Group #49088045 — subgroups

Subgroups — C₂×C₃×C₅×C₁₇×D₃₅ #49088045

Order 35700.

192 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 88 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	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₇×D₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₅×D₇×C₁₇	—	5	1	no	maximal
6	C₂×C₃×C₁₇×D₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×C₁₇×D₃₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₅²×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅×D₅×C₁₇	—	7	1	no	maximal, Hall
10	C₃×C₁₇×D₃₅	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅×D₇×C₁₇	—	5	2	no	—
12	C₂×C₃×C₅×C₇×C₁₇	—	2	2	no	—
13	C₂×C₃×C₅×C₇×C₁₇	D₅	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
15	C₅²×C₇×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×D₅×C₁₇	—	7	2	no	—
17	C₂×C₃×C₅²×C₁₇	D₇	1	1	yes	characteristic, complemented
18	C₂×C₅×D₇×C₁₇	—	5	1	no	—
19	C₂×C₁₇×D₃₅	C₃×C₅	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₅×D₃₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃×C₅×C₇×C₁₇	—	2	2	no	—
22	C₃×C₅×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₇×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented
24	C₂×C₅×D₅×C₁₇	—	7	1	no	Hall
25	C₂×C₃×D₇×C₁₇	—	5	1	no	Hall
26	C₃×C₅²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₇×C₁₇	—	2	2	no	—
28	C₂×C₅×C₇×C₁₇	C₃×D₅	1	1	yes	characteristic, complemented
29	C₂×C₅×C₇×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
30	C₁₇×D₃₅	C₂×C₃×C₅	1	2	yes	direct product factor
31	C₅×D₇×C₁₇	—	5	2	no	—
32	C₂×C₃×C₅²×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented
33	C₃×C₅×D₃₅	C₂×C₁₇	1	2	yes	direct product factor
34	C₂²×C₃×C₅×C₁₇	—	35	1	no	—
35	C₂×C₃×D₅×C₁₇	—	7	1	no	—
36	C₂×C₅²×C₁₇	C₃×D₇	1	1	yes	characteristic, complemented
37	C₅×D₅×C₁₇	—	7	2	no	—
38	C₂×C₃×C₇×C₁₇	C₅×D₅	1	1	yes	characteristic, complemented
39	C₃×D₇×C₁₇	—	5	2	no	—
40	C₂×C₅×D₃₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
41	C₅×C₇×C₁₇	—	2	2	no	—
42	C₅×C₇×C₁₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
43	C₅×C₇×C₁₇	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
44	C₃×C₅²×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅×C₁₇	—	2	2	no	—
46	C₂×C₃×C₅×C₁₇	—	35	2	no	—
47	C₂×C₃×C₅×C₁₇	C₅×D₇	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅×C₁₇	D₃₅	1	1	yes	characteristic, direct product factor
49	C₃×D₅×C₁₇	—	7	2	no	—
50	C₂×D₇×C₁₇	—	5	1	no	Hall
51	C₅²×C₁₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
52	C₂×C₃×D₃₅	C₅×C₁₇	1	1	yes	characteristic, direct product factor
53	C₂×C₃×C₅×D₇	—	5	1	no	—
54	C₃×C₇×C₁₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₅²×C₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
56	C₅×D₃₅	C₂×C₃×C₁₇	1	2	yes	direct product factor
57	C₂²×C₅×C₁₇	—	35	1	no	—
58	C₂×D₅×C₁₇	—	7	1	no	—
59	C₂×C₃×C₅×D₅	—	7	1	no	Hall
60	C₃×C₅×C₁₇	—	2	2	no	—
61	C₃×C₅×C₁₇	C₂×C₅×D₇	1	1	yes	characteristic, complemented
62	C₃×C₅×C₁₇	C₂×D₃₅	1	1	yes	characteristic, direct product factor
63	C₂×C₇×C₁₇	C₃×C₅×D₅	1	1	yes	characteristic, complemented
64	D₇×C₁₇	—	5	2	no	—
65	C₂×C₃×C₅×C₇	—	2	2	no	—
66	C₂×C₃×C₅×C₇	D₅×C₁₇	1	1	yes	characteristic, complemented
67	C₂×C₃×C₅×C₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
68	C₃×D₃₅	C₂×C₅×C₁₇	1	2	yes	direct product factor
69	C₃×C₅×D₇	—	5	2	no	—
