Group #44568848 — subgroups

Subgroups — C₅×D₇₇⋊D₂₁ #44568848

Order 32340.

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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×C₇×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₂₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×(C₇⋊D₇)⋊D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₇₇⋊D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₇⋊D₇	—	3	1	no	—
8	C₅×C₇×D₇₇	—	3	1	no	—
9	C₅×C₇×D₇₇	D₃	1	1	yes	characteristic, complemented
10	C₅×D₂₁⋊D₁₁	—	7	1	no	maximal
11	C₅×D₁₁×D₂₁	—	7	1	no	maximal
12	C₁₁×C₃⋊(C₇⋊D₇)	C₂×C₅	1	1	yes	characteristic, complemented
13	C₇×D₂₃₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₇×D₇₇	C₂×C₅	1	1	yes	characteristic, complemented
15	C₅×D₇×D₂₁	—	11	1	no	maximal, Hall
16	C₅×C₇²×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
17	C₅×D₂₃₁	D₇	1	1	yes	characteristic, complemented
18	C₅×C₁₁×D₂₁	—	7	1	no	—
19	C₅×C₁₁×D₂₁	—	7	1	no	—
20	C₅×C₁₁×D₂₁	—	14	3	no	—
21	C₅×C₇×D₃₃	—	7	1	no	—
22	C₃×C₅×D₇₇	D₇	1	1	yes	characteristic, complemented
23	C₃×C₅×C₇×D₁₁	—	7	1	no	—
24	(C₇⋊D₇)⋊D₁₁	—	3	1	no	Hall
25	C₃×C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
26	C₅×D₇×D₁₁	—	21	1	no	—
27	C₅×D₇×D₁₁	—	21	1	no	—
28	C₅×C₃⋊(C₇⋊D₇)	D₁₁	1	1	yes	characteristic, complemented
29	C₅×C₇×D₂₁	—	11	1	no	—
30	C₃×C₅×C₇×D₇	—	11	1	no	—
31	C₃×C₅×C₇×C₁₁	—	2	3	no	—
32	C₃×C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented
33	C₃×C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic, complemented
34	C₁₁×C₇⋊D₇	—	3	1	no	—
35	C₇×D₇₇	—	3	1	no	—
36	C₇×D₇₇	C₅×D₃	1	1	yes	characteristic, complemented
37	C₅×D₇²	—	33	1	no	Hall
38	D₂₁⋊D₁₁	—	7	1	no	—
39	D₁₁×D₂₁	—	7	1	no	—
40	C₅×D₇₇	—	3	1	no	—
41	C₅×D₇₇	D₂₁	1	1	yes	characteristic, complemented
42	C₅×C₁₁×D₇	—	21	1	no	—
43	C₅×C₁₁×D₇	—	21	1	no	—
44	C₅×C₁₁×D₇	—	42	3	no	—
45	C₅×C₇×D₁₁	—	7	1	no	—
46	C₅×C₇×D₁₁	—	21	1	no	—
47	C₃×C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
48	C₅×D₃×D₁₁	—	49	1	no	Hall
49	D₇×D₂₁	—	11	1	no	Hall
50	C₇²×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
51	C₅×C₇⋊D₇	—	3	1	no	—
52	C₅×C₇×D₇	—	11	1	no	—
53	C₅×C₇×D₇	—	33	1	no	—
54	D₂₃₁	C₅×D₇	1	1	yes	characteristic, complemented
55	C₁₁×D₂₁	—	7	1	no	—
56	C₁₁×D₂₁	—	7	1	no	—
57	C₁₁×D₂₁	—	14	3	no	—
58	C₇×D₃₃	—	7	1	no	—
59	C₃×D₇₇	C₅×D₇	1	1	yes	characteristic, complemented
60	C₃×C₇×D₁₁	—	7	1	no	—
61	C₂×C₅×D₂₁	—	77	1	no	—
62	C₅×D₃×D₇	—	77	1	no	—
63	C₅×C₇×C₁₁	—	2	3	no	—
64	C₅×C₇×C₁₁	D₃×D₇	1	1	yes	characteristic, complemented
65	C₅×C₇×C₁₁	C₂×D₂₁	1	1	yes	characteristic, complemented
66	C₅×D₃₃	—	7	1	no	—
67	C₅×D₃×C₁₁	—	49	1	no	—
68	C₃×C₅×D₁₁	—	7	1	no	—
69	D₇×D₁₁	—	21	1	no	—
70	D₇×D₁₁	—	21	1	no	—
71	C₃⋊(C₇⋊D₇)	C₅×D₁₁	1	1	yes	characteristic, complemented
72	C₇×D₂₁	—	11	1	no	—
73	C₃×C₇×D₇	—	11	1	no	—
74	C₅×C₇²	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
75	C₃×C₇×C₁₁	—	2	3	no	—
76	C₃×C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented
77	C₃×C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented
78	C₂×C₅×D₁₁	—	147	1	no	Hall
