Group #36339488 — subgroups

Subgroups — C₃×C₁₇×D₁₅⋊D₇ #36339488

Order 21420.

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

normal subgroups only

This group has 176 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	C₃²×C₁₇×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×C₁₇×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₇×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×D₁₅⋊D₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₅×D₇×C₁₇	—	3	1	no	maximal
6	C₃²×C₅×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃×D₇×C₁₇	—	5	1	no	maximal, Hall
8	C₇×C₁₇×D₁₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₇×D₂₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₁₇×D₃₅	—	2	1	no	—
11	C₃×C₁₇×D₃₅	D₃	1	1	yes	characteristic, complemented
12	C₃×C₁₇×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₅×C₁₇	—	3	1	no	—
14	C₃×C₅×D₇×C₁₇	—	3	1	no	—
15	C₃×D₃×D₅×C₁₇	—	7	1	no	maximal, Hall
16	D₅×D₇×C₁₇	—	3	1	no	Hall
17	C₃×C₁₇×D₂₁	D₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₇×C₁₇	—	5	1	no	—
19	C₃²×D₇×C₁₇	—	5	1	no	—
20	C₃×C₅×C₇×C₁₇	—	2	1	no	—
21	C₃×C₅×C₇×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
22	C₃×C₅×C₇×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented
23	C₃×C₁₇×D₁₅	D₇	1	1	yes	characteristic, complemented
24	C₃×C₅×D₃×C₁₇	—	7	1	no	—
25	C₃²×D₅×C₁₇	—	7	1	no	—
26	C₂×C₃×D₇×C₁₇	—	15	1	no	—
27	D₃×D₇×C₁₇	—	5	1	no	—
28	C₃×D₁₅⋊D₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₁₇×D₃₅	C₃×D₃	1	1	yes	characteristic, complemented
30	C₇×D₅×C₁₇	—	3	1	no	—
31	C₅×D₇×C₁₇	—	3	1	no	—
32	C₃²×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₅×C₁₇	—	21	1	no	—
34	D₃×D₅×C₁₇	—	7	1	no	—
35	C₃²×C₅×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₇×C₁₇	—	15	1	no	—
37	C₁₇×D₂₁	C₃×D₅	1	1	yes	characteristic, complemented
38	D₃×C₇×C₁₇	—	5	1	no	—
39	C₃×D₇×C₁₇	—	3	1	no	—
40	C₃×D₇×C₁₇	—	5	1	no	—
41	C₃×D₇×C₁₇	—	5	1	no	—
42	C₃×D₇×C₁₇	—	10	1	no	—
43	C₃×C₇×D₁₅	C₂×C₁₇	1	1	yes	characteristic, complemented
44	C₃×C₅×D₂₁	C₂×C₁₇	1	1	yes	characteristic, complemented
45	C₃²×D₃₅	C₂×C₁₇	1	1	yes	characteristic, complemented
46	C₂×C₃×D₃×C₁₇	—	35	1	no	Hall
47	C₅×C₇×C₁₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₅×C₁₇	—	21	1	no	—
