Group #30655792 — subgroups

Subgroups — C₂×C₃×C₅×C₁₃×D₂₁ #30655792

Order 16380.

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

normal subgroups only

This group has 176 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×C₁₃×D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₃×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅×C₁₃×D₇	—	3	1	no	maximal
5	C₃²×C₅×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×D₂₁	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₅×C₁₃×D₇	—	3	2	no	—
9	C₂×C₃×C₅×C₇×C₁₃	—	2	1	no	—
10	C₂×C₃×C₅×C₇×C₁₃	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×D₃×C₁₃	—	7	1	no	maximal, Hall
13	C₂×C₅×C₁₃×D₇	—	3	1	no	Hall
14	C₂×C₃²×C₇×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃×C₁₃×D₂₁	C₂×C₅	1	2	yes	direct product factor
16	C₃×C₅×C₇×C₁₃	—	2	1	no	—
17	C₃×C₅×C₇×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃²×C₅×C₁₃	D₇	1	1	yes	characteristic, complemented
21	C₃×C₅×D₃×C₁₃	—	7	2	no	—
22	C₂×C₁₃×D₂₁	C₃×C₅	1	1	yes	characteristic, direct product factor
23	C₂×C₃×C₁₃×D₇	—	3	1	no	—
24	C₂×C₅×C₇×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented
25	C₅×C₁₃×D₇	—	3	2	no	—
26	C₃²×C₇×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₅×C₁₃	—	21	1	no	—
28	C₂×C₅×D₃×C₁₃	—	7	1	no	—
29	C₂×C₃²×C₅×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
30	C₃×C₅×D₂₁	C₂×C₁₃	1	2	yes	direct product factor
31	C₃²×C₅×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₇×C₁₃	—	2	1	no	—
33	C₂×C₃×C₇×C₁₃	C₅×D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
35	C₁₃×D₂₁	C₂×C₃×C₅	1	2	yes	direct product factor
36	C₃×C₁₃×D₇	—	3	2	no	—
37	C₂×C₃×D₃×C₁₃	—	7	1	no	Hall
38	C₅×C₇×C₁₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₅×D₂₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₅×D₇	—	3	1	no	—
41	C₂×C₃×C₅×C₁₃	—	2	1	no	—
42	C₂×C₃×C₅×C₁₃	—	21	2	no	—
43	C₂×C₃×C₅×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
44	C₂×C₃×C₅×C₁₃	D₂₁	1	1	yes	characteristic, direct product factor
45	C₅×D₃×C₁₃	—	7	2	no	—
46	C₂×C₁₃×D₇	—	3	1	no	Hall
47	C₃²×C₅×C₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
48	C₃×C₇×C₁₃	—	2	1	no	—
49	C₃×C₇×C₁₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
50	C₃×C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
51	C₂²×C₅×C₁₃	—	21	1	no	Hall
52	C₂×C₃×D₂₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₃²×C₁₃	C₅×D₇	1	1	yes	characteristic, complemented
54	C₃×D₃×C₁₃	—	7	2	no	—
55	C₂×C₃×C₅×C₇	—	2	1	no	—
56	C₂×C₃×C₅×C₇	D₃×C₁₃	1	1	yes	characteristic, complemented
57	C₂×C₃×C₅×C₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
58	C₅×D₂₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
59	C₃×C₅×D₇	—	3	2	no	—
60	C₃×C₅×C₁₃	—	2	1	no	—
61	C₃×C₅×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
62	C₃×C₅×C₁₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor
63	C₂×C₇×C₁₃	C₃×C₅×D₃	1	1	yes	characteristic, complemented
64	C₁₃×D₇	—	3	2	no	—
65	C₂×C₃×C₅×D₃	—	7	1	no	Hall
66	C₂²×C₃×C₁₃	—	21	1	no	—
67	C₂×D₃×C₁₃	—	7	1	no	—
68	C₂×C₅×D₇	—	3	1	no	Hall
69	C₂×C₅×C₁₃	—	21	2	no	—
70	C₂×C₅×C₁₃	C₃×D₂₁	1	1	yes	characteristic, direct product factor
71	C₂×C₃²×C₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
72	C₃×D₂₁	C₂×C₅×C₁₃	1	2	yes	direct product factor