79	C₂×C₃×C₅×C₇	—	77	1	no	—
80	C₅×D₂₁	—	7	1	no	—
81	C₅×D₂₁	—	7	1	no	—
82	C₅×D₂₁	—	11	1	no	—
83	C₅×D₂₁	—	14	3	no	—
84	C₅×D₃×C₇	—	77	1	no	—
85	C₃×C₅×D₇	—	11	1	no	—
86	D₇²	—	33	1	no	Hall
87	C₃×C₅×C₁₁	D₇²	1	1	yes	characteristic, complemented, Hall
88	D₇₇	—	3	1	no	—
89	D₇₇	C₅×D₂₁	1	1	yes	characteristic, complemented
90	C₇×D₁₁	—	7	1	no	—
91	C₇×D₁₁	—	21	1	no	—
92	C₁₁×D₇	—	21	1	no	—
93	C₁₁×D₇	—	21	1	no	—
94	C₁₁×D₇	—	42	3	no	—
95	C₃×C₇²	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
96	C₂×C₅×D₇	—	231	1	no	—
97	C₂×C₅×D₇	—	231	1	no	—
98	D₃×D₁₁	—	49	1	no	Hall
99	C₂×C₅×C₁₁	—	147	1	no	—
100	C₅×D₁₁	—	7	1	no	—
101	C₅×D₁₁	—	21	1	no	—
102	C₃×C₅×C₇	—	2	3	no	—
103	C₃×C₅×C₇	D₇×D₁₁	1	1	yes	characteristic, complemented
104	C₃×C₅×C₇	D₇×D₁₁	1	1	yes	characteristic, complemented
105	C₇⋊D₇	—	3	1	no	—
106	C₇×D₇	—	11	1	no	—
107	C₇×D₇	—	33	1	no	—
108	C₂×D₂₁	—	77	1	no	—
109	D₃×D₇	—	77	1	no	—
110	C₇×C₁₁	—	2	3	no	—
111	C₇×C₁₁	C₅×D₃×D₇	1	1	yes	characteristic, complemented
112	C₇×C₁₁	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented
113	C₂×C₅×C₇	—	77	1	no	—
114	C₂×C₅×C₇	—	231	1	no	—
115	C₅×D₇	—	11	1	no	—
116	C₅×D₇	—	21	1	no	—
117	C₅×D₇	—	21	1	no	—
118	C₅×D₇	—	33	1	no	—
119	C₅×D₇	—	42	3	no	—
120	D₃₃	—	7	1	no	—
121	C₃×D₁₁	—	7	1	no	—
122	D₃×C₁₁	—	49	1	no	—
123	C₂×C₅×D₃	—	539	1	no	Hall
124	C₅×C₁₁	D₇×D₂₁	1	1	yes	characteristic, complemented, Hall
125	C₇²	C₅×D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
126	C₂×D₁₁	—	147	1	no	Hall
127	C₂×C₃×C₇	—	77	1	no	—
128	D₂₁	—	7	1	no	—
129	D₂₁	—	7	1	no	—
130	D₂₁	—	11	1	no	—
131	D₂₁	—	14	3	no	—
132	C₃×D₇	—	11	1	no	—
133	D₃×C₇	—	77	1	no	—
134	C₅×C₇	—	2	3	no	—
135	C₅×C₇	D₁₁×D₂₁	1	1	yes	characteristic, complemented
136	C₅×C₇	D₂₁⋊D₁₁	1	1	yes	characteristic, complemented
137	C₃×C₁₁	C₅×D₇²	1	1	yes	characteristic, complemented, Hall
138	C₂×C₃×C₅	—	77	1	no	—
139	C₅×D₃	—	49	1	no	—
140	C₅×D₃	—	77	1	no	—
141	C₂×D₇	—	231	1	no	—
142	C₂×D₇	—	231	1	no	—
143	C₂×C₁₁	—	147	1	no	—
144	D₁₁	—	7	1	no	—
145	D₁₁	—	21	1	no	—
146	C₃×C₇	—	2	3	no	—
147	C₃×C₇	C₅×D₇×D₁₁	1	1	yes	characteristic, complemented
148	C₃×C₇	C₅×D₇×D₁₁	1	1	yes	characteristic, complemented
149	C₂²×C₅	—	1617	1	no	Hall
150	C₃×C₅	(C₇⋊D₇)⋊D₁₁	1	1	yes	characteristic, complemented, Hall
151	C₂×C₇	—	77	1	no	—
152	C₂×C₇	—	231	1	no	—
153	D₇	—	11	1	no	—
154	D₇	—	21	1	no	—
155	D₇	—	21	1	no	—
156	D₇	—	33	1	no	—
157	D₇	—	42	3	no	—
158	C₂×D₃	—	539	1	no	Hall
159	C₁₁	C₅×D₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
160	C₂×C₅	—	77	1	no	—
161	C₂×C₅	—	147	1	no	—
162	C₂×C₅	—	231	1	no	—
163	C₇	—	2	3	no	—
164	C₇	C₅×D₁₁×D₂₁	1	1	yes	characteristic, complemented
165	C₇	C₅×D₂₁⋊D₁₁	1	1	yes	characteristic, complemented
166	C₂×C₃	—	77	1	no	—
167	D₃	—	49	1	no	—
168	D₃	—	77	1	no	—
169	C₅	D₇₇⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
170	C₂²	—	1617	1	no	Sylow
171	C₃	C₅×(C₇⋊D₇)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
172	C₂	—	77	1	no	—
173	C₂	—	147	1	no	—
174	C₂	—	231	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₇×D₇₇