49	C₁₇×D₁₅	C₃×D₇	1	1	yes	characteristic, complemented
50	C₅×D₃×C₁₇	—	7	1	no	—
51	C₃×D₅×C₁₇	—	3	1	no	—
52	C₃×D₅×C₁₇	—	7	1	no	—
53	C₃×D₅×C₁₇	—	7	1	no	—
54	C₃×D₅×C₁₇	—	14	1	no	—
55	C₂×D₇×C₁₇	—	15	1	no	Hall
56	D₁₅⋊D₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor
57	C₃×D₅×D₇	—	3	1	no	—
58	C₃×C₇×C₁₇	—	2	1	no	—
59	C₃×C₇×C₁₇	D₃×D₅	1	1	yes	characteristic, complemented
60	C₃×C₇×C₁₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
61	C₂×D₅×C₁₇	—	21	1	no	Hall
62	C₃²×C₅×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
63	C₂×C₃²×C₁₇	—	35	1	no	—
64	C₃×D₃×C₁₇	—	5	1	no	—
65	C₃×D₃×C₁₇	—	7	1	no	—
66	C₃×C₅×C₁₇	—	2	1	no	—
67	C₃×C₅×C₁₇	D₃×D₇	1	1	yes	characteristic, complemented
68	C₃×C₅×C₁₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
69	C₃×D₃×D₇	—	5	1	no	Hall
70	C₂×C₇×C₁₇	—	15	1	no	—
71	D₇×C₁₇	—	3	1	no	—
72	D₇×C₁₇	—	5	1	no	—
73	C₇×D₁₅	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
74	C₅×D₂₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
75	C₃×D₃₅	—	2	1	no	—
76	C₃×D₃₅	D₃×C₁₇	1	1	yes	characteristic, complemented
77	C₃×D₃₅	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
78	C₃×C₇×D₅	—	3	1	no	—
79	C₃×C₅×D₇	—	3	1	no	—
80	C₂²×C₃×C₁₇	—	105	1	no	—
81	C₂×D₃×C₁₇	—	35	1	no	—
82	C₃×D₃×D₅	—	7	1	no	Hall
83	C₂×C₅×C₁₇	—	21	1	no	—
84	D₅×C₁₇	—	3	1	no	—
85	D₅×C₁₇	—	7	1	no	—
86	C₃²×C₁₇	D₅×D₇	1	1	yes	characteristic, complemented, Hall
87	D₅×D₇	—	3	1	no	Hall
88	C₃×D₂₁	D₅×C₁₇	1	1	yes	characteristic, complemented
89	C₃×D₃×C₇	—	5	1	no	—
90	C₃²×D₇	—	5	1	no	—
91	C₇×C₁₇	C₃×D₃×D₅	1	1	yes	characteristic, complemented, Hall
92	C₃×C₅×C₇	—	2	1	no	—
93	C₃×C₅×C₇	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
94	C₃×C₅×C₇	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented
95	C₂×C₃×C₁₇	—	15	1	no	—
96	C₂×C₃×C₁₇	—	21	1	no	—
97	C₂×C₃×C₁₇	—	35	1	no	—
98	C₂×C₃×C₁₇	—	35	1	no	—
99	C₂×C₃×C₁₇	—	70	1	no	—
100	D₃×C₁₇	—	5	1	no	—
101	D₃×C₁₇	—	7	1	no	—
102	C₃×D₁₅	D₇×C₁₇	1	1	yes	characteristic, complemented
103	C₃×C₅×D₃	—	7	1	no	—
104	C₃²×D₅	—	7	1	no	—
105	C₅×C₁₇	C₃×D₃×D₇	1	1	yes	characteristic, complemented, Hall
106	C₂×C₃×D₇	—	15	1	no	—
107	D₃×D₇	—	5	1	no	—
108	D₃₅	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented
