Group #49087981 — subgroups

Subgroups — C₁₇×D₃₅⋊D₁₅ #49087981

Order 35700.

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

normal subgroups only

This group has 192 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×C₁₇×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₇×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×(C₅⋊D₅)⋊D₇	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₁₅⋊D₇	—	5	1	no	maximal
7	D₇×C₁₇×D₁₅	—	5	1	no	maximal
8	C₇×C₁₇×C₅⋊D₅	—	3	1	no	—
9	C₅×C₁₇×D₃₅	—	3	1	no	—
10	C₅×C₁₇×D₃₅	D₃	1	1	yes	characteristic, complemented
11	D₅×C₁₇×D₁₅	—	7	1	no	maximal, Hall
12	C₁₇×D₁₀₅	D₅	1	1	yes	characteristic, complemented
13	C₇×C₁₇×D₁₅	—	5	1	no	—
14	C₇×C₁₇×D₁₅	—	5	1	no	—
15	C₇×C₁₇×D₁₅	—	10	2	no	—
16	C₅×C₁₇×D₂₁	—	5	1	no	—
17	C₃×C₁₇×D₃₅	D₅	1	1	yes	characteristic, complemented
18	C₃×C₅×D₇×C₁₇	—	5	1	no	—
19	C₅²×C₇×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
20	C₁₇×C₃⋊(C₅⋊D₅)	D₇	1	1	yes	characteristic, complemented
21	C₅×C₁₇×D₁₅	—	7	1	no	—
22	C₃×C₅×D₅×C₁₇	—	7	1	no	—
23	D₅×D₇×C₁₇	—	15	1	no	—
24	D₅×D₇×C₁₇	—	15	1	no	—
25	D₃₅⋊D₁₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₃×C₅×C₇×C₁₇	—	2	2	no	—
27	C₃×C₅×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
28	C₃×C₅×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
29	D₅²×C₁₇	—	21	1	no	Hall
30	D₃×D₇×C₁₇	—	25	1	no	Hall
31	C₃×C₅²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
32	C₁₇×D₃₅	—	3	1	no	—
33	C₁₇×D₃₅	D₁₅	1	1	yes	characteristic, complemented
34	C₇×D₅×C₁₇	—	15	1	no	—
35	C₇×D₅×C₁₇	—	15	1	no	—
36	C₇×D₅×C₁₇	—	30	2	no	—
37	C₅×D₇×C₁₇	—	5	1	no	—
38	C₅×D₇×C₁₇	—	15	1	no	—
39	C₇×C₃⋊(C₅⋊D₅)	C₂×C₁₇	1	1	yes	characteristic, complemented
40	C₅×D₁₀₅	C₂×C₁₇	1	1	yes	characteristic, complemented
41	C₃×C₅×D₃₅	C₂×C₁₇	1	1	yes	characteristic, complemented
42	C₂×C₁₇×D₁₅	—	35	1	no	—
43	D₃×D₅×C₁₇	—	35	1	no	—
44	C₁₇×C₅⋊D₅	—	3	1	no	—
45	C₅×D₅×C₁₇	—	7	1	no	—
46	C₅×D₅×C₁₇	—	21	1	no	—
47	C₁₇×D₂₁	—	5	1	no	—
48	D₃×C₇×C₁₇	—	25	1	no	—
49	C₃×D₇×C₁₇	—	5	1	no	—
50	(C₅⋊D₅)⋊D₇	—	3	1	no	Hall
51	C₅×C₇×C₁₇	—	2	2	no	—
52	C₅×C₇×C₁₇	D₃×D₅	1	1	yes	characteristic, complemented
53	C₅×C₇×C₁₇	C₂×D₁₅	1	1	yes	characteristic, complemented
54	C₃×C₅²×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅×C₁₇	—	35	1	no	—
56	C₁₇×D₁₅	—	5	1	no	—
57	C₁₇×D₁₅	—	5	1	no	—
58	C₁₇×D₁₅	—	7	1	no	—
59	C₁₇×D₁₅	—	10	2	no	—
60	C₅×D₃×C₁₇	—	35	1	no	—
61	C₃×D₅×C₁₇	—	7	1	no	—
62	C₂×D₇×C₁₇	—	75	1	no	Hall
63	C₅²×C₁₇	D₃×D₇	1	1	yes	characteristic, complemented, Hall
64	D₁₅⋊D₇	—	5	1	no	—
65	D₇×D₁₅	—	5	1	no	—
66	C₃×C₇×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
67	C₇×C₅⋊D₅	—	3	1	no	—
68	C₅×D₃₅	—	3	1	no	—
69	C₅×D₃₅	D₃×C₁₇	1	1	yes	characteristic, complemented
70	C₂×D₅×C₁₇	—	105	1	no	—
71	C₂×D₅×C₁₇	—	105	1	no	—
72	D₅×D₁₅	—	7	1	no	Hall
73	C₃×C₅×C₁₇	—	2	2	no	—
74	C₃×C₅×C₁₇	D₅×D₇	1	1	yes	characteristic, complemented
75	C₃×C₅×C₁₇	D₅×D₇	1	1	yes	characteristic, complemented
76	C₂×C₇×C₁₇	—	75	1	no	—
77	D₇×C₁₇	—	5	1	no	—
78	D₇×C₁₇	—	15	1	no	—
79	D₁₀₅	D₅×C₁₇	1	1	yes	characteristic, complemented