73	C₃²×C₁₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
74	C₃×C₅×C₇	—	2	1	no	—
75	C₃×C₅×C₇	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
76	C₃×C₅×C₇	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
77	C₇×C₁₃	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
78	C₂×C₃²×C₅	C₁₃×D₇	1	1	yes	characteristic, complemented
79	C₃×C₅×D₃	—	7	2	no	—
80	C₂×D₂₁	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor
81	C₂×C₃×D₇	—	3	1	no	—
82	C₂×C₃×C₁₃	—	2	1	no	—
83	C₂×C₃×C₁₃	—	21	2	no	—
84	C₂×C₃×C₁₃	C₃×C₅×D₇	1	1	yes	characteristic, complemented
85	C₂×C₃×C₁₃	C₅×D₂₁	1	1	yes	characteristic, direct product factor
86	D₃×C₁₃	—	7	2	no	—
87	C₂×C₅×C₇	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
88	C₅×D₇	—	3	2	no	—
89	C₅×C₁₃	C₂×C₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
90	C₃²×C₇	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
91	C₂²×C₃×C₅	—	21	1	no	—
92	C₂×C₅×D₃	—	7	1	no	—
93	C₂²×C₁₃	—	21	1	no	Hall
94	C₃²×C₅	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
95	C₂×C₃×C₇	—	2	1	no	—
96	C₂×C₃×C₇	C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
97	C₂×C₃×C₇	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
98	D₂₁	C₂×C₃×C₅×C₁₃	1	2	yes	direct product factor
99	C₃×D₇	—	3	2	no	—
100	C₃×C₁₃	—	2	1	no	—
101	C₃×C₁₃	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented
102	C₃×C₁₃	C₂×C₅×D₂₁	1	1	yes	characteristic, direct product factor
103	C₂×C₃×D₃	—	7	1	no	Hall
104	C₅×C₇	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
105	C₂×C₃×C₅	—	2	1	no	—
106	C₂×C₃×C₅	—	21	2	no	—
107	C₂×C₃×C₅	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented
108	C₂×C₃×C₅	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
109	C₅×D₃	—	7	2	no	—
110	C₂×D₇	—	3	1	no	Hall
111	C₂×C₁₃	—	21	2	no	—
112	C₂×C₁₃	C₃×C₅×D₂₁	1	1	yes	characteristic, direct product factor
113	C₃×C₇	—	2	1	no	—
114	C₃×C₇	C₂×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
115	C₃×C₇	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
116	C₂²×C₅	—	21	1	no	Hall
117	C₂×C₃²	C₅×C₁₃×D₇	1	1	yes	characteristic, complemented
118	C₃×D₃	—	7	2	no	—
119	C₃×C₅	—	2	1	no	—
120	C₃×C₅	C₂×C₃×C₁₃×D₇	1	1	yes	characteristic, complemented
121	C₃×C₅	C₂×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
122	C₂×C₇	C₃×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented
123	D₇	—	3	2	no	—
124	C₁₃	C₂×C₃×C₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
125	C₂²×C₃	—	21	1	no	—
126	C₂×D₃	—	7	1	no	—
127	C₂×C₅	—	21	2	no	—
128	C₂×C₅	C₃×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
129	C₃²	C₂×C₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
130	C₇	C₂×C₃×C₅×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
131	C₂×C₃	—	2	1	no	—
132	C₂×C₃	—	21	2	no	—
133	C₂×C₃	C₃×C₅×C₁₃×D₇	1	1	yes	characteristic, complemented
134	C₂×C₃	C₅×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
135	D₃	—	7	2	no	—
136	C₅	C₂×C₃×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	—	21	1	no	Sylow
138	C₃	—	2	1	no	—
139	C₃	C₂×C₃×C₅×C₁₃×D₇	1	1	yes	characteristic, complemented
140	C₃	C₂×C₅×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
141	C₂	—	21	2	no	—
142	C₂	C₃×C₅×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₁₃×D₂₁