109	C₅×D₇	—	3	1	no	—
110	C₇×D₅	—	3	1	no	—
111	C₂²×C₁₇	—	105	1	no	Hall
112	C₃²×C₇	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
113	C₂×C₃×D₅	—	21	1	no	—
114	D₃×D₅	—	7	1	no	—
115	C₃×C₁₇	—	2	1	no	—
116	C₃×C₁₇	C₃×D₅×D₇	1	1	yes	characteristic, complemented
117	C₃×C₁₇	D₁₅⋊D₇	1	1	yes	characteristic, direct product factor
118	C₃²×C₅	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
119	C₂×C₃×C₇	—	15	1	no	—
120	D₂₁	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented
121	C₃×D₇	—	3	1	no	—
122	C₃×D₇	—	5	1	no	—
123	C₃×D₇	—	5	1	no	—
124	C₃×D₇	—	10	1	no	—
125	D₃×C₇	—	5	1	no	—
126	C₂×C₃×D₃	—	35	1	no	Hall
127	C₅×C₇	C₂×C₃×D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
128	C₂×C₁₇	—	15	1	no	—
129	C₂×C₁₇	—	21	1	no	—
130	C₂×C₁₇	—	35	1	no	—
131	C₂×C₃×C₅	—	21	1	no	—
132	D₁₅	C₃×D₇×C₁₇	1	1	yes	characteristic, complemented
133	C₃×D₅	—	3	1	no	—
134	C₃×D₅	—	7	1	no	—
135	C₃×D₅	—	7	1	no	—
136	C₃×D₅	—	14	1	no	—
137	C₅×D₃	—	7	1	no	—
138	C₂×D₇	—	15	1	no	Hall
139	C₃×C₇	—	2	1	no	—
140	C₃×C₇	D₃×D₅×C₁₇	1	1	yes	characteristic, complemented
141	C₃×C₇	C₂×C₃×D₅×C₁₇	1	1	yes	characteristic, complemented
142	C₂×D₅	—	21	1	no	Hall
143	C₂×C₃²	—	35	1	no	—
144	C₃×D₃	—	5	1	no	—
145	C₃×D₃	—	7	1	no	—
146	C₁₇	C₃×D₁₅⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
147	C₃×C₅	—	2	1	no	—
148	C₃×C₅	D₃×D₇×C₁₇	1	1	yes	characteristic, complemented
149	C₃×C₅	C₂×C₃×D₇×C₁₇	1	1	yes	characteristic, complemented
150	C₂×C₇	—	15	1	no	—
151	D₇	—	3	1	no	—
152	D₇	—	5	1	no	—
153	C₂²×C₃	—	105	1	no	—
154	C₂×D₃	—	35	1	no	—
155	C₂×C₅	—	21	1	no	—
156	D₅	—	3	1	no	—
157	D₅	—	7	1	no	—
158	C₃²	D₅×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
159	C₇	C₃×D₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
160	C₂×C₃	—	15	1	no	—
161	C₂×C₃	—	21	1	no	—
162	C₂×C₃	—	35	1	no	—
163	C₂×C₃	—	35	1	no	—
164	C₂×C₃	—	70	1	no	—
165	D₃	—	5	1	no	—
166	D₃	—	7	1	no	—
167	C₅	C₃×D₃×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
168	C₂²	—	105	1	no	Sylow
169	C₃	—	2	1	no	—
170	C₃	C₃×D₅×D₇×C₁₇	1	1	yes	characteristic, complemented
171	C₃	C₁₇×D₁₅⋊D₇	1	1	yes	characteristic, direct product factor
172	C₂	—	15	1	no	—
173	C₂	—	21	1	no	—
174	C₂	—	35	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₇×D₃₅

