C₁₃

D₇

yes

characteristic, complemented

C₃×C₇×D₅×C₁₃

C₂×C₇

yes

characteristic, complemented

C₂×C₇×C₁₃×D₇

—

Hall

C₃×C₇²×C₁₃

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₇×D₅×C₁₃

—

D₅×C₁₃×D₇

—

C₇×D₁₀₅

C₂×C₁₃

yes

characteristic, complemented

C₅×C₇×D₂₁

C₂×C₁₃

yes

characteristic, complemented

C₃×C₇²×D₅

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×C₁₃×D₂₁

—

C₂×D₃×C₇×C₁₃

—

C₇×D₅×D₇

—

Hall

C₂×C₅×C₇×C₁₃

—

C₁₃×D₃₅

—

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

—

C₇×D₅×C₁₃

D₃×C₇

yes

characteristic, complemented

C₇×D₅×C₁₃

D₂₁

yes

characteristic, direct product factor

C₅×C₁₃×D₇

—

D₃×D₅×C₁₃

—

Hall

C₃×C₅×C₇²

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₇²×C₁₃

D₃×D₅

yes

characteristic, complemented, Hall

C₂×C₇×D₂₁

—

Hall

C₂×C₃×C₇×C₁₃

—

C₂×C₃×C₇×C₁₃

—

C₂×C₃×C₇×C₁₃

—

C₁₃×D₂₁

—

C₁₃×D₂₁

C₇×D₅

yes

characteristic, direct product factor

D₃×C₇×C₁₃

—

D₃×C₇×C₁₃

—

C₇×D₃₅

—

C₇²×D₅

D₃×C₁₃

yes

characteristic, complemented

C₅×C₇×D₇

—

C₅×C₇×C₁₃

—

C₅×C₇×C₁₃

C₂×D₃×C₇

yes

characteristic, complemented

C₅×C₇×C₁₃

C₂×D₂₁

yes

characteristic, complemented

D₅×D₂₁

C₇×C₁₃

yes

characteristic, direct product factor

D₃×C₇×D₅

—

C₁₃×D₁₅

—

C₅×D₃×C₁₃

—

C₃×D₅×C₁₃

C₇×D₇

yes

characteristic, complemented

C₂²×C₇×C₁₃

—

105

—

C₂×C₁₃×D₇

—

C₂×C₃×C₇²

—

C₇×D₂₁

—

C₇×D₂₁

D₅×C₁₃

yes

characteristic, direct product factor

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

D₁₀₅

C₂×C₇×C₁₃

yes

characteristic, complemented

C₇×D₁₅

—

C₅×D₂₁

C₂×C₇×C₁₃

yes

characteristic, complemented

C₅×D₃×C₇

—

C₃×C₇×D₅

—

C₃×C₇×D₅

C₁₃×D₇

yes

characteristic, complemented

C₃×C₇×D₅

C₂×C₇×C₁₃

yes

characteristic, complemented

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

—

105

—

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

C₇×D₂₁

yes

characteristic, direct product factor

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

D₅×D₂₁

yes

characteristic, direct product factor

111

C₂×D₂₁

—

112

C₂×D₃×C₇

—

113

C₂×C₃×C₁₃

—

114

D₃×C₁₃

—

115

D₃×C₁₃

—

116

C₂×C₅×C₇

—

117

D₃₅

—

118

C₅×D₇

—

119

C₇×D₅

—

120

C₇×D₅

—

121

C₇×D₅

D₃×C₇×C₁₃

yes

characteristic, complemented

122

C₇×D₅

C₁₃×D₂₁

yes

characteristic, direct product factor

123

C₅×C₁₃

C₂×C₇×D₂₁

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

C₂×C₃×C₇

—

129

C₂×C₃×C₇

—

130

D₂₁

—

131

D₂₁

C₇×D₅×C₁₃

yes

characteristic, direct product factor

132

D₃×C₇

—

133

D₃×C₇

—

134

C₃×C₁₃

C₇×D₅×D₇

yes

characteristic, complemented, Hall

135

C₅×C₇

—

136

C₅×C₇

C₂×D₃×C₇×C₁₃

yes

characteristic, complemented

137

C₅×C₇

C₂×C₁₃×D₂₁

yes

characteristic, complemented

138

D₁₅

—

139

C₃×D₅

C₇×C₁₃×D₇

yes

characteristic, complemented

140

C₅×D₃

—

141

C₂²×C₇

—

105

—

142

C₂×D₇

—

143

C₂×C₁₃

—

144

C₂×C₁₃

—

145

C₂×C₁₃

—

105

—

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

—

105

—

156

D₇

—

157

D₇

—

158

C₁₃

C₇×D₅×D₂₁

yes

characteristic, direct product factor, Sylow

159

C₂×D₃

—

Hall

160

C₂×C₅

—

161

D₅

—

162

D₅

C₇×C₁₃×D₂₁

yes

characteristic, direct product factor

163

C₇

—

164

C₇

D₃×C₇×D₅×C₁₃

yes

characteristic, complemented

165

C₇

D₅×C₁₃×D₂₁

yes

characteristic, direct product factor

166

C₂×C₃

—

167

D₃

—

168

D₃

—

169

C₅

C₂×C₇×C₁₃×D₂₁

yes

characteristic, complemented, Sylow

170

C₂²

—

105

Sylow

171

C₃

C₇×D₅×C₁₃×D₇

yes

characteristic, complemented, Sylow

172

C₂

—

173

C₂

—

174

C₂

—

105

—

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₅×D₂₁
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