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅×C₇×C₁₃

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₁₃×D₂₁

C₃

yes

maximal, characteristic, direct product factor

C₂×C₃×C₅×C₁₃×D₇

—

maximal

C₃²×C₅×C₇×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×C₁₃×D₂₁

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₃×D₂₁

C₂×C₃

yes

direct product factor

C₃×C₅×C₁₃×D₇

—

C₂×C₃×C₅×C₇×C₁₃

—

C₂×C₃×C₅×C₇×C₁₃

D₃

yes

characteristic, complemented

C₂×C₃×C₅×C₇×C₁₃

C₂×C₃

yes

characteristic, complemented

C₂×C₃×C₅×D₃×C₁₃

—

maximal, Hall

C₂×C₅×C₁₃×D₇

—

Hall

C₂×C₃²×C₇×C₁₃

C₂×C₅

yes

characteristic, complemented

C₃×C₁₃×D₂₁

C₂×C₅

yes

direct product factor

C₃×C₅×C₇×C₁₃

—

C₃×C₅×C₇×C₁₃

C₂×D₃

yes

characteristic, complemented

C₃×C₅×C₇×C₁₃

C₂²×C₃

yes

characteristic, complemented

C₂×C₃×C₅×D₂₁

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃²×C₅×C₁₃

D₇

yes

characteristic, complemented

C₃×C₅×D₃×C₁₃

—

C₂×C₁₃×D₂₁

C₃×C₅

yes

characteristic, direct product factor

C₂×C₃×C₁₃×D₇

—

C₂×C₅×C₇×C₁₃

C₃×D₃

yes

characteristic, complemented

C₅×C₁₃×D₇

—

C₃²×C₇×C₁₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂²×C₃×C₅×C₁₃

—

C₂×C₅×D₃×C₁₃

—

C₂×C₃²×C₅×C₇

C₂×C₁₃

yes

characteristic, complemented

C₃×C₅×D₂₁

C₂×C₁₃

yes

direct product factor

C₃²×C₅×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₃

—

C₂×C₃×C₇×C₁₃

C₅×D₃

yes

characteristic, complemented

C₂×C₃×C₇×C₁₃

C₂×C₃×C₅

yes

characteristic, complemented

C₁₃×D₂₁

C₂×C₃×C₅

yes

direct product factor

C₃×C₁₃×D₇

—

C₂×C₃×D₃×C₁₃

—

Hall

C₅×C₇×C₁₃

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₅×D₂₁

C₃×C₁₃

yes

characteristic, direct product factor

C₂×C₃×C₅×D₇

—

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

—

C₂×C₃×C₅×C₁₃

C₃×D₇

yes

characteristic, complemented

C₂×C₃×C₅×C₁₃

D₂₁

yes

characteristic, direct product factor

C₅×D₃×C₁₃

—

C₂×C₁₃×D₇

—

Hall

C₃²×C₅×C₇

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₃×C₇×C₁₃

—

C₃×C₇×C₁₃

C₂×C₅×D₃

yes

characteristic, complemented

C₃×C₇×C₁₃

C₂²×C₃×C₅

yes

characteristic, complemented

C₂²×C₅×C₁₃

—

Hall

C₂×C₃×D₂₁

C₅×C₁₃

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₁₃

C₅×D₇

yes

characteristic, complemented

C₃×D₃×C₁₃

—

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

D₃×C₁₃

yes

characteristic, complemented

C₂×C₃×C₅×C₇

C₂×C₃×C₁₃

yes

characteristic, complemented

C₅×D₂₁

C₂×C₃×C₁₃

yes

direct product factor

C₃×C₅×D₇

—

C₃×C₅×C₁₃

—

C₃×C₅×C₁₃

C₂×C₃×D₇

yes

characteristic, complemented

C₃×C₅×C₁₃

C₂×D₂₁

yes

characteristic, direct product factor

C₂×C₇×C₁₃

C₃×C₅×D₃

yes

characteristic, complemented

C₁₃×D₇

—

C₂×C₃×C₅×D₃

—

Hall

C₂²×C₃×C₁₃

—

C₂×D₃×C₁₃

—

C₂×C₅×D₇

—

Hall

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

C₃×D₂₁

yes

characteristic, direct product factor

C₂×C₃²×C₇

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃×D₂₁

C₂×C₅×C₁₃