C₂

yes

maximal, characteristic, complemented

C₅×C₇×D₂₃₁

C₂

yes

maximal, characteristic, complemented

C₅×C₁₁×C₃⋊(C₇⋊D₇)

C₂

yes

maximal, characteristic, complemented

C₅×(C₇⋊D₇)⋊D₁₁

—

maximal, Hall

C₃×C₅×C₇²×C₁₁

C₂²

yes

characteristic, complemented, Hall

D₇₇⋊D₂₁

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₁×C₇⋊D₇

—

C₅×C₇×D₇₇

—

C₅×C₇×D₇₇

D₃

yes

characteristic, complemented

C₅×D₂₁⋊D₁₁

—

maximal

C₅×D₁₁×D₂₁

—

maximal

C₁₁×C₃⋊(C₇⋊D₇)

C₂×C₅

yes

characteristic, complemented

C₇×D₂₃₁

C₂×C₅

yes

characteristic, complemented

C₃×C₇×D₇₇

C₂×C₅

yes

characteristic, complemented

C₅×D₇×D₂₁

—

maximal, Hall

C₅×C₇²×C₁₁

C₂×D₃

yes

characteristic, complemented, Hall

C₅×D₂₃₁

D₇

yes

characteristic, complemented

C₅×C₁₁×D₂₁

—

C₅×C₁₁×D₂₁

—

C₅×C₁₁×D₂₁

—

C₅×C₇×D₃₃

—

C₃×C₅×D₇₇

D₇

yes

characteristic, complemented

C₃×C₅×C₇×D₁₁

—

(C₇⋊D₇)⋊D₁₁

—

Hall

C₃×C₇²×C₁₁

C₂²×C₅

yes

characteristic, complemented, Hall

C₅×D₇×D₁₁

—

C₅×D₇×D₁₁

—

C₅×C₃⋊(C₇⋊D₇)