70	C₂²×C₃×C₁₇	—	35	1	no	Hall
71	C₅²×C₇	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
72	C₂×C₅×C₁₇	—	2	2	no	—
73	C₂×C₅×C₁₇	—	35	2	no	—
74	C₂×C₅×C₁₇	C₃×C₅×D₇	1	1	yes	characteristic, complemented
75	C₂×C₅×C₁₇	C₃×D₃₅	1	1	yes	characteristic, direct product factor
76	D₅×C₁₇	—	7	2	no	—
77	C₂×C₃×C₅²	D₇×C₁₇	1	1	yes	characteristic, complemented
78	C₃×C₅×D₅	—	7	2	no	—
79	C₂×D₃₅	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor
80	C₂×C₅×D₇	—	5	1	no	—
81	C₇×C₁₇	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
82	C₃×C₅×C₇	—	2	2	no	—
83	C₃×C₅×C₇	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented
84	C₃×C₅×C₇	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented
85	C₂×C₃×C₁₇	—	35	2	no	—
86	C₂×C₃×C₁₇	C₅×D₃₅	1	1	yes	characteristic, direct product factor
87	C₂×C₅×D₅	—	7	1	no	Hall
88	C₅×C₁₇	—	2	2	no	—
89	C₅×C₁₇	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented
90	C₅×C₁₇	C₂×C₃×D₃₅	1	1	yes	characteristic, direct product factor
91	C₂×C₃×D₇	—	5	1	no	Hall
92	C₃×C₅²	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
93	C₂×C₅×C₇	—	2	2	no	—
94	C₂×C₅×C₇	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented
95	C₂×C₅×C₇	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
96	D₃₅	C₂×C₃×C₅×C₁₇	1	2	yes	direct product factor
97	C₅×D₇	—	5	2	no	—
98	C₂²×C₁₇	—	35	1	no	Hall
99	C₂²×C₃×C₅	—	35	1	no	—
100	C₂×C₃×D₅	—	7	1	no	—
101	C₃×C₁₇	C₂×C₅×D₃₅	1	1	yes	characteristic, direct product factor, Hall
102	C₂×C₅²	C₃×D₇×C₁₇	1	1	yes	characteristic, complemented
103	C₅×D₅	—	7	2	no	—
104	C₂×C₃×C₇	C₅×D₅×C₁₇	1	1	yes	characteristic, complemented
105	C₃×D₇	—	5	2	no	—
106	C₅×C₇	—	2	2	no	—
107	C₅×C₇	C₂×C₃×D₅×C₁₇	1	1	yes	characteristic, complemented
108	C₅×C₇	C₂²×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
109	C₂×C₁₇	—	35	2	no	—
110	C₂×C₁₇	C₃×C₅×D₃₅	1	1	yes	characteristic, direct product factor
111	C₂×C₃×C₅	—	2	2	no	—
112	C₂×C₃×C₅	—	35	2	no	—
113	C₂×C₃×C₅	C₅×D₇×C₁₇	1	1	yes	characteristic, complemented
114	C₂×C₃×C₅	C₁₇×D₃₅	1	1	yes	characteristic, direct product factor
115	C₃×D₅	—	7	2	no	—
116	C₂×D₇	—	5	1	no	Hall
117	C₅²	C₂×C₃×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
118	C₃×C₇	C₂×C₅×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
119	C₂²×C₅	—	35	1	no	—
120	C₂×D₅	—	7	1	no	—
121	C₁₇	C₂×C₃×C₅×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
122	C₃×C₅	—	2	2	no	—
123	C₃×C₅	C₂×C₁₇×D₃₅	1	1	yes	characteristic, direct product factor
124	C₃×C₅	C₂×C₅×D₇×C₁₇	1	1	yes	characteristic, complemented
125	C₂×C₇	C₃×C₅×D₅×C₁₇	1	1	yes	characteristic, complemented
126	D₇	—	5	2	no	—
127	C₂²×C₃	—	35	1	no	Hall
128	C₂×C₅	—	2	2	no	—
129	C₂×C₅	—	35	2	no	—
130	C₂×C₅	C₃×C₅×D₇×C₁₇	1	1	yes	characteristic, complemented
131	C₂×C₅	C₃×C₁₇×D₃₅	1	1	yes	characteristic, direct product factor
132	D₅	—	7	2	no	—
133	C₇	C₂×C₃×C₅×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
134	C₂×C₃	—	35	2	no	—
135	C₂×C₃	C₅×C₁₇×D₃₅	1	1	yes	characteristic, direct product factor
136	C₅	—	2	2	no	—
137	C₅	C₂×C₃×C₁₇×D₃₅	1	1	yes	characteristic, direct product factor
138	C₅	C₂×C₃×C₅×D₇×C₁₇	1	1	yes	characteristic, complemented
139	C₂²	—	35	1	no	Sylow
140	C₃	C₂×C₅×C₁₇×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
141	C₂	—	35	2	no	—
142	C₂	C₃×C₅×C₁₇×D₃₅	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₁₇×D₃₅