yes

direct product factor

C₃²×C₁₃

C₂×C₅×D₇

yes

characteristic, complemented, Hall

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×D₃×C₁₃

yes

characteristic, complemented

C₃×C₅×C₇

C₂²×C₃×C₁₃

yes

characteristic, complemented

C₇×C₁₃

C₂×C₃×C₅×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅

C₁₃×D₇

yes

characteristic, complemented

C₃×C₅×D₃

—

C₂×D₂₁

C₃×C₅×C₁₃

yes

characteristic, direct product factor

C₂×C₃×D₇

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

C₃×C₅×D₇

yes

characteristic, complemented

C₂×C₃×C₁₃

C₅×D₂₁

yes

characteristic, direct product factor

D₃×C₁₃

—

C₂×C₅×C₇

C₃×D₃×C₁₃

yes

characteristic, complemented

C₅×D₇

—

C₅×C₁₃

C₂×C₃×D₂₁

yes

characteristic, direct product factor, Hall

C₃²×C₇

C₂²×C₅×C₁₃

yes

characteristic, complemented, Hall

C₂²×C₃×C₅

—

C₂×C₅×D₃

—

C₂²×C₁₃

—

Hall

C₃²×C₅

C₂×C₁₃×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

C₂×C₃×C₇

C₅×D₃×C₁₃

yes

characteristic, complemented

C₂×C₃×C₇

C₂×C₃×C₅×C₁₃

yes

characteristic, complemented

D₂₁

C₂×C₃×C₅×C₁₃

yes

direct product factor

C₃×D₇

—

100

C₃×C₁₃

—

101

C₃×C₁₃

C₂×C₃×C₅×D₇

yes

characteristic, complemented

102

C₃×C₁₃

C₂×C₅×D₂₁

yes

characteristic, direct product factor

103

C₂×C₃×D₃

—

Hall

104

C₅×C₇

C₂×C₃×D₃×C₁₃

yes

characteristic, complemented, Hall

105

C₂×C₃×C₅

—

106

C₂×C₃×C₅

—

107

C₂×C₃×C₅

C₃×C₁₃×D₇

yes

characteristic, complemented

108

C₂×C₃×C₅

C₁₃×D₂₁

yes

characteristic, direct product factor

109

C₅×D₃

—

110

C₂×D₇

—

Hall

111

C₂×C₁₃

—

112

C₂×C₁₃

C₃×C₅×D₂₁

yes

characteristic, direct product factor

113

C₃×C₇

—

114

C₃×C₇

C₂×C₅×D₃×C₁₃

yes

characteristic, complemented

115

C₃×C₇

C₂²×C₃×C₅×C₁₃

yes

characteristic, complemented

116

C₂²×C₅

—

Hall

117

C₂×C₃²

C₅×C₁₃×D₇

yes

characteristic, complemented

118

C₃×D₃

—

119

C₃×C₅

—

120

C₃×C₅

C₂×C₃×C₁₃×D₇

yes

characteristic, complemented

121

C₃×C₅

C₂×C₁₃×D₂₁

yes

characteristic, direct product factor

122

C₂×C₇

C₃×C₅×D₃×C₁₃

yes

characteristic, complemented

123

D₇

—

124

C₁₃

C₂×C₃×C₅×D₂₁

yes

characteristic, direct product factor, Sylow

125

C₂²×C₃

—

126

C₂×D₃

—

127

C₂×C₅

—

128

C₂×C₅

C₃×C₁₃×D₂₁

yes

characteristic, direct product factor

129

C₃²

C₂×C₅×C₁₃×D₇

yes

characteristic, complemented, Sylow

130

C₇

C₂×C₃×C₅×D₃×C₁₃

yes

characteristic, complemented, Sylow

131

C₂×C₃

—

132

C₂×C₃

—

133

C₂×C₃

C₃×C₅×C₁₃×D₇

yes

characteristic, complemented

134

C₂×C₃

C₅×C₁₃×D₂₁

yes

characteristic, direct product factor

135

D₃

—

136

C₅

C₂×C₃×C₁₃×D₂₁

yes

characteristic, direct product factor, Sylow

137

C₂²

—

Sylow

138

C₃

—

139

C₃

C₂×C₃×C₅×C₁₃×D₇

yes

characteristic, complemented

140

C₃

C₂×C₅×C₁₃×D₂₁

yes

characteristic, direct product factor

141

C₂

—

142

C₂

C₃×C₅×C₁₃×D₂₁

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃×C₅×C₁₃

subgroup

G/H

center, hypercenter