C₂

yes

maximal, characteristic, complemented

C₃×C₅×C₁₇×D₂₁

C₂

yes

maximal, characteristic, complemented

C₃×C₇×C₁₇×D₁₅

C₂

yes

maximal, characteristic, complemented

C₁₇×D₁₅⋊D₇

C₃

yes

maximal, characteristic, direct product factor

C₃×D₅×D₇×C₁₇

—

maximal

C₃²×C₅×C₇×C₁₇

C₂²

yes

characteristic, complemented, Hall

C₃×D₃×D₇×C₁₇

—

maximal, Hall

C₇×C₁₇×D₁₅

C₂×C₃

yes

characteristic, complemented

C₅×C₁₇×D₂₁

C₂×C₃

yes

characteristic, complemented

C₃×C₁₇×D₃₅

—

C₃×C₁₇×D₃₅

D₃

yes

characteristic, complemented

C₃×C₁₇×D₃₅

C₂×C₃

yes

characteristic, complemented

C₃×C₇×D₅×C₁₇

—

C₃×C₅×D₇×C₁₇

—

C₃×D₃×D₅×C₁₇

—

maximal, Hall

D₅×D₇×C₁₇

—

Hall

C₃×C₁₇×D₂₁

D₅

yes

characteristic, complemented

C₃×D₃×C₇×C₁₇

—

C₃²×D₇×C₁₇

—

C₃×C₅×C₇×C₁₇

—

C₃×C₅×C₇×C₁₇

C₂×D₃

yes

characteristic, complemented

C₃×C₅×C₇×C₁₇

C₂²×C₃

yes

characteristic, complemented

C₃×C₁₇×D₁₅

D₇

yes

characteristic, complemented

C₃×C₅×D₃×C₁₇

—

C₃²×D₅×C₁₇

—

C₂×C₃×D₇×C₁₇

—

D₃×D₇×C₁₇

—

C₃×D₁₅⋊D₇

C₁₇

yes

maximal, characteristic, direct product factor, Hall

C₁₇×D₃₅

C₃×D₃

yes

characteristic, complemented

C₇×D₅×C₁₇

—

C₅×D₇×C₁₇

—

C₃²×C₇×C₁₇

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₃×D₅×C₁₇

—

D₃×D₅×C₁₇

—

C₃²×C₅×C₁₇

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₇

—

C₁₇×D₂₁

C₃×D₅

yes

characteristic, complemented

D₃×C₇×C₁₇

—

C₃×D₇×C₁₇

—

C₃×D₇×C₁₇

—

C₃×D₇×C₁₇

—

C₃×D₇×C₁₇

—

C₃×C₇×D₁₅

C₂×C₁₇

yes

characteristic, complemented

C₃×C₅×D₂₁

C₂×C₁₇

yes

characteristic, complemented

C₃²×D₃₅

C₂×C₁₇

yes

characteristic, complemented

C₂×C₃×D₃×C₁₇

—

Hall

C₅×C₇×C₁₇

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₁₇

—

C₁₇×D₁₅

C₃×D₇

yes

characteristic, complemented

C₅×D₃×C₁₇

—

C₃×D₅×C₁₇

—

C₃×D₅×C₁₇

—

C₃×D₅×C₁₇

—

C₃×D₅×C₁₇

—

C₂×D₇×C₁₇

—

Hall

D₁₅⋊D₇

C₃×C₁₇

yes

characteristic, direct product factor

C₃×D₅×D₇

—

C₃×C₇×C₁₇

—

C₃×C₇×C₁₇

D₃×D₅

yes

characteristic, complemented

C₃×C₇×C₁₇

C₂×C₃×D₅

yes

characteristic, complemented

C₂×D₅×C₁₇

—

Hall

C₃²×C₅×C₇

C₂²×C₁₇

yes

characteristic, complemented, Hall

C₂×C₃²×C₁₇

—

C₃×D₃×C₁₇

—

C₃×D₃×C₁₇

—

C₃×C₅×C₁₇

—

C₃×C₅×C₁₇

D₃×D₇

yes

characteristic, complemented

C₃×C₅×C₁₇

C₂×C₃×D₇

yes

characteristic, complemented

C₃×D₃×D₇

—

Hall

C₂×C₇×C₁₇

—

D₇×C₁₇

—

D₇×C₁₇

—

C₇×D₁₅

C₂×C₃×C₁₇

yes

characteristic, complemented

C₅×D₂₁

C₂×C₃×C₁₇

yes

characteristic, complemented

C₃×D₃₅

—

C₃×D₃₅

D₃×C₁₇

yes

characteristic, complemented

C₃×D₃₅

C₂×C₃×C₁₇

yes

characteristic, complemented

C₃×C₇×D₅

—

C₃×C₅×D₇

—

C₂²×C₃×C₁₇

—

105

—

C₂×D₃×C₁₇

—

C₃×D₃×D₅

—

Hall

C₂×C₅×C₁₇

—

D₅×C₁₇

—