C₂

yes

maximal, direct product factor

C₂×C₃×C₅²×C₇×C₁₇

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₁₇×D₃₅

C₃

yes

maximal, characteristic, direct product factor, Hall

C₃×C₅²×C₇×C₁₇

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×D₇×C₁₇

—

maximal

C₂×C₃×C₁₇×D₃₅

C₅

yes

maximal, characteristic, direct product factor

C₅×C₁₇×D₃₅

C₂×C₃

yes

direct product factor

C₂×C₅²×C₇×C₁₇

C₂×C₃

yes

characteristic, complemented

C₂×C₃×C₅×D₅×C₁₇

—

maximal, Hall

C₃×C₁₇×D₃₅

C₂×C₅

yes

direct product factor

C₃×C₅×D₇×C₁₇

—

C₂×C₃×C₅×C₇×C₁₇

—

C₂×C₃×C₅×C₇×C₁₇

D₅

yes

characteristic, complemented

C₂×C₃×C₅×C₇×C₁₇

C₂×C₅

yes

characteristic, complemented

C₅²×C₇×C₁₇

C₂²×C₃

yes

characteristic, complemented, Hall

C₃×C₅×D₅×C₁₇

—

C₂×C₃×C₅²×C₁₇

D₇

yes

characteristic, complemented

C₂×C₅×D₇×C₁₇

—

C₂×C₁₇×D₃₅

C₃×C₅

yes

characteristic, direct product factor

C₂×C₃×C₅×D₃₅

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

C₂²×C₅

yes

characteristic, complemented

C₂×C₅×D₅×C₁₇

—

Hall

C₂×C₃×D₇×C₁₇

—

Hall

C₃×C₅²×C₁₇

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₅×C₇×C₁₇

—

C₂×C₅×C₇×C₁₇

C₃×D₅

yes

characteristic, complemented

C₂×C₅×C₇×C₁₇

C₂×C₃×C₅

yes

characteristic, complemented

C₁₇×D₃₅

C₂×C₃×C₅

yes

direct product factor

C₅×D₇×C₁₇

—

C₂×C₃×C₅²×C₇

C₂×C₁₇

yes

characteristic, complemented

C₃×C₅×D₃₅

C₂×C₁₇

yes

direct product factor

C₂²×C₃×C₅×C₁₇

—

C₂×C₃×D₅×C₁₇

—

C₂×C₅²×C₁₇

C₃×D₇

yes

characteristic, complemented

C₅×D₅×C₁₇

—

C₂×C₃×C₇×C₁₇

C₅×D₅

yes

characteristic, complemented

C₃×D₇×C₁₇

—

C₂×C₅×D₃₅

C₃×C₁₇

yes

characteristic, direct product factor, Hall

C₅×C₇×C₁₇

—

C₅×C₇×C₁₇

C₂×C₃×D₅

yes

characteristic, complemented

C₅×C₇×C₁₇

C₂²×C₃×C₅

yes

characteristic, complemented

C₃×C₅²×C₇

C₂²×C₁₇

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₁₇

—

C₂×C₃×C₅×C₁₇

—

C₂×C₃×C₅×C₁₇

C₅×D₇

yes

characteristic, complemented

C₂×C₃×C₅×C₁₇

D₃₅

yes

characteristic, direct product factor

C₃×D₅×C₁₇

—

C₂×D₇×C₁₇

—

Hall

C₅²×C₁₇

C₂×C₃×D₇

yes

characteristic, complemented, Hall

C₂×C₃×D₃₅

C₅×C₁₇

yes

characteristic, direct product factor

C₂×C₃×C₅×D₇

—

C₃×C₇×C₁₇

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₅²×C₇

C₂×C₃×C₁₇

yes

characteristic, complemented

C₅×D₃₅

C₂×C₃×C₁₇

yes

direct product factor

C₂²×C₅×C₁₇

—

C₂×D₅×C₁₇

—

C₂×C₃×C₅×D₅

—

Hall

C₃×C₅×C₁₇

—

C₃×C₅×C₁₇

C₂×C₅×D₇

yes

characteristic, complemented

C₃×C₅×C₁₇

C₂×D₃₅

yes

characteristic, direct product factor

C₂×C₇×C₁₇

C₃×C₅×D₅

yes

characteristic, complemented

D₇×C₁₇

—

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

D₅×C₁₇

yes

characteristic, complemented

C₂×C₃×C₅×C₇

C₂×C₅×C₁₇

yes

characteristic, complemented

C₃×D₃₅

C₂×C₅×C₁₇

yes

direct product factor

C₃×C₅×D₇

—

C₂²×C₃×C₁₇

—

Hall

C₅²×C₇

C₂²×C₃×C₁₇

yes

characteristic, complemented, Hall

C₂×C₅×C₁₇

—

C₂×C₅×C₁₇

—

C₂×C₅×C₁₇