C₂×C₃×C₅×C₁₃

D₂₁

commutator, cosocle, hypocenter

C₃×C₇

C₂²×C₃×C₅×C₁₃

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅×C₇×C₁₃

C₂

LCS

G ▷ C₃×C₇

UCS

C₁ ◁ C₂×C₃×C₅×C₁₃

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₃	C₂	semidirect
3. C₂×C₅×C₁₃×D₂₁	C₃	direct (N × H)
5. C₃²×C₅×C₇×C₁₃	C₂²	semidirect
6. C₂×C₃×C₁₃×D₂₁	C₅	direct (N × H)
7. C₅×C₁₃×D₂₁	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₇×C₁₃	D₃	semidirect
11. C₂×C₃×C₅×C₇×C₁₃	C₂×C₃	semidirect
14. C₂×C₃²×C₇×C₁₃	C₂×C₅	semidirect
15. C₃×C₁₃×D₂₁	C₂×C₅	direct (N × H)
17. C₃×C₅×C₇×C₁₃	C₂×D₃	semidirect
18. C₃×C₅×C₇×C₁₃	C₂²×C₃	semidirect
19. C₂×C₃×C₅×D₂₁	C₁₃	direct (N × H)
20. C₂×C₃²×C₅×C₁₃	D₇	semidirect
22. C₂×C₁₃×D₂₁	C₃×C₅	direct (N × H)
24. C₂×C₅×C₇×C₁₃	C₃×D₃	semidirect
26. C₃²×C₇×C₁₃	C₂²×C₅	semidirect
29. C₂×C₃²×C₅×C₇	C₂×C₁₃	semidirect
30. C₃×C₅×D₂₁	C₂×C₁₃	direct (N × H)
31. C₃²×C₅×C₁₃	C₂×D₇	semidirect
33. C₂×C₃×C₇×C₁₃	C₅×D₃	semidirect
34. C₂×C₃×C₇×C₁₃	C₂×C₃×C₅	semidirect
35. C₁₃×D₂₁	C₂×C₃×C₅	direct (N × H)
38. C₅×C₇×C₁₃	C₂×C₃×D₃	semidirect
39. C₂×C₅×D₂₁	C₃×C₁₃	direct (N × H)
43. C₂×C₃×C₅×C₁₃	C₃×D₇	semidirect
44. C₂×C₃×C₅×C₁₃	D₂₁	direct (N × H)
47. C₃²×C₅×C₇	C₂²×C₁₃	semidirect
49. C₃×C₇×C₁₃	C₂×C₅×D₃	semidirect
50. C₃×C₇×C₁₃	C₂²×C₃×C₅	semidirect
52. C₂×C₃×D₂₁	C₅×C₁₃	direct (N × H)
53. C₂×C₃²×C₁₃	C₅×D₇	semidirect
56. C₂×C₃×C₅×C₇	D₃×C₁₃	semidirect
57. C₂×C₃×C₅×C₇	C₂×C₃×C₁₃	semidirect
58. C₅×D₂₁	C₂×C₃×C₁₃	direct (N × H)
61. C₃×C₅×C₁₃	C₂×C₃×D₇	semidirect
62. C₃×C₅×C₁₃	C₂×D₂₁	direct (N × H)
63. C₂×C₇×C₁₃	C₃×C₅×D₃	semidirect
70. C₂×C₅×C₁₃	C₃×D₂₁	direct (N × H)
71. C₂×C₃²×C₇	C₂×C₅×C₁₃	semidirect
72. C₃×D₂₁	C₂×C₅×C₁₃	direct (N × H)
73. C₃²×C₁₃	C₂×C₅×D₇	semidirect
75. C₃×C₅×C₇	C₂×D₃×C₁₃	semidirect
76. C₃×C₅×C₇	C₂²×C₃×C₁₃	semidirect
77. C₇×C₁₃	C₂×C₃×C₅×D₃	semidirect
78. C₂×C₃²×C₅	C₁₃×D₇	semidirect
80. C₂×D₂₁	C₃×C₅×C₁₃	direct (N × H)
84. C₂×C₃×C₁₃	C₃×C₅×D₇	semidirect
85. C₂×C₃×C₁₃	C₅×D₂₁	direct (N × H)
87. C₂×C₅×C₇	C₃×D₃×C₁₃	semidirect
89. C₅×C₁₃	C₂×C₃×D₂₁	direct (N × H)
90. C₃²×C₇	C₂²×C₅×C₁₃	semidirect
94. C₃²×C₅	C₂×C₁₃×D₇	semidirect
96. C₂×C₃×C₇	C₅×D₃×C₁₃	semidirect
97. C₂×C₃×C₇	C₂×C₃×C₅×C₁₃	semidirect
98. D₂₁	C₂×C₃×C₅×C₁₃	direct (N × H)
101. C₃×C₁₃	C₂×C₃×C₅×D₇	semidirect
102. C₃×C₁₃	C₂×C₅×D₂₁	direct (N × H)
104. C₅×C₇	C₂×C₃×D₃×C₁₃	semidirect
107. C₂×C₃×C₅	C₃×C₁₃×D₇	semidirect
108. C₂×C₃×C₅	C₁₃×D₂₁	direct (N × H)
112. C₂×C₁₃	C₃×C₅×D₂₁	direct (N × H)
114. C₃×C₇	C₂×C₅×D₃×C₁₃	semidirect
115. C₃×C₇	C₂²×C₃×C₅×C₁₃	semidirect
117. C₂×C₃²	C₅×C₁₃×D₇	semidirect
120. C₃×C₅	C₂×C₃×C₁₃×D₇	semidirect
121. C₃×C₅	C₂×C₁₃×D₂₁	direct (N × H)
122. C₂×C₇	C₃×C₅×D₃×C₁₃	semidirect
124. C₁₃	C₂×C₃×C₅×D₂₁	direct (N × H)
128. C₂×C₅	C₃×C₁₃×D₂₁	direct (N × H)
129. C₃²	C₂×C₅×C₁₃×D₇	semidirect
130. C₇	C₂×C₃×C₅×D₃×C₁₃	semidirect
133. C₂×C₃	C₃×C₅×C₁₃×D₇	semidirect
134. C₂×C₃	C₅×C₁₃×D₂₁	direct (N × H)
136. C₅	C₂×C₃×C₁₃×D₂₁	direct (N × H)
139. C₃	C₂×C₃×C₅×C₁₃×D₇	semidirect
140. C₃	C₂×C₅×C₁₃×D₂₁	direct (N × H)
142. C₂	C₃×C₅×C₁₃×D₂₁	direct (N × H)