D₁₁

yes

characteristic, complemented

C₅×C₇×D₂₁

—

C₃×C₅×C₇×D₇

—

C₃×C₅×C₇×C₁₁

—

C₃×C₅×C₇×C₁₁

C₂×D₇

yes

characteristic, complemented

C₃×C₅×C₇×C₁₁

C₂×D₇

yes

characteristic, complemented

C₁₁×C₇⋊D₇

—

C₇×D₇₇

—

C₇×D₇₇

C₅×D₃

yes

characteristic, complemented

C₅×D₇²

—

Hall

D₂₁⋊D₁₁

—

D₁₁×D₂₁

—

C₅×D₇₇

—

C₅×D₇₇

D₂₁

yes

characteristic, complemented

C₅×C₁₁×D₇

—

C₅×C₁₁×D₇

—

C₅×C₁₁×D₇

—

C₅×C₇×D₁₁

—

C₅×C₇×D₁₁

—

C₃×C₅×C₇²

C₂×D₁₁

yes

characteristic, complemented, Hall

C₅×D₃×D₁₁

—

Hall

D₇×D₂₁

—

Hall

C₇²×C₁₁

C₂×C₅×D₃

yes

characteristic, complemented, Hall

C₅×C₇⋊D₇

—

C₅×C₇×D₇

—

C₅×C₇×D₇

—

D₂₃₁

C₅×D₇

yes

characteristic, complemented

C₁₁×D₂₁

—

C₁₁×D₂₁

—

C₁₁×D₂₁

—

C₇×D₃₃

—

C₃×D₇₇

C₅×D₇

yes

characteristic, complemented

C₃×C₇×D₁₁

—

C₂×C₅×D₂₁

—

C₅×D₃×D₇

—

C₅×C₇×C₁₁

—

C₅×C₇×C₁₁

D₃×D₇

yes

characteristic, complemented

C₅×C₇×C₁₁

C₂×D₂₁

yes

characteristic, complemented

C₅×D₃₃

—

C₅×D₃×C₁₁

—

C₃×C₅×D₁₁

—

D₇×D₁₁

—

D₇×D₁₁

—

C₃⋊(C₇⋊D₇)