80	C₇×D₁₅	—	5	1	no	—
81	C₇×D₁₅	—	5	1	no	—
82	C₇×D₁₅	—	10	2	no	—
83	C₅×D₂₁	—	5	1	no	—
84	C₃×D₃₅	D₅×C₁₇	1	1	yes	characteristic, complemented
85	C₃×C₅×D₇	—	5	1	no	—
86	C₂×D₃×C₁₇	—	175	1	no	Hall
87	C₅²×C₇	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
88	C₂×C₅×C₁₇	—	35	1	no	—
89	C₂×C₅×C₁₇	—	105	1	no	—
90	D₅×C₁₇	—	7	1	no	—
91	D₅×C₁₇	—	15	1	no	—
92	D₅×C₁₇	—	15	1	no	—
93	D₅×C₁₇	—	21	1	no	—
94	D₅×C₁₇	—	30	2	no	—
95	C₃⋊(C₅⋊D₅)	D₇×C₁₇	1	1	yes	characteristic, complemented
96	C₅×D₁₅	—	7	1	no	—
97	C₃×C₅×D₅	—	7	1	no	—
98	D₅×D₇	—	15	1	no	—
99	D₅×D₇	—	15	1	no	—
100	C₇×C₁₇	D₅×D₁₅	1	1	yes	characteristic, complemented, Hall
101	C₃×C₅×C₇	—	2	2	no	—
102	C₃×C₅×C₇	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented
103	C₃×C₅×C₇	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented
104	C₂×C₃×C₁₇	—	35	1	no	—
105	D₃×C₁₇	—	25	1	no	—
106	D₃×C₁₇	—	35	1	no	—
107	D₅²	—	21	1	no	Hall
108	C₅×C₁₇	—	2	2	no	—
109	C₅×C₁₇	D₇×D₁₅	1	1	yes	characteristic, complemented
110	C₅×C₁₇	D₁₅⋊D₇	1	1	yes	characteristic, complemented
111	D₃×D₇	—	25	1	no	Hall
112	C₃×C₅²	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
113	D₃₅	—	3	1	no	—
114	D₃₅	C₁₇×D₁₅	1	1	yes	characteristic, complemented
115	C₅×D₇	—	5	1	no	—
116	C₅×D₇	—	15	1	no	—
117	C₇×D₅	—	15	1	no	—
118	C₇×D₅	—	15	1	no	—
119	C₇×D₅	—	30	2	no	—
120	C₂²×C₁₇	—	525	1	no	Hall
121	C₂×D₁₅	—	35	1	no	—
122	D₃×D₅	—	35	1	no	—
123	C₃×C₁₇	(C₅⋊D₅)⋊D₇	1	1	yes	characteristic, complemented, Hall
124	C₅⋊D₅	—	3	1	no	—
125	C₅×D₅	—	7	1	no	—
126	C₅×D₅	—	21	1	no	—
127	D₂₁	—	5	1	no	—
128	C₃×D₇	—	5	1	no	—
129	D₃×C₇	—	25	1	no	—
130	C₅×C₇	—	2	2	no	—
131	C₅×C₇	D₃×D₅×C₁₇	1	1	yes	characteristic, complemented
132	C₅×C₇	C₂×C₁₇×D₁₅	1	1	yes	characteristic, complemented
133	C₂×C₁₇	—	35	1	no	—
134	C₂×C₁₇	—	75	1	no	—
135	C₂×C₁₇	—	105	1	no	—
136	C₂×C₃×C₅	—	35	1	no	—
137	D₁₅	—	5	1	no	—
138	D₁₅	—	5	1	no	—
139	D₁₅	—	7	1	no	—
140	D₁₅	—	10	2	no	—
141	C₃×D₅	—	7	1	no	—
142	C₅×D₃	—	35	1	no	—
143	C₂×D₇	—	75	1	no	Hall
144	C₅²	D₃×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
145	C₃×C₇	D₅²×C₁₇	1	1	yes	characteristic, complemented, Hall
146	C₂×D₅	—	105	1	no	—
147	C₂×D₅	—	105	1	no	—
148	C₁₇	D₃₅⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
149	C₃×C₅	—	2	2	no	—
150	C₃×C₅	D₅×D₇×C₁₇	1	1	yes	characteristic, complemented
151	C₃×C₅	D₅×D₇×C₁₇	1	1	yes	characteristic, complemented
152	C₂×C₇	—	75	1	no	—
153	D₇	—	5	1	no	—
154	D₇	—	15	1	no	—
155	C₂×D₃	—	175	1	no	Hall
156	C₂×C₅	—	35	1	no	—
157	C₂×C₅	—	105	1	no	—
158	D₅	—	7	1	no	—
159	D₅	—	15	1	no	—
160	D₅	—	15	1	no	—
161	D₅	—	21	1	no	—
162	D₅	—	30	2	no	—
163	C₇	D₅×C₁₇×D₁₅	1	1	yes	characteristic, complemented, Sylow
164	C₂×C₃	—	35	1	no	—
165	D₃	—	25	1	no	—
166	D₃	—	35	1	no	—
167	C₅	—	2	2	no	—
168	C₅	D₇×C₁₇×D₁₅	1	1	yes	characteristic, complemented
169	C₅	C₁₇×D₁₅⋊D₇	1	1	yes	characteristic, complemented
170	C₂²	—	525	1	no	Sylow
171	C₃	C₁₇×(C₅⋊D₅)⋊D₇	1	1	yes	characteristic, complemented, Sylow
172	C₂	—	35	1	no	—
173	C₂	—	75	1	no	—
174	C₂	—	105	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₁₇×D₃₅