H ≅ G/N

type

1. C₃×C₅×C₁₃×D₂₁

C₂

direct (N × H)

2. C₂×C₃²×C₅×C₇×C₁₃

C₂

semidirect

3. C₂×C₅×C₁₃×D₂₁

C₃

direct (N × H)

5. C₃²×C₅×C₇×C₁₃

C₂²

semidirect

6. C₂×C₃×C₁₃×D₂₁

C₅

direct (N × H)

7. C₅×C₁₃×D₂₁

C₂×C₃

direct (N × H)

10. C₂×C₃×C₅×C₇×C₁₃

D₃

semidirect

11. C₂×C₃×C₅×C₇×C₁₃

C₂×C₃

semidirect

14. C₂×C₃²×C₇×C₁₃

C₂×C₅

semidirect

15. C₃×C₁₃×D₂₁

C₂×C₅

direct (N × H)

17. C₃×C₅×C₇×C₁₃

C₂×D₃

semidirect

18. C₃×C₅×C₇×C₁₃

C₂²×C₃

semidirect

19. C₂×C₃×C₅×D₂₁

C₁₃

direct (N × H)

20. C₂×C₃²×C₅×C₁₃

D₇

semidirect

22. C₂×C₁₃×D₂₁

C₃×C₅

direct (N × H)

24. C₂×C₅×C₇×C₁₃

C₃×D₃

semidirect

26. C₃²×C₇×C₁₃

C₂²×C₅

semidirect

29. C₂×C₃²×C₅×C₇

C₂×C₁₃

semidirect

30. C₃×C₅×D₂₁

C₂×C₁₃

direct (N × H)

31. C₃²×C₅×C₁₃

C₂×D₇

semidirect

33. C₂×C₃×C₇×C₁₃

C₅×D₃

semidirect

34. C₂×C₃×C₇×C₁₃

C₂×C₃×C₅

semidirect

35. C₁₃×D₂₁

C₂×C₃×C₅

direct (N × H)