D₅×C₁₇

—

C₃²×C₁₇

D₅×D₇

yes

characteristic, complemented, Hall

D₅×D₇

—

Hall

C₃×D₂₁

D₅×C₁₇

yes

characteristic, complemented

C₃×D₃×C₇

—

C₃²×D₇

—

C₇×C₁₇

C₃×D₃×D₅

yes

characteristic, complemented, Hall

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×D₃×C₁₇

yes

characteristic, complemented

C₃×C₅×C₇

C₂²×C₃×C₁₇

yes

characteristic, complemented

C₂×C₃×C₁₇

—

C₂×C₃×C₁₇

—

C₂×C₃×C₁₇

—

C₂×C₃×C₁₇

—

C₂×C₃×C₁₇

—

100

D₃×C₁₇

—

101

D₃×C₁₇

—

102

C₃×D₁₅

D₇×C₁₇

yes

characteristic, complemented

103

C₃×C₅×D₃

—

104

C₃²×D₅

—

105

C₅×C₁₇

C₃×D₃×D₇

yes

characteristic, complemented, Hall

106

C₂×C₃×D₇

—

107

D₃×D₇

—

108

D₃₅

C₃×D₃×C₁₇

yes

characteristic, complemented

109

C₅×D₇

—

110

C₇×D₅

—

111

C₂²×C₁₇

—

105

Hall

112

C₃²×C₇

C₂×D₅×C₁₇

yes

characteristic, complemented, Hall

113

C₂×C₃×D₅

—

114

D₃×D₅

—

115

C₃×C₁₇

—

116

C₃×C₁₇

C₃×D₅×D₇

yes

characteristic, complemented

117

C₃×C₁₇

D₁₅⋊D₇

yes

characteristic, direct product factor

118

C₃²×C₅

C₂×D₇×C₁₇

yes

characteristic, complemented, Hall

119

C₂×C₃×C₇

—

120

D₂₁

C₃×D₅×C₁₇

yes

characteristic, complemented

121

C₃×D₇

—

122

C₃×D₇

—

123

C₃×D₇

—

124

C₃×D₇

—

125

D₃×C₇

—

126

C₂×C₃×D₃

—

Hall

127

C₅×C₇

C₂×C₃×D₃×C₁₇

yes

characteristic, complemented, Hall

128

C₂×C₁₇

—

129

C₂×C₁₇

—

130

C₂×C₁₇

—

131

C₂×C₃×C₅

—

132

D₁₅

C₃×D₇×C₁₇

yes

characteristic, complemented

133

C₃×D₅

—

134

C₃×D₅

—

135

C₃×D₅

—

136

C₃×D₅

—

137

C₅×D₃

—

138

C₂×D₇

—

Hall

139

C₃×C₇

—

140

C₃×C₇

D₃×D₅×C₁₇

yes

characteristic, complemented

141

C₃×C₇

C₂×C₃×D₅×C₁₇

yes

characteristic, complemented

142

C₂×D₅

—

Hall

143

C₂×C₃²

—

144

C₃×D₃

—

145

C₃×D₃

—

146

C₁₇

C₃×D₁₅⋊D₇

yes

characteristic, direct product factor, Sylow

147

C₃×C₅

—

148

C₃×C₅

D₃×D₇×C₁₇

yes

characteristic, complemented

149

C₃×C₅

C₂×C₃×D₇×C₁₇

yes

characteristic, complemented

150

C₂×C₇

—

151

D₇

—

152

D₇

—

153

C₂²×C₃

—

105

—

154

C₂×D₃

—

155

C₂×C₅

—

156

D₅

—

157

D₅

—

158

C₃²

D₅×D₇×C₁₇

yes

characteristic, complemented, Sylow

159

C₇

C₃×D₃×D₅×C₁₇

yes

characteristic, complemented, Sylow

160

C₂×C₃

—

161

C₂×C₃

—

162

C₂×C₃

—

163

C₂×C₃

—

164

C₂×C₃

—

165

D₃

—

166

D₃

—

167

C₅

C₃×D₃×D₇×C₁₇

yes

characteristic, complemented, Sylow

168

C₂²

—

105

Sylow

169

C₃

—

170

C₃

C₃×D₅×D₇×C₁₇

yes

characteristic, complemented

171

C₃

C₁₇×D₁₅⋊D₇

yes

characteristic, direct product factor

172

C₂

—

173

C₂

—

174

C₂

—

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₁₅⋊D₇
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₃×C₁₇