C₃×C₅×D₇

yes

characteristic, complemented

C₂×C₅×C₁₇

C₃×D₃₅

yes

characteristic, direct product factor

D₅×C₁₇

—

C₂×C₃×C₅²

D₇×C₁₇

yes

characteristic, complemented

C₃×C₅×D₅

—

C₂×D₃₅

C₃×C₅×C₁₇

yes

characteristic, direct product factor

C₂×C₅×D₇

—

C₇×C₁₇

C₂×C₃×C₅×D₅

yes

characteristic, complemented, Hall

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×D₅×C₁₇

yes

characteristic, complemented

C₃×C₅×C₇

C₂²×C₅×C₁₇

yes

characteristic, complemented

C₂×C₃×C₁₇

—

C₂×C₃×C₁₇

C₅×D₃₅

yes

characteristic, direct product factor

C₂×C₅×D₅

—

Hall

C₅×C₁₇

—

C₅×C₁₇

C₂×C₃×C₅×D₇

yes

characteristic, complemented

C₅×C₁₇

C₂×C₃×D₃₅

yes

characteristic, direct product factor

C₂×C₃×D₇

—

Hall

C₃×C₅²

C₂×D₇×C₁₇

yes

characteristic, complemented, Hall

C₂×C₅×C₇

—

C₂×C₅×C₇

C₃×D₅×C₁₇

yes

characteristic, complemented

C₂×C₅×C₇

C₂×C₃×C₅×C₁₇

yes

characteristic, complemented

D₃₅

C₂×C₃×C₅×C₁₇

yes

direct product factor

C₅×D₇

—

C₂²×C₁₇

—

Hall

C₂²×C₃×C₅

—

100

C₂×C₃×D₅

—

101

C₃×C₁₇

C₂×C₅×D₃₅

yes

characteristic, direct product factor, Hall

102

C₂×C₅²

C₃×D₇×C₁₇

yes

characteristic, complemented

103

C₅×D₅

—

104

C₂×C₃×C₇

C₅×D₅×C₁₇

yes

characteristic, complemented

105

C₃×D₇

—

106

C₅×C₇

—

107

C₅×C₇

C₂×C₃×D₅×C₁₇

yes

characteristic, complemented

108

C₅×C₇

C₂²×C₃×C₅×C₁₇

yes

characteristic, complemented

109

C₂×C₁₇

—

110

C₂×C₁₇

C₃×C₅×D₃₅

yes

characteristic, direct product factor

111

C₂×C₃×C₅

—

112

C₂×C₃×C₅

—

113

C₂×C₃×C₅

C₅×D₇×C₁₇

yes

characteristic, complemented

114

C₂×C₃×C₅

C₁₇×D₃₅

yes

characteristic, direct product factor

115

C₃×D₅

—

116

C₂×D₇

—

Hall

117

C₅²

C₂×C₃×D₇×C₁₇

yes

characteristic, complemented, Sylow

118

C₃×C₇

C₂×C₅×D₅×C₁₇

yes

characteristic, complemented, Hall

119

C₂²×C₅

—

120

C₂×D₅

—

121

C₁₇

C₂×C₃×C₅×D₃₅

yes

characteristic, direct product factor, Sylow

122

C₃×C₅

—

123

C₃×C₅

C₂×C₁₇×D₃₅

yes

characteristic, direct product factor

124

C₃×C₅

C₂×C₅×D₇×C₁₇

yes

characteristic, complemented

125

C₂×C₇

C₃×C₅×D₅×C₁₇

yes

characteristic, complemented

126

D₇

—

127

C₂²×C₃

—

Hall

128

C₂×C₅

—

129

C₂×C₅

—

130

C₂×C₅

C₃×C₅×D₇×C₁₇

yes

characteristic, complemented

131

C₂×C₅

C₃×C₁₇×D₃₅

yes

characteristic, direct product factor

132

D₅

—

133

C₇

C₂×C₃×C₅×D₅×C₁₇

yes

characteristic, complemented, Sylow

134

C₂×C₃

—

135

C₂×C₃

C₅×C₁₇×D₃₅

yes

characteristic, direct product factor

136

C₅

—

137

C₅

C₂×C₃×C₁₇×D₃₅

yes

characteristic, direct product factor

138

C₅

C₂×C₃×C₅×D₇×C₁₇

yes

characteristic, complemented

139

C₂²

—

Sylow

140

C₃

C₂×C₅×C₁₇×D₃₅

yes

characteristic, direct product factor, Sylow

141

C₂

—

142

C₂

C₃×C₅×C₁₇×D₃₅

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₇	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₇×C₁₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₃×C₅×C₁₇