D₅×D₂₁

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×C₇²×D₅×C₁₃	C₂	semidirect
2. C₅×C₇×C₁₃×D₂₁	C₂	semidirect
3. C₇×C₁₃×D₁₀₅	C₂	semidirect
5. C₃×C₅×C₇²×C₁₃	C₂²	semidirect
8. C₇²×D₅×C₁₃	D₃	semidirect
10. D₅×C₁₃×D₂₁	C₇	direct (N × H)
13. C₇×C₁₃×D₂₁	D₅	direct (N × H)
15. C₅×C₇²×C₁₃	C₂×D₃	semidirect
16. C₇×D₅×D₂₁	C₁₃	direct (N × H)
17. C₁₃×D₁₀₅	C₂×C₇	semidirect
19. C₅×C₁₃×D₂₁	C₂×C₇	semidirect
22. C₃×C₇×D₅×C₁₃	D₇	semidirect
23. C₃×C₇×D₅×C₁₃	C₂×C₇	semidirect
25. C₃×C₇²×C₁₃	C₂×D₅	semidirect
28. C₇×D₁₀₅	C₂×C₁₃	semidirect
29. C₅×C₇×D₂₁	C₂×C₁₃	semidirect
30. C₃×C₇²×D₅	C₂×C₁₃	semidirect
32. C₃×C₅×C₇×C₁₃	C₂×D₇	semidirect
33. C₃×C₅×C₇×C₁₃	C₂²×C₇	semidirect
44. C₇×D₅×C₁₃	D₃×C₇	semidirect
45. C₇×D₅×C₁₃	D₂₁	direct (N × H)
48. C₃×C₅×C₇²	C₂²×C₁₃	semidirect
49. C₇²×C₁₃	D₃×D₅	semidirect
55. C₁₃×D₂₁	C₇×D₅	direct (N × H)
59. C₇²×D₅	D₃×C₁₃	semidirect
62. C₅×C₇×C₁₃	C₂×D₃×C₇	semidirect
63. C₅×C₇×C₁₃	C₂×D₂₁	semidirect
64. D₅×D₂₁	C₇×C₁₃	direct (N × H)
68. C₃×D₅×C₁₃	C₇×D₇	semidirect
73. C₇×D₂₁	D₅×C₁₃	direct (N × H)
75. C₃×C₇×C₁₃	D₅×D₇	semidirect
76. C₃×C₇×C₁₃	C₂×C₇×D₅	semidirect
78. C₅×C₇²	C₂×D₃×C₁₃	semidirect
79. D₁₀₅	C₂×C₇×C₁₃	semidirect
81. C₅×D₂₁	C₂×C₇×C₁₃	semidirect
84. C₃×C₇×D₅	C₁₃×D₇	semidirect
85. C₃×C₇×D₅	C₂×C₇×C₁₃	semidirect
87. C₃×C₅×C₁₃	C₂×C₇×D₇	semidirect
96. C₃×C₇²	C₂×D₅×C₁₃	semidirect
101. D₅×C₁₃	C₇×D₂₁	direct (N × H)
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	D₅×D₂₁	direct (N × H)
121. C₇×D₅	D₃×C₇×C₁₃	semidirect
122. C₇×D₅	C₁₃×D₂₁	direct (N × H)
123. C₅×C₁₃	C₂×C₇×D₂₁	semidirect
126. C₇²	D₃×D₅×C₁₃	semidirect
131. D₂₁	C₇×D₅×C₁₃	direct (N × H)
134. C₃×C₁₃	C₇×D₅×D₇	semidirect
136. C₅×C₇	C₂×D₃×C₇×C₁₃	semidirect
137. C₅×C₇	C₂×C₁₃×D₂₁	semidirect
139. C₃×D₅	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×D₅×D₂₁	direct (N × H)
162. D₅	C₇×C₁₃×D₂₁	direct (N × H)
164. C₇	D₃×C₇×D₅×C₁₃	semidirect
165. C₇	D₅×C₁₃×D₂₁	direct (N × H)
169. C₅	C₂×C₇×C₁₃×D₂₁	semidirect
171. C₃	C₇×D₅×C₁₃×D₇	semidirect