C₂

yes

maximal, characteristic, complemented

C₅×C₁₇×D₁₀₅

C₂

yes

maximal, characteristic, complemented

C₇×C₁₇×C₃⋊(C₅⋊D₅)

C₂

yes

maximal, characteristic, complemented

C₁₇×(C₅⋊D₅)⋊D₇

—

maximal, Hall

C₃×C₅²×C₇×C₁₇

C₂²

yes

characteristic, complemented, Hall

C₁₇×D₁₅⋊D₇

—

maximal

D₇×C₁₇×D₁₅

—

maximal

C₇×C₁₇×C₅⋊D₅

—

C₅×C₁₇×D₃₅

—

C₅×C₁₇×D₃₅

D₃

yes

characteristic, complemented

D₅×C₁₇×D₁₅

—

maximal, Hall

C₁₇×D₁₀₅

D₅

yes

characteristic, complemented

C₇×C₁₇×D₁₅

—

C₇×C₁₇×D₁₅

—

C₇×C₁₇×D₁₅

—

C₅×C₁₇×D₂₁

—

C₃×C₁₇×D₃₅

D₅

yes

characteristic, complemented

C₃×C₅×D₇×C₁₇

—

C₅²×C₇×C₁₇

C₂×D₃

yes

characteristic, complemented, Hall

C₁₇×C₃⋊(C₅⋊D₅)