subgroup

G/H

center, hypercenter

C₂×C₃×C₅×C₁₇

D₃₅

commutator, cosocle, hypocenter

C₅×C₇

C₂²×C₃×C₅×C₁₇

Frattini

C₁

Fitting, socle

C₂×C₃×C₅²×C₇×C₁₇

C₂

LCS

G ▷ C₅×C₇

UCS

C₁ ◁ C₂×C₃×C₅×C₁₇

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×D₃₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₇×C₁₇	C₂	semidirect
3. C₂×C₅×C₁₇×D₃₅	C₃	direct (N × H)
4. C₃×C₅²×C₇×C₁₇	C₂²	semidirect
6. C₂×C₃×C₁₇×D₃₅	C₅	direct (N × H)
7. C₅×C₁₇×D₃₅	C₂×C₃	direct (N × H)
8. C₂×C₅²×C₇×C₁₇	C₂×C₃	semidirect
10. C₃×C₁₇×D₃₅	C₂×C₅	direct (N × H)
13. C₂×C₃×C₅×C₇×C₁₇	D₅	semidirect
14. C₂×C₃×C₅×C₇×C₁₇	C₂×C₅	semidirect
15. C₅²×C₇×C₁₇	C₂²×C₃	semidirect
17. C₂×C₃×C₅²×C₁₇	D₇	semidirect
19. C₂×C₁₇×D₃₅	C₃×C₅	direct (N × H)
20. C₂×C₃×C₅×D₃₅	C₁₇	direct (N × H)
22. C₃×C₅×C₇×C₁₇	C₂×D₅	semidirect
23. C₃×C₅×C₇×C₁₇	C₂²×C₅	semidirect
26. C₃×C₅²×C₁₇	C₂×D₇	semidirect
28. C₂×C₅×C₇×C₁₇	C₃×D₅	semidirect
29. C₂×C₅×C₇×C₁₇	C₂×C₃×C₅	semidirect
30. C₁₇×D₃₅	C₂×C₃×C₅	direct (N × H)
32. C₂×C₃×C₅²×C₇	C₂×C₁₇	semidirect
33. C₃×C₅×D₃₅	C₂×C₁₇	direct (N × H)
36. C₂×C₅²×C₁₇	C₃×D₇	semidirect
38. C₂×C₃×C₇×C₁₇	C₅×D₅	semidirect
40. C₂×C₅×D₃₅	C₃×C₁₇	direct (N × H)
42. C₅×C₇×C₁₇	C₂×C₃×D₅	semidirect
43. C₅×C₇×C₁₇	C₂²×C₃×C₅	semidirect
44. C₃×C₅²×C₇	C₂²×C₁₇	semidirect
47. C₂×C₃×C₅×C₁₇	C₅×D₇	semidirect
48. C₂×C₃×C₅×C₁₇	D₃₅	direct (N × H)
51. C₅²×C₁₇	C₂×C₃×D₇	semidirect
52. C₂×C₃×D₃₅	C₅×C₁₇	direct (N × H)
54. C₃×C₇×C₁₇	C₂×C₅×D₅	semidirect
55. C₂×C₅²×C₇	C₂×C₃×C₁₇	semidirect
56. C₅×D₃₅	C₂×C₃×C₁₇	direct (N × H)
61. C₃×C₅×C₁₇	C₂×C₅×D₇	semidirect