C₅×D₁₁

yes

characteristic, complemented

C₇×D₂₁

—

C₃×C₇×D₇

—

C₅×C₇²

D₃×D₁₁

yes

characteristic, complemented, Hall

C₃×C₇×C₁₁

—

C₃×C₇×C₁₁

C₂×C₅×D₇

yes

characteristic, complemented

C₃×C₇×C₁₁

C₂×C₅×D₇

yes

characteristic, complemented

C₂×C₅×D₁₁

—

147

Hall

C₂×C₃×C₅×C₇

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₂₁

—

C₅×D₃×C₇

—

C₃×C₅×D₇

—

D₇²

—

Hall

C₃×C₅×C₁₁

D₇²

yes

characteristic, complemented, Hall

D₇₇

—

D₇₇

C₅×D₂₁

yes

characteristic, complemented

C₇×D₁₁

—

C₇×D₁₁

—

C₁₁×D₇

—

C₁₁×D₇

—

C₁₁×D₇

—

C₃×C₇²

C₂×C₅×D₁₁

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

231

—

C₂×C₅×D₇

—

231

—

D₃×D₁₁

—

Hall

C₂×C₅×C₁₁

—

147

—

100

C₅×D₁₁

—

101

C₅×D₁₁

—

102

C₃×C₅×C₇

—

103

C₃×C₅×C₇

D₇×D₁₁

yes

characteristic, complemented

104

C₃×C₅×C₇

D₇×D₁₁

yes

characteristic, complemented

105

C₇⋊D₇

—

106

C₇×D₇

—

107

C₇×D₇

—

108

C₂×D₂₁

—

109

D₃×D₇

—

110

C₇×C₁₁

—

111

C₇×C₁₁

C₅×D₃×D₇

yes

characteristic, complemented

112

C₇×C₁₁

C₂×C₅×D₂₁

yes

characteristic, complemented

113

C₂×C₅×C₇

—

114

C₂×C₅×C₇

—

231

—

115

C₅×D₇

—

116

C₅×D₇

—

117

C₅×D₇

—

118

C₅×D₇

—

119

C₅×D₇

—

120

D₃₃

—

121

C₃×D₁₁

—

122

D₃×C₁₁

—

123

C₂×C₅×D₃

—

539

Hall

124

C₅×C₁₁

D₇×D₂₁

yes

characteristic, complemented, Hall

125

C₇²

C₅×D₃×D₁₁

yes

characteristic, complemented, Sylow

126

C₂×D₁₁

—

147

Hall

127

C₂×C₃×C₇

—

128

D₂₁

—

129

D₂₁

—

130

D₂₁

—

131

D₂₁

—

132

C₃×D₇

—

133

D₃×C₇

—

134

C₅×C₇

—

135

C₅×C₇

D₁₁×D₂₁

yes

characteristic, complemented

136

C₅×C₇

D₂₁⋊D₁₁

yes

characteristic, complemented

137

C₃×C₁₁

C₅×D₇²

yes

characteristic, complemented, Hall

138

C₂×C₃×C₅

—

139

C₅×D₃

—

140

C₅×D₃

—

141

C₂×D₇

—

231

—

142

C₂×D₇

—

231

—

143

C₂×C₁₁

—

147

—

144

D₁₁

—

145

D₁₁

—

146

C₃×C₇

—

147

C₃×C₇

C₅×D₇×D₁₁

yes

characteristic, complemented

148

C₃×C₇

C₅×D₇×D₁₁

yes

characteristic, complemented

149

C₂²×C₅

—

1617

Hall

150

C₃×C₅

(C₇⋊D₇)⋊D₁₁

yes

characteristic, complemented, Hall

151

C₂×C₇

—

152

C₂×C₇

—

231

—

153

D₇

—

154

D₇

—

155

D₇

—

156

D₇

—

157

D₇

—

158

C₂×D₃

—

539

Hall

159

C₁₁

C₅×D₇×D₂₁

yes

characteristic, complemented, Sylow

160

C₂×C₅

—

161

C₂×C₅

—

147

—

162

C₂×C₅

—

231

—

163

C₇

—

164

C₇

C₅×D₁₁×D₂₁

yes

characteristic, complemented

165

C₇

C₅×D₂₁⋊D₁₁

yes

characteristic, complemented

166

C₂×C₃

—

167

D₃

—

168

D₃

—

169

C₅

D₇₇⋊D₂₁

yes

characteristic, direct product factor, Sylow

170

C₂²

—

1617

Sylow

171

C₃

C₅×(C₇⋊D₇)⋊D₁₁

yes

characteristic, complemented, Sylow

172

C₂

—

173

C₂

—

147

—

174

C₂

—

231

—

	subgroup	G/H
center, hypercenter	C₅	D₇₇⋊D₂₁
commutator, cosocle, hypocenter	C₃×C₇²×C₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₃×C₇²×C₁₁
UCS	C₁ ◁ C₅