D₇

yes

characteristic, complemented

C₅×C₁₇×D₁₅

—

C₃×C₅×D₅×C₁₇

—

D₅×D₇×C₁₇

—

D₅×D₇×C₁₇

—

D₃₅⋊D₁₅

C₁₇

yes

maximal, characteristic, direct product factor, Hall

C₃×C₅×C₇×C₁₇

—

C₃×C₅×C₇×C₁₇

C₂×D₅

yes

characteristic, complemented

C₃×C₅×C₇×C₁₇

C₂×D₅

yes

characteristic, complemented

D₅²×C₁₇

—

Hall

D₃×D₇×C₁₇

—

Hall

C₃×C₅²×C₁₇

C₂×D₇

yes

characteristic, complemented, Hall

C₁₇×D₃₅

—

C₁₇×D₃₅

D₁₅

yes

characteristic, complemented

C₇×D₅×C₁₇

—

C₇×D₅×C₁₇

—

C₇×D₅×C₁₇

—

C₅×D₇×C₁₇

—

C₅×D₇×C₁₇

—

C₇×C₃⋊(C₅⋊D₅)

C₂×C₁₇

yes

characteristic, complemented

C₅×D₁₀₅

C₂×C₁₇

yes

characteristic, complemented

C₃×C₅×D₃₅

C₂×C₁₇

yes

characteristic, complemented

C₂×C₁₇×D₁₅

—

D₃×D₅×C₁₇

—

C₁₇×C₅⋊D₅

—

C₅×D₅×C₁₇

—

C₅×D₅×C₁₇

—

C₁₇×D₂₁

—

D₃×C₇×C₁₇

—

C₃×D₇×C₁₇

—

(C₅⋊D₅)⋊D₇

—

Hall

C₅×C₇×C₁₇

—

C₅×C₇×C₁₇

D₃×D₅

yes

characteristic, complemented

C₅×C₇×C₁₇

C₂×D₁₅

yes

characteristic, complemented

C₃×C₅²×C₇

C₂²×C₁₇

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₁₇

—

C₁₇×D₁₅

—

C₁₇×D₁₅

—

C₁₇×D₁₅

—

C₁₇×D₁₅

—

C₅×D₃×C₁₇

—

C₃×D₅×C₁₇

—

C₂×D₇×C₁₇

—

Hall

C₅²×C₁₇

D₃×D₇

yes

characteristic, complemented, Hall

D₁₅⋊D₇

—

D₇×D₁₅

—

C₃×C₇×C₁₇

D₅²

yes

characteristic, complemented, Hall

C₇×C₅⋊D₅

—

C₅×D₃₅

—

C₅×D₃₅

D₃×C₁₇

yes

characteristic, complemented

C₂×D₅×C₁₇

—

105

—

C₂×D₅×C₁₇

—

105

—

D₅×D₁₅

—

Hall

C₃×C₅×C₁₇

—

C₃×C₅×C₁₇

D₅×D₇

yes

characteristic, complemented

C₃×C₅×C₁₇

D₅×D₇

yes

characteristic, complemented

C₂×C₇×C₁₇

—

D₇×C₁₇

—

D₇×C₁₇

—

D₁₀₅

D₅×C₁₇

yes

characteristic, complemented

C₇×D₁₅

—

C₇×D₁₅

—

C₇×D₁₅

—

C₅×D₂₁

—

C₃×D₃₅

D₅×C₁₇

yes

characteristic, complemented

C₃×C₅×D₇

—

C₂×D₃×C₁₇

—

175

Hall

C₅²×C₇

C₂×D₃×C₁₇

yes

characteristic, complemented, Hall

C₂×C₅×C₁₇

—

C₂×C₅×C₁₇

—

105

—

D₅×C₁₇

—

D₅×C₁₇

—

D₅×C₁₇

—

D₅×C₁₇

—

D₅×C₁₇

—

C₃⋊(C₅⋊D₅)