38. C₅×C₇×C₁₃

C₂×C₃×D₃

semidirect

39. C₂×C₅×D₂₁

C₃×C₁₃

direct (N × H)

43. C₂×C₃×C₅×C₁₃

C₃×D₇

semidirect

44. C₂×C₃×C₅×C₁₃

D₂₁

direct (N × H)

47. C₃²×C₅×C₇

C₂²×C₁₃

semidirect

49. C₃×C₇×C₁₃

C₂×C₅×D₃

semidirect

50. C₃×C₇×C₁₃

C₂²×C₃×C₅

semidirect

52. C₂×C₃×D₂₁

C₅×C₁₃

direct (N × H)

53. C₂×C₃²×C₁₃

C₅×D₇

semidirect

56. C₂×C₃×C₅×C₇

D₃×C₁₃

semidirect

57. C₂×C₃×C₅×C₇

C₂×C₃×C₁₃

semidirect

58. C₅×D₂₁

C₂×C₃×C₁₃

direct (N × H)

61. C₃×C₅×C₁₃

C₂×C₃×D₇

semidirect

62. C₃×C₅×C₁₃

C₂×D₂₁

direct (N × H)

63. C₂×C₇×C₁₃

C₃×C₅×D₃

semidirect

70. C₂×C₅×C₁₃

C₃×D₂₁

direct (N × H)

71. C₂×C₃²×C₇

C₂×C₅×C₁₃

semidirect

72. C₃×D₂₁

C₂×C₅×C₁₃

direct (N × H)

73. C₃²×C₁₃

C₂×C₅×D₇

semidirect

75. C₃×C₅×C₇

C₂×D₃×C₁₃

semidirect

76. C₃×C₅×C₇

C₂²×C₃×C₁₃

semidirect

77. C₇×C₁₃

C₂×C₃×C₅×D₃

semidirect

78. C₂×C₃²×C₅

C₁₃×D₇

semidirect

80. C₂×D₂₁

C₃×C₅×C₁₃

direct (N × H)

84. C₂×C₃×C₁₃

C₃×C₅×D₇

semidirect

85. C₂×C₃×C₁₃

C₅×D₂₁

direct (N × H)

87. C₂×C₅×C₇

C₃×D₃×C₁₃

semidirect

89. C₅×C₁₃

C₂×C₃×D₂₁

direct (N × H)

90. C₃²×C₇

C₂²×C₅×C₁₃

semidirect

94. C₃²×C₅

C₂×C₁₃×D₇

semidirect

96. C₂×C₃×C₇

C₅×D₃×C₁₃

semidirect

97. C₂×C₃×C₇

C₂×C₃×C₅×C₁₃

semidirect

98. D₂₁

C₂×C₃×C₅×C₁₃

direct (N × H)

101. C₃×C₁₃

C₂×C₃×C₅×D₇

semidirect

102. C₃×C₁₃

C₂×C₅×D₂₁

direct (N × H)

104. C₅×C₇

C₂×C₃×D₃×C₁₃

semidirect

107. C₂×C₃×C₅

C₃×C₁₃×D₇

semidirect

108. C₂×C₃×C₅

C₁₃×D₂₁

direct (N × H)

112. C₂×C₁₃

C₃×C₅×D₂₁

direct (N × H)

114. C₃×C₇

C₂×C₅×D₃×C₁₃

semidirect

115. C₃×C₇

C₂²×C₃×C₅×C₁₃

semidirect

117. C₂×C₃²

C₅×C₁₃×D₇

semidirect

120. C₃×C₅

C₂×C₃×C₁₃×D₇

semidirect

121. C₃×C₅

C₂×C₁₃×D₂₁

direct (N × H)

122. C₂×C₇

C₃×C₅×D₃×C₁₃

semidirect

124. C₁₃

C₂×C₃×C₅×D₂₁

direct (N × H)

128. C₂×C₅

C₃×C₁₃×D₂₁

direct (N × H)

129. C₃²

C₂×C₅×C₁₃×D₇

semidirect

130. C₇

C₂×C₃×C₅×D₃×C₁₃

semidirect

133. C₂×C₃

C₃×C₅×C₁₃×D₇

semidirect

134. C₂×C₃

C₅×C₁₃×D₂₁

direct (N × H)

136. C₅

C₂×C₃×C₁₃×D₂₁

direct (N × H)

139. C₃

C