subgroup

G/H

center, hypercenter

C₃×C₁₇

D₁₅⋊D₇

commutator, cosocle, hypocenter

C₃×C₅×C₇

C₂²×C₃×C₁₇

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₁₇

C₂²

LCS

G ▷ C₃×C₅×C₇

UCS

C₁ ◁ C₃×C₁₇

N	H ≅ G/N	type
1. C₃²×C₁₇×D₃₅	C₂	semidirect
2. C₃×C₅×C₁₇×D₂₁	C₂	semidirect
3. C₃×C₇×C₁₇×D₁₅	C₂	semidirect
4. C₁₇×D₁₅⋊D₇	C₃	direct (N × H)
6. C₃²×C₅×C₇×C₁₇	C₂²	semidirect
8. C₇×C₁₇×D₁₅	C₂×C₃	semidirect
9. C₅×C₁₇×D₂₁	C₂×C₃	semidirect
11. C₃×C₁₇×D₃₅	D₃	semidirect
12. C₃×C₁₇×D₃₅	C₂×C₃	semidirect
17. C₃×C₁₇×D₂₁	D₅	semidirect
21. C₃×C₅×C₇×C₁₇	C₂×D₃	semidirect
22. C₃×C₅×C₇×C₁₇	C₂²×C₃	semidirect
23. C₃×C₁₇×D₁₅	D₇	semidirect
28. C₃×D₁₅⋊D₇	C₁₇	direct (N × H)
29. C₁₇×D₃₅	C₃×D₃	semidirect
32. C₃²×C₇×C₁₇	C₂×D₅	semidirect
35. C₃²×C₅×C₁₇	C₂×D₇	semidirect
37. C₁₇×D₂₁	C₃×D₅	semidirect
43. C₃×C₇×D₁₅	C₂×C₁₇	semidirect
44. C₃×C₅×D₂₁	C₂×C₁₇	semidirect
45. C₃²×D₃₅	C₂×C₁₇	semidirect
47. C₅×C₇×C₁₇	C₂×C₃×D₃	semidirect
49. C₁₇×D₁₅	C₃×D₇	semidirect
56. D₁₅⋊D₇	C₃×C₁₇	direct (N × H)
59. C₃×C₇×C₁₇	D₃×D₅	semidirect
60. C₃×C₇×C₁₇	C₂×C₃×D₅	semidirect
62. C₃²×C₅×C₇	C₂²×C₁₇	semidirect
67. C₃×C₅×C₁₇	D₃×D₇	semidirect
68. C₃×C₅×C₁₇	C₂×C₃×D₇	semidirect
73. C₇×D₁₅	C₂×C₃×C₁₇	semidirect
74. C₅×D₂₁	C₂×C₃×C₁₇	semidirect
76. C₃×D₃₅	D₃×C₁₇	semidirect
77. C₃×D₃₅	C₂×C₃×C₁₇	semidirect
86. C₃²×C₁₇	D₅×D₇	semidirect
88. C₃×D₂₁	D₅×C₁₇	semidirect
91. C₇×C₁₇	C₃×D₃×D₅	semidirect
93. C₃×C₅×C₇	C₂×D₃×C₁₇	semidirect
94. C₃×C₅×C₇	C₂²×C₃×C₁₇	semidirect
102. C₃×D₁₅	D₇×C₁₇	semidirect
105. C₅×C₁₇	C₃×D₃×D₇	semidirect
108. D₃₅	C₃×D₃×C₁₇	semidirect
112. C₃²×C₇	C₂×D₅×C₁₇	semidirect
116. C₃×C₁₇	C₃×D₅×D₇	semidirect
117. C₃×C₁₇	D₁₅⋊D₇	direct (N × H)
118. C₃²×C₅	C₂×D₇×C₁₇	semidirect
120. D₂₁	C₃×D₅×C₁₇	semidirect
127. C₅×C₇	C₂×C₃×D₃×C₁₇	semidirect
132. D₁₅	C₃×D₇×C₁₇	semidirect
140. C₃×C₇	D₃×D₅×C₁₇	semidirect
141. C₃×C₇	C₂×C₃×D₅×C₁₇	semidirect
146. C₁₇	C₃×D₁₅⋊D₇	direct (N × H)
148. C₃×C₅	D₃×D₇×C₁₇	semidirect
149. C₃×C₅	C₂×C₃×D₇×C₁₇	semidirect
158. C₃²	D₅×D₇×C₁₇	semidirect
159. C₇	C₃×D₃×D₅×C₁₇	semidirect
167. C₅	C₃×D₃×D₇×C₁₇	semidirect
170. C₃	C₃×D₅×D₇×C₁₇	semidirect
171. C₃	C₁₇×D₁₅⋊D₇	direct (N × H)

H ≅ G/N

type

1. C₃²×C₁₇×D₃₅

C₂

semidirect

2. C₃×C₅×C₁₇×D₂₁

C₂

semidirect

3. C₃×C₇×C₁₇×D₁₅

C₂

semidirect

4. C₁₇×D₁₅⋊D₇

C₃

direct (N × H)

6. C₃²×C₅×C₇×C₁₇

C₂²

semidirect

8. C₇×C₁₇×D₁₅

C₂×C₃

semidirect

9. C₅×C₁₇×D₂₁

C₂×C₃

semidirect

11. C₃×C₁₇×D₃₅

D₃

semidirect

12. C₃×C₁₇×D₃₅

C₂×C₃

semidirect

17. C₃×C₁₇×D₂₁

D₅

semidirect

21. C₃×C₅×C₇×C₁₇

C₂×D₃

semidirect

22. C₃×C₅×C₇×C₁₇

C₂²×C₃

semidirect

23. C₃×C₁₇×D₁₅

D₇

semidirect

28. C₃×D₁₅⋊D₇

C₁₇

direct (N × H)