subgroup

G/H

center, hypercenter

C₅

D₇₇⋊D₂₁

commutator, cosocle, hypocenter

C₃×C₇²×C₁₁

C₂²×C₅

Frattini

C₁

Fitting, socle

C₃×C₅×C₇²×C₁₁

C₂²

LCS

G ▷ C₃×C₇²×C₁₁

UCS

C₁ ◁ C₅

N	H ≅ G/N	type
1. C₃×C₅×C₇×D₇₇	C₂	semidirect
2. C₅×C₇×D₂₃₁	C₂	semidirect
3. C₅×C₁₁×C₃⋊(C₇⋊D₇)	C₂	semidirect
5. C₃×C₅×C₇²×C₁₁	C₂²	semidirect
6. D₇₇⋊D₂₁	C₅	direct (N × H)
9. C₅×C₇×D₇₇	D₃	semidirect
12. C₁₁×C₃⋊(C₇⋊D₇)	C₂×C₅	semidirect
13. C₇×D₂₃₁	C₂×C₅	semidirect
14. C₃×C₇×D₇₇	C₂×C₅	semidirect
16. C₅×C₇²×C₁₁	C₂×D₃	semidirect
17. C₅×D₂₃₁	D₇	semidirect
22. C₃×C₅×D₇₇	D₇	semidirect
25. C₃×C₇²×C₁₁	C₂²×C₅	semidirect
28. C₅×C₃⋊(C₇⋊D₇)	D₁₁	semidirect
32. C₃×C₅×C₇×C₁₁	C₂×D₇	semidirect
33. C₃×C₅×C₇×C₁₁	C₂×D₇	semidirect
36. C₇×D₇₇	C₅×D₃	semidirect
41. C₅×D₇₇	D₂₁	semidirect
47. C₃×C₅×C₇²	C₂×D₁₁	semidirect
50. C₇²×C₁₁	C₂×C₅×D₃	semidirect
54. D₂₃₁	C₅×D₇	semidirect
59. C₃×D₇₇	C₅×D₇	semidirect
64. C₅×C₇×C₁₁	D₃×D₇	semidirect
65. C₅×C₇×C₁₁	C₂×D₂₁	semidirect
71. C₃⋊(C₇⋊D₇)	C₅×D₁₁	semidirect
74. C₅×C₇²	D₃×D₁₁	semidirect
76. C₃×C₇×C₁₁	C₂×C₅×D₇	semidirect
77. C₃×C₇×C₁₁	C₂×C₅×D₇	semidirect
87. C₃×C₅×C₁₁	D₇²	semidirect
89. D₇₇	C₅×D₂₁	semidirect
95. C₃×C₇²	C₂×C₅×D₁₁	semidirect
103. C₃×C₅×C₇	D₇×D₁₁	semidirect
104. C₃×C₅×C₇	D₇×D₁₁	semidirect
111. C₇×C₁₁	C₅×D₃×D₇	semidirect
112. C₇×C₁₁	C₂×C₅×D₂₁	semidirect
124. C₅×C₁₁	D₇×D₂₁	semidirect
125. C₇²	C₅×D₃×D₁₁	semidirect
135. C₅×C₇	D₁₁×D₂₁	semidirect
136. C₅×C₇	D₂₁⋊D₁₁	semidirect
137. C₃×C₁₁	C₅×D₇²	semidirect
147. C₃×C₇	C₅×D₇×D₁₁	semidirect
148. C₃×C₇	C₅×D₇×D₁₁	semidirect
150. C₃×C₅	(C₇⋊D₇)⋊D₁₁	semidirect
159. C₁₁	C₅×D₇×D₂₁	semidirect
164. C₇	C₅×D₁₁×D₂₁	semidirect
165. C₇	C₅×D₂₁⋊D₁₁	semidirect
169. C₅	D₇₇⋊D₂₁	direct (N × H)
171. C₃	C₅×(C₇⋊D₇)⋊D₁₁	semidirect

H ≅ G/N

type

1. C₃×C₅×C₇×D₇₇

C₂

semidirect

2. C₅×C₇×D₂₃₁

C₂

semidirect

3. C₅×C₁₁×C₃⋊(C₇⋊D₇)

C₂

semidirect

5. C₃×C₅×C₇²×C₁₁

C₂²

semidirect

6. D₇₇⋊D₂₁

C₅

direct (N × H)