D₇×C₁₇

yes

characteristic, complemented

C₅×D₁₅

—

C₃×C₅×D₅

—

D₅×D₇

—

D₅×D₇

—

100

C₇×C₁₇

D₅×D₁₅

yes

characteristic, complemented, Hall

101

C₃×C₅×C₇

—

102

C₃×C₅×C₇

C₂×D₅×C₁₇

yes

characteristic, complemented

103

C₃×C₅×C₇

C₂×D₅×C₁₇

yes

characteristic, complemented

104

C₂×C₃×C₁₇

—

105

D₃×C₁₇

—

106

D₃×C₁₇

—

107

D₅²

—

Hall

108

C₅×C₁₇

—

109

C₅×C₁₇

D₇×D₁₅

yes

characteristic, complemented

110

C₅×C₁₇

D₁₅⋊D₇

yes

characteristic, complemented

111

D₃×D₇

—

Hall

112

C₃×C₅²

C₂×D₇×C₁₇

yes

characteristic, complemented, Hall

113

D₃₅

—

114

D₃₅

C₁₇×D₁₅

yes

characteristic, complemented

115

C₅×D₇

—

116

C₅×D₇

—

117

C₇×D₅

—

118

C₇×D₅

—

119

C₇×D₅

—

120

C₂²×C₁₇

—

525

Hall

121

C₂×D₁₅

—

122

D₃×D₅

—

123

C₃×C₁₇

(C₅⋊D₅)⋊D₇

yes

characteristic, complemented, Hall

124

C₅⋊D₅

—

125

C₅×D₅

—

126

C₅×D₅

—

127

D₂₁

—

128

C₃×D₇

—

129

D₃×C₇

—

130

C₅×C₇

—

131

C₅×C₇

D₃×D₅×C₁₇

yes

characteristic, complemented

132

C₅×C₇

C₂×C₁₇×D₁₅

yes

characteristic, complemented

133

C₂×C₁₇

—

134

C₂×C₁₇

—

135

C₂×C₁₇

—

105

—

136

C₂×C₃×C₅

—

137

D₁₅

—

138

D₁₅

—

139

D₁₅

—

140

D₁₅

—

141

C₃×D₅

—

142

C₅×D₃

—

143

C₂×D₇

—

Hall

144

C₅²

D₃×D₇×C₁₇

yes

characteristic, complemented, Sylow

145

C₃×C₇

D₅²×C₁₇

yes

characteristic, complemented, Hall

146

C₂×D₅

—

105

—

147

C₂×D₅

—

105

—

148

C₁₇

D₃₅⋊D₁₅

yes

characteristic, direct product factor, Sylow

149

C₃×C₅

—

150

C₃×C₅

D₅×D₇×C₁₇

yes

characteristic, complemented

151

C₃×C₅

D₅×D₇×C₁₇

yes

characteristic, complemented

152

C₂×C₇

—

153

D₇

—

154

D₇

—

155

C₂×D₃

—

175

Hall

156

C₂×C₅

—

157

C₂×C₅

—

105

—

158

D₅

—

159

D₅

—

160

D₅

—

161

D₅

—

162

D₅

—

163

C₇

D₅×C₁₇×D₁₅

yes

characteristic, complemented, Sylow

164

C₂×C₃

—

165

D₃

—

166

D₃

—

167

C₅

—

168

C₅

D₇×C₁₇×D₁₅

yes

characteristic, complemented

169

C₅

C₁₇×D₁₅⋊D₇

yes

characteristic, complemented

170

C₂²

—

525

Sylow

171

C₃

C₁₇×(C₅⋊D₅)⋊D₇

yes

characteristic, complemented, Sylow

172

C₂

—

173

C₂

—

174

C₂

—

105

—

	subgroup	G/H
center, hypercenter	C₁₇	D₃₅⋊D₁₅
commutator, cosocle, hypocenter	C₃×C₅²×C₇	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₁₇