62. C₃×C₅×C₁₇	C₂×D₃₅	direct (N × H)
63. C₂×C₇×C₁₇	C₃×C₅×D₅	semidirect
66. C₂×C₃×C₅×C₇	D₅×C₁₇	semidirect
67. C₂×C₃×C₅×C₇	C₂×C₅×C₁₇	semidirect
68. C₃×D₃₅	C₂×C₅×C₁₇	direct (N × H)
71. C₅²×C₇	C₂²×C₃×C₁₇	semidirect
74. C₂×C₅×C₁₇	C₃×C₅×D₇	semidirect
75. C₂×C₅×C₁₇	C₃×D₃₅	direct (N × H)
77. C₂×C₃×C₅²	D₇×C₁₇	semidirect
79. C₂×D₃₅	C₃×C₅×C₁₇	direct (N × H)
81. C₇×C₁₇	C₂×C₃×C₅×D₅	semidirect
83. C₃×C₅×C₇	C₂×D₅×C₁₇	semidirect
84. C₃×C₅×C₇	C₂²×C₅×C₁₇	semidirect
86. C₂×C₃×C₁₇	C₅×D₃₅	direct (N × H)
89. C₅×C₁₇	C₂×C₃×C₅×D₇	semidirect
90. C₅×C₁₇	C₂×C₃×D₃₅	direct (N × H)
92. C₃×C₅²	C₂×D₇×C₁₇	semidirect
94. C₂×C₅×C₇	C₃×D₅×C₁₇	semidirect
95. C₂×C₅×C₇	C₂×C₃×C₅×C₁₇	semidirect
96. D₃₅	C₂×C₃×C₅×C₁₇	direct (N × H)
101. C₃×C₁₇	C₂×C₅×D₃₅	direct (N × H)
102. C₂×C₅²	C₃×D₇×C₁₇	semidirect
104. C₂×C₃×C₇	C₅×D₅×C₁₇	semidirect
107. C₅×C₇	C₂×C₃×D₅×C₁₇	semidirect
108. C₅×C₇	C₂²×C₃×C₅×C₁₇	semidirect
110. C₂×C₁₇	C₃×C₅×D₃₅	direct (N × H)
113. C₂×C₃×C₅	C₅×D₇×C₁₇	semidirect
114. C₂×C₃×C₅	C₁₇×D₃₅	direct (N × H)
117. C₅²	C₂×C₃×D₇×C₁₇	semidirect
118. C₃×C₇	C₂×C₅×D₅×C₁₇	semidirect
121. C₁₇	C₂×C₃×C₅×D₃₅	direct (N × H)
123. C₃×C₅	C₂×C₁₇×D₃₅	direct (N × H)
124. C₃×C₅	C₂×C₅×D₇×C₁₇	semidirect
125. C₂×C₇	C₃×C₅×D₅×C₁₇	semidirect
130. C₂×C₅	C₃×C₅×D₇×C₁₇	semidirect
131. C₂×C₅	C₃×C₁₇×D₃₅	direct (N × H)
133. C₇	C₂×C₃×C₅×D₅×C₁₇	semidirect
135. C₂×C₃	C₅×C₁₇×D₃₅	direct (N × H)
137. C₅	C₂×C₃×C₁₇×D₃₅	direct (N × H)
138. C₅	C₂×C₃×C₅×D₇×C₁₇	semidirect
140. C₃	C₂×C₅×C₁₇×D₃₅	direct (N × H)
142. C₂	C₃×C₅×C₁₇×D₃₅	direct (N × H)