29. C₁₇×D₃₅

C₃×D₃

semidirect

32. C₃²×C₇×C₁₇

C₂×D₅

semidirect

35. C₃²×C₅×C₁₇

C₂×D₇

semidirect

37. C₁₇×D₂₁

C₃×D₅

semidirect

43. C₃×C₇×D₁₅

C₂×C₁₇

semidirect

44. C₃×C₅×D₂₁

C₂×C₁₇

semidirect

45. C₃²×D₃₅

C₂×C₁₇

semidirect

47. C₅×C₇×C₁₇

C₂×C₃×D₃

semidirect

49. C₁₇×D₁₅

C₃×D₇

semidirect

56. D₁₅⋊D₇

C₃×C₁₇

direct (N × H)

59. C₃×C₇×C₁₇

D₃×D₅

semidirect

60. C₃×C₇×C₁₇

C₂×C₃×D₅

semidirect

62. C₃²×C₅×C₇

C₂²×C₁₇

semidirect

67. C₃×C₅×C₁₇

D₃×D₇

semidirect

68. C₃×C₅×C₁₇

C₂×C₃×D₇

semidirect

73. C₇×D₁₅

C₂×C₃×C₁₇

semidirect

74. C₅×D₂₁

C₂×C₃×C₁₇

semidirect

76. C₃×D₃₅

D₃×C₁₇

semidirect

77. C₃×D₃₅

C₂×C₃×C₁₇

semidirect

86. C₃²×C₁₇

D₅×D₇

semidirect

88. C₃×D₂₁

D₅×C₁₇

semidirect

91. C₇×C₁₇

C₃×D₃×D₅

semidirect

93. C₃×C₅×C₇

C₂×D₃×C₁₇

semidirect

94. C₃×C₅×C₇

C₂²×C₃×C₁₇

semidirect

102. C₃×D₁₅

D₇×C₁₇

semidirect

105. C₅×C₁₇

C₃×D₃×D₇

semidirect

108. D₃₅

C₃×D₃×C₁₇

semidirect

112. C₃²×C₇

C₂×D₅×C₁₇

semidirect

116. C₃×C₁₇

C₃×D₅×D₇

semidirect

117. C₃×C₁₇

D₁₅⋊D₇

direct (N × H)

118. C₃²×C₅

C₂×D₇×C₁₇

semidirect

120. D₂₁

C₃×D₅×C₁₇

semidirect

127. C₅×C₇

C₂×C₃×D₃×C₁₇

semidirect

132. D₁₅

C₃×D₇×C₁₇

semidirect

140. C₃×C₇

D₃×D₅×C₁₇

semidirect

141. C₃×C₇

C₂×C₃×D₅×C₁₇

semidirect

146. C₁₇

C₃×D₁₅⋊D₇

direct (N × H)

148. C₃×C₅

D₃×D₇×C₁₇

semidirect

149. C₃×C₅

C₂×C₃×D₇×C₁₇

semidirect

158. C₃²

D₅×D₇×C₁₇

semidirect

159. C₇

C₃×D₃×D₅×C₁₇

semidirect

167. C₅

C₃×D₃×D₇×C₁₇

semidirect

170. C₃

C₃×D₅×D₇×C₁₇

semidirect

171. C₃

C₁₇×D₁₅⋊D₇

direct (N × H)

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

subgroup	index
C₃²×C₁₇×D₃₅	2
C₃×C₅×C₁₇×D₂₁	2
C₃×C₇×C₁₇×D₁₅	2
C₁₇×D₁₅⋊D₇	3
C₃×D₅×D₇×C₁₇	3
C₃×D₃×D₇×C₁₇	5
C₃×D₃×D₅×C₁₇	7
C₃×D₁₅⋊D₇	17

subgroup

index

C₃²×C₁₇×D₃₅

C₃×C₅×C₁₇×D₂₁

C₃×C₇×C₁₇×D₁₅

C₁₇×D₁₅⋊D₇

C₃×D₅×D₇×C₁₇

C₃×D₃×D₇×C₁₇

C₃×D₃×D₅×C₁₇

C₃×D₁₅⋊D₇

Subgroups — C₃×C₁₇×D₁₅⋊D₇ #36339488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×C17×D15⋊D7 #36339488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₁₅⋊D₇ #36339488