subgroup

G/H

center, hypercenter

C₁₇

D₃₅⋊D₁₅

commutator, cosocle, hypocenter

C₃×C₅²×C₇

C₂²×C₁₇

Frattini

C₁

Fitting, socle

C₃×C₅²×C₇×C₁₇

C₂²

LCS

G ▷ C₃×C₅²×C₇

UCS

C₁ ◁ C₁₇

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×D₃₅	C₂	semidirect
2. C₅×C₁₇×D₁₀₅	C₂	semidirect
3. C₇×C₁₇×C₃⋊(C₅⋊D₅)	C₂	semidirect
5. C₃×C₅²×C₇×C₁₇	C₂²	semidirect
10. C₅×C₁₇×D₃₅	D₃	semidirect
12. C₁₇×D₁₀₅	D₅	semidirect
17. C₃×C₁₇×D₃₅	D₅	semidirect
19. C₅²×C₇×C₁₇	C₂×D₃	semidirect
20. C₁₇×C₃⋊(C₅⋊D₅)	D₇	semidirect
25. D₃₅⋊D₁₅	C₁₇	direct (N × H)
27. C₃×C₅×C₇×C₁₇	C₂×D₅	semidirect
28. C₃×C₅×C₇×C₁₇	C₂×D₅	semidirect
31. C₃×C₅²×C₁₇	C₂×D₇	semidirect
33. C₁₇×D₃₅	D₁₅	semidirect
39. C₇×C₃⋊(C₅⋊D₅)	C₂×C₁₇	semidirect
40. C₅×D₁₀₅	C₂×C₁₇	semidirect
41. C₃×C₅×D₃₅	C₂×C₁₇	semidirect
52. C₅×C₇×C₁₇	D₃×D₅	semidirect
53. C₅×C₇×C₁₇	C₂×D₁₅	semidirect
54. C₃×C₅²×C₇	C₂²×C₁₇	semidirect
63. C₅²×C₁₇	D₃×D₇	semidirect
66. C₃×C₇×C₁₇	D₅²	semidirect
69. C₅×D₃₅	D₃×C₁₇	semidirect
74. C₃×C₅×C₁₇	D₅×D₇	semidirect
75. C₃×C₅×C₁₇	D₅×D₇	semidirect
79. D₁₀₅	D₅×C₁₇	semidirect
84. C₃×D₃₅	D₅×C₁₇	semidirect
87. C₅²×C₇	C₂×D₃×C₁₇	semidirect
95. C₃⋊(C₅⋊D₅)	D₇×C₁₇	semidirect
100. C₇×C₁₇	D₅×D₁₅	semidirect
102. C₃×C₅×C₇	C₂×D₅×C₁₇	semidirect
103. C₃×C₅×C₇	C₂×D₅×C₁₇	semidirect
109. C₅×C₁₇	D₇×D₁₅	semidirect
110. C₅×C₁₇	D₁₅⋊D₇	semidirect
112. C₃×C₅²	C₂×D₇×C₁₇	semidirect
114. D₃₅	C₁₇×D₁₅	semidirect
123. C₃×C₁₇	(C₅⋊D₅)⋊D₇	semidirect
131. C₅×C₇	D₃×D₅×C₁₇	semidirect
132. C₅×C₇	C₂×C₁₇×D₁₅	semidirect
144. C₅²	D₃×D₇×C₁₇	semidirect
145. C₃×C₇	D₅²×C₁₇	semidirect
148. C₁₇	D₃₅⋊D₁₅	direct (N × H)
150. C₃×C₅	D₅×D₇×C₁₇	semidirect
151. C₃×C₅	D₅×D₇×C₁₇	semidirect
163. C₇	D₅×C₁₇×D₁₅	semidirect
168. C₅	D₇×C₁₇×D₁₅	semidirect
169. C₅	C₁₇×D₁₅⋊D₇	semidirect
171. C₃	C₁₇×(C₅⋊D₅)⋊D₇	semidirect

H ≅ G/N

type

1. C₃×C₅×C₁₇×D₃₅

C₂

semidirect

2. C₅×C₁₇×D₁₀₅

C₂

semidirect

3. C₇×C₁₇×C₃⋊(C₅⋊D₅)

C₂

semidirect

5. C₃×C₅²×C₇×C₁₇

C₂²

semidirect

10. C₅×C₁₇×D₃₅

D₃

semidirect

12. C₁₇×D₁₀₅

D₅

semidirect

17. C₃×C₁₇×D₃₅

D₅

semidirect

19. C₅²×C₇×C₁₇

C₂×D₃

semidirect

20. C₁₇×C₃⋊(C₅⋊D₅)

D₇

semidirect

25. D₃₅⋊D₁₅

C₁₇

direct (N × H)