H ≅ G/N

type

1. C₃×C₇²×D₅×C₁₃

C₂

semidirect

2. C₅×C₇×C₁₃×D₂₁

C₂

semidirect

3. C₇×C₁₃×D₁₀₅

C₂

semidirect

5. C₃×C₅×C₇²×C₁₃

C₂²

semidirect

8. C₇²×D₅×C₁₃

D₃

semidirect

10. D₅×C₁₃×D₂₁

C₇

direct (N × H)

13. C₇×C₁₃×D₂₁

D₅

direct (N × H)

15. C₅×C₇²×C₁₃

C₂×D₃

semidirect

16. C₇×D₅×D₂₁

C₁₃

direct (N × H)

17. C₁₃×D₁₀₅

C₂×C₇

semidirect

19. C₅×C₁₃×D₂₁

C₂×C₇

semidirect

22. C₃×C₇×D₅×C₁₃

D₇

semidirect

23. C₃×C₇×D₅×C₁₃

C₂×C₇

semidirect

25. C₃×C₇²×C₁₃

C₂×D₅

semidirect

28. C₇×D₁₀₅

C₂×C₁₃

semidirect

29. C₅×C₇×D₂₁

C₂×C₁₃

semidirect

30. C₃×C₇²×D₅

C₂×C₁₃

semidirect

32. C₃×C₅×C₇×C₁₃

C₂×D₇

semidirect

33. C₃×C₅×C₇×C₁₃

C₂²×C₇

semidirect

44. C₇×D₅×C₁₃

D₃×C₇

semidirect

45. C₇×D₅×C₁₃

D₂₁

direct (N × H)

48. C₃×C₅×C₇²

C₂²×C₁₃

semidirect

49. C₇²×C₁₃

D₃×D₅

semidirect

55. C₁₃×D₂₁

C₇×D₅

direct (N × H)

59. C₇²×D₅

D₃×C₁₃

semidirect

62. C₅×C₇×C₁₃

C₂×D₃×C₇

semidirect

63. C₅×C₇×C₁₃

C₂×D₂₁

semidirect

64. D₅×D₂₁

C₇×C₁₃

direct (N × H)

68. C₃×D₅×C₁₃

C₇×D₇

semidirect

73. C₇×D₂₁

D₅×C₁₃

direct (N × H)

75. C₃×C₇×C₁₃

D₅×D₇

semidirect

76. C₃×C₇×C₁₃

C₂×C₇×D₅

semidirect

78. C₅×C₇²

C₂×D₃×C₁₃

semidirect

79. D₁₀₅

C₂×C₇×C₁₃

semidirect

81. C₅×D₂₁

C₂×C₇×C₁₃

semidirect

84. C₃×C₇×D₅

C₁₃×D₇

semidirect

85. C₃×C₇×D₅

C₂×C₇×C₁₃

semidirect

87. C₃×C₅×C₁₃

C₂×C₇×D₇

semidirect

96. C₃×C₇²

C₂×D₅×C₁₃

semidirect

101. D₅×C₁₃

C₇×D₂₁

direct (N × H)

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

D₅×D₂₁

direct (N × H)

121. C₇×D₅

D₃×C₇×C₁₃

semidirect

122. C₇×D₅

C₁₃×D₂₁

direct (N × H)

123. C₅×C₁₃

C₂×C₇×D₂₁

semidirect

126. C₇²

D₃×D₅×C₁₃

semidirect

131. D₂₁

C₇×D₅×C₁₃

direct (N × H)

134. C₃×C₁₃

C₇×D₅×D₇

semidirect

136. C₅×C₇

C₂×D₃×C₇×C₁₃

semidirect

137. C₅×C₇

C₂×C₁₃×D₂₁

semidirect

139. C₃×D₅

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×D₅×D₂₁

direct (N × H)

162. D₅

C₇×C₁₃×D₂₁

direct (N × H)

164. C₇

D₃×C₇×D₅×C₁₃

semidirect

165. C₇

D₅×C₁₃×D₂₁

direct (N × H)

169. C₅

C₂×C₇×C₁₃×D₂₁

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×C₇²×D₅×C₁₃	2
C₅×C₇×C₁₃×D₂₁	2
C₇×C₁₃×D₁₀₅	2
C₇×D₅×C₁₃×D₇	3
C₂×C₇×C₁₃×D₂₁	5
D₅×C₁₃×D₂₁	7
D₃×C₇×D₅×C₁₃	7
C₇×D₅×D₂₁	13

subgroup

index

C₃×C₇²×D₅×C₁₃

C₅×C₇×C₁₃×D₂₁

C₇×C₁₃×D₁₀₅

C₇×D₅×C₁₃×D₇

C₂×C₇×C₁₃×D₂₁

D₅×C₁₃×D₂₁

D₃×C₇×D₅×C₁₃

C₇×D₅×D₂₁

Subgroups — C₇×D₅×C₁₃×D₂₁ #50304455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C7×D5×C13×D21 #50304455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₅×C₁₃×D₂₁ #50304455