H ≅ G/N

type

1. C₃×C₅×C₁₇×D₃₅

C₂

direct (N × H)

2. C₂×C₃×C₅²×C₇×C₁₇

C₂

semidirect

3. C₂×C₅×C₁₇×D₃₅

C₃

direct (N × H)

4. C₃×C₅²×C₇×C₁₇

C₂²

semidirect

6. C₂×C₃×C₁₇×D₃₅

C₅

direct (N × H)

7. C₅×C₁₇×D₃₅

C₂×C₃

direct (N × H)

8. C₂×C₅²×C₇×C₁₇

C₂×C₃

semidirect

10. C₃×C₁₇×D₃₅

C₂×C₅

direct (N × H)

13. C₂×C₃×C₅×C₇×C₁₇

D₅

semidirect

14. C₂×C₃×C₅×C₇×C₁₇

C₂×C₅

semidirect

15. C₅²×C₇×C₁₇

C₂²×C₃

semidirect

17. C₂×C₃×C₅²×C₁₇

D₇

semidirect

19. C₂×C₁₇×D₃₅

C₃×C₅

direct (N × H)

20. C₂×C₃×C₅×D₃₅

C₁₇

direct (N × H)

22. C₃×C₅×C₇×C₁₇

C₂×D₅

semidirect

23. C₃×C₅×C₇×C₁₇

C₂²×C₅

semidirect

26. C₃×C₅²×C₁₇

C₂×D₇

semidirect

28. C₂×C₅×C₇×C₁₇

C₃×D₅

semidirect

29. C₂×C₅×C₇×C₁₇

C₂×C₃×C₅

semidirect

30. C₁₇×D₃₅

C₂×C₃×C₅

direct (N × H)

32. C₂×C₃×C₅²×C₇

C₂×C₁₇

semidirect

33. C₃×C₅×D₃₅

C₂×C₁₇

direct (N × H)

36. C₂×C₅²×C₁₇

C₃×D₇

semidirect

38. C₂×C₃×C₇×C₁₇

C₅×D₅

semidirect

40. C₂×C₅×D₃₅

C₃×C₁₇

direct (N × H)

42. C₅×C₇×C₁₇

C₂×C₃×D₅

semidirect

43. C₅×C₇×C₁₇

C₂²×C₃×C₅

semidirect

44. C₃×C₅²×C₇

C₂²×C₁₇

semidirect

47. C₂×C₃×C₅×C₁₇

C₅×D₇

semidirect

48. C₂×C₃×C₅×C₁₇

D₃₅

direct (N × H)

51. C₅²×C₁₇

C₂×C₃×D₇

semidirect

52. C₂×C₃×D₃₅

C₅×C₁₇

direct (N × H)

54. C₃×C₇×C₁₇

C₂×C₅×D₅

semidirect

55. C₂×C₅²×C₇

C₂×C₃×C₁₇

semidirect

56. C₅×D₃₅

C₂×C₃×C₁₇

direct (N × H)

61. C₃×C₅×C₁₇

C₂×C₅×D₇

semidirect

62. C₃×C₅×C₁₇

C₂×D₃₅

direct (N × H)

63. C₂×C₇×C₁₇

C₃×C₅×D₅

semidirect

66. C₂×C₃×C₅×C₇

D₅×C₁₇

semidirect

67. C₂×C₃×C₅×C₇

C₂×C₅×C₁₇

semidirect

68. C₃×D₃₅

C₂×C₅×C₁₇

direct (N × H)