27. C₃×C₅×C₇×C₁₇

C₂×D₅

semidirect

28. C₃×C₅×C₇×C₁₇

C₂×D₅

semidirect

31. C₃×C₅²×C₁₇

C₂×D₇

semidirect

33. C₁₇×D₃₅

D₁₅

semidirect

39. C₇×C₃⋊(C₅⋊D₅)

C₂×C₁₇

semidirect

40. C₅×D₁₀₅

C₂×C₁₇

semidirect

41. C₃×C₅×D₃₅

C₂×C₁₇

semidirect

52. C₅×C₇×C₁₇

D₃×D₅

semidirect

53. C₅×C₇×C₁₇

C₂×D₁₅

semidirect

54. C₃×C₅²×C₇

C₂²×C₁₇

semidirect

63. C₅²×C₁₇

D₃×D₇

semidirect

66. C₃×C₇×C₁₇

D₅²

semidirect

69. C₅×D₃₅

D₃×C₁₇

semidirect

74. C₃×C₅×C₁₇

D₅×D₇

semidirect

75. C₃×C₅×C₁₇

D₅×D₇

semidirect

79. D₁₀₅

D₅×C₁₇

semidirect

84. C₃×D₃₅

D₅×C₁₇

semidirect

87. C₅²×C₇

C₂×D₃×C₁₇

semidirect

95. C₃⋊(C₅⋊D₅)

D₇×C₁₇

semidirect

100. C₇×C₁₇

D₅×D₁₅

semidirect

102. C₃×C₅×C₇

C₂×D₅×C₁₇

semidirect

103. C₃×C₅×C₇

C₂×D₅×C₁₇

semidirect

109. C₅×C₁₇

D₇×D₁₅

semidirect

110. C₅×C₁₇

D₁₅⋊D₇

semidirect

112. C₃×C₅²

C₂×D₇×C₁₇

semidirect

114. D₃₅

C₁₇×D₁₅

semidirect

123. C₃×C₁₇

(C₅⋊D₅)⋊D₇

semidirect

131. C₅×C₇

D₃×D₅×C₁₇

semidirect

132. C₅×C₇

C₂×C₁₇×D₁₅

semidirect

144. C₅²

D₃×D₇×C₁₇

semidirect

145. C₃×C₇

D₅²×C₁₇

semidirect

148. C₁₇

D₃₅⋊D₁₅

direct (N × H)

150. C₃×C₅

D₅×D₇×C₁₇

semidirect

151. C₃×C₅

D₅×D₇×C₁₇

semidirect

163. C₇

D₅×C₁₇×D₁₅

semidirect

168. C₅

D₇×C₁₇×D₁₅

semidirect

169. C₅

C₁₇×D₁₅⋊D₇

semidirect

171. C₃

C₁₇×(C₅⋊D₅)⋊D₇

semidirect

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

subgroup	index
C₃×C₅×C₁₇×D₃₅	2
C₅×C₁₇×D₁₀₅	2
C₇×C₁₇×C₃⋊(C₅⋊D₅)	2
C₁₇×(C₅⋊D₅)⋊D₇	3
C₁₇×D₁₅⋊D₇	5
D₇×C₁₇×D₁₅	5
D₅×C₁₇×D₁₅	7
D₃₅⋊D₁₅	17

subgroup

index

C₃×C₅×C₁₇×D₃₅

C₅×C₁₇×D₁₀₅

C₇×C₁₇×C₃⋊(C₅⋊D₅)

C₁₇×(C₅⋊D₅)⋊D₇

C₁₇×D₁₅⋊D₇

D₇×C₁₇×D₁₅

D₅×C₁₇×D₁₅

D₃₅⋊D₁₅

Subgroups — C₁₇×D₃₅⋊D₁₅ #49087981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C17×D35⋊D15 #49087981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₃₅⋊D₁₅ #49087981