9. C₅×C₇×D₇₇

D₃

semidirect

12. C₁₁×C₃⋊(C₇⋊D₇)

C₂×C₅

semidirect

13. C₇×D₂₃₁

C₂×C₅

semidirect

14. C₃×C₇×D₇₇

C₂×C₅

semidirect

16. C₅×C₇²×C₁₁

C₂×D₃

semidirect

17. C₅×D₂₃₁

D₇

semidirect

22. C₃×C₅×D₇₇

D₇

semidirect

25. C₃×C₇²×C₁₁

C₂²×C₅

semidirect

28. C₅×C₃⋊(C₇⋊D₇)

D₁₁

semidirect

32. C₃×C₅×C₇×C₁₁

C₂×D₇

semidirect

33. C₃×C₅×C₇×C₁₁

C₂×D₇

semidirect

36. C₇×D₇₇

C₅×D₃

semidirect

41. C₅×D₇₇

D₂₁

semidirect

47. C₃×C₅×C₇²

C₂×D₁₁

semidirect

50. C₇²×C₁₁

C₂×C₅×D₃

semidirect

54. D₂₃₁

C₅×D₇

semidirect

59. C₃×D₇₇

C₅×D₇

semidirect

64. C₅×C₇×C₁₁

D₃×D₇

semidirect

65. C₅×C₇×C₁₁

C₂×D₂₁

semidirect

71. C₃⋊(C₇⋊D₇)

C₅×D₁₁

semidirect

74. C₅×C₇²

D₃×D₁₁

semidirect

76. C₃×C₇×C₁₁

C₂×C₅×D₇

semidirect

77. C₃×C₇×C₁₁

C₂×C₅×D₇

semidirect

87. C₃×C₅×C₁₁

D₇²

semidirect

89. D₇₇

C₅×D₂₁

semidirect

95. C₃×C₇²

C₂×C₅×D₁₁

semidirect

103. C₃×C₅×C₇

D₇×D₁₁

semidirect

104. C₃×C₅×C₇

D₇×D₁₁

semidirect

111. C₇×C₁₁

C₅×D₃×D₇

semidirect

112. C₇×C₁₁

C₂×C₅×D₂₁

semidirect

124. C₅×C₁₁

D₇×D₂₁

semidirect

125. C₇²

C₅×D₃×D₁₁

semidirect

135. C₅×C₇

D₁₁×D₂₁

semidirect

136. C₅×C₇

D₂₁⋊D₁₁

semidirect

137. C₃×C₁₁

C₅×D₇²

semidirect

147. C₃×C₇

C₅×D₇×D₁₁

semidirect

148. C₃×C₇

C₅×D₇×D₁₁

semidirect

150. C₃×C₅

(C₇⋊D₇)⋊D₁₁

semidirect

159. C₁₁

C₅×D₇×D₂₁

semidirect

164. C₇

C₅×D₁₁×D₂₁

semidirect

165. C₇

C₅×D₂₁⋊D₁₁

semidirect

169. C₅

D₇₇⋊D₂₁

direct (N × H)

171. C₃

C₅×(C₇⋊D₇)⋊D₁₁

semidirect

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

subgroup	index
C₃×C₅×C₇×D₇₇	2
C₅×C₇×D₂₃₁	2
C₅×C₁₁×C₃⋊(C₇⋊D₇)	2
C₅×(C₇⋊D₇)⋊D₁₁	3
D₇₇⋊D₂₁	5
C₅×D₂₁⋊D₁₁	7
C₅×D₁₁×D₂₁	7
C₅×D₇×D₂₁	11

subgroup

index

C₃×C₅×C₇×D₇₇

C₅×C₇×D₂₃₁

C₅×C₁₁×C₃⋊(C₇⋊D₇)

C₅×(C₇⋊D₇)⋊D₁₁

D₇₇⋊D₂₁

C₅×D₂₁⋊D₁₁

C₅×D₁₁×D₂₁

C₅×D₇×D₂₁

Subgroups — C₅×D₇₇⋊D₂₁ #44568848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D77⋊D21 #44568848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇₇⋊D₂₁ #44568848