71. C₅²×C₇

C₂²×C₃×C₁₇

semidirect

74. C₂×C₅×C₁₇

C₃×C₅×D₇

semidirect

75. C₂×C₅×C₁₇

C₃×D₃₅

direct (N × H)

77. C₂×C₃×C₅²

D₇×C₁₇

semidirect

79. C₂×D₃₅

C₃×C₅×C₁₇

direct (N × H)

81. C₇×C₁₇

C₂×C₃×C₅×D₅

semidirect

83. C₃×C₅×C₇

C₂×D₅×C₁₇

semidirect

84. C₃×C₅×C₇

C₂²×C₅×C₁₇

semidirect

86. C₂×C₃×C₁₇

C₅×D₃₅

direct (N × H)

89. C₅×C₁₇

C₂×C₃×C₅×D₇

semidirect

90. C₅×C₁₇

C₂×C₃×D₃₅

direct (N × H)

92. C₃×C₅²

C₂×D₇×C₁₇

semidirect

94. C₂×C₅×C₇

C₃×D₅×C₁₇

semidirect

95. C₂×C₅×C₇

C₂×C₃×C₅×C₁₇

semidirect

96. D₃₅

C₂×C₃×C₅×C₁₇

direct (N × H)

101. C₃×C₁₇

C₂×C₅×D₃₅

direct (N × H)

102. C₂×C₅²

C₃×D₇×C₁₇

semidirect

104. C₂×C₃×C₇

C₅×D₅×C₁₇

semidirect

107. C₅×C₇

C₂×C₃×D₅×C₁₇

semidirect

108. C₅×C₇

C₂²×C₃×C₅×C₁₇

semidirect

110. C₂×C₁₇

C₃×C₅×D₃₅

direct (N × H)

113. C₂×C₃×C₅

C₅×D₇×C₁₇

semidirect

114. C₂×C₃×C₅

C₁₇×D₃₅

direct (N × H)

117. C₅²

C₂×C₃×D₇×C₁₇

semidirect

118. C₃×C₇

C₂×C₅×D₅×C₁₇

semidirect

121. C₁₇

C₂×C₃×C₅×D₃₅

direct (N × H)

123. C₃×C₅

C₂×C₁₇×D₃₅

direct (N × H)

124. C₃×C₅

C₂×C₅×D₇×C₁₇

semidirect

125. C₂×C₇

C₃×C₅×D₅×C₁₇

semidirect

130. C₂×C₅

C₃×C₅×D₇×C₁₇

semidirect

131. C₂×C₅

C₃×C₁₇×D₃₅

direct (N × H)

133. C₇

C₂×C₃×C₅×D₅×C₁₇

semidirect

135. C₂×C₃

C₅×C₁₇×D₃₅

direct (N × H)

137. C₅

C₂×C₃×C₁₇×D₃₅

direct (N × H)

138. C₅

C₂×C₃×C₅×D₇×C₁₇

semidirect

140. C₃

C₂×C₅×C₁₇×D₃₅

direct (N × H)

142. C₂

C₃×C₅×C₁₇×D₃₅

direct (N × H)

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

subgroup	index
C₃×C₅×C₁₇×D₃₅	2
C₂×C₃×C₅²×C₇×C₁₇	2
C₂×C₅×C₁₇×D₃₅	3
C₂×C₃×C₅×D₇×C₁₇	5
C₂×C₃×C₁₇×D₃₅	5
C₂×C₃×C₅×D₅×C₁₇	7
C₂×C₃×C₅×D₃₅	17

subgroup

index

C₃×C₅×C₁₇×D₃₅

C₂×C₃×C₅²×C₇×C₁₇

C₂×C₅×C₁₇×D₃₅

C₂×C₃×C₅×D₇×C₁₇

C₂×C₃×C₁₇×D₃₅

C₂×C₃×C₅×D₅×C₁₇

C₂×C₃×C₅×D₃₅

Subgroups — C₂×C₃×C₅×C₁₇×D₃₅ #49088045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C5×C17×D35 #49088045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₇×D₃₅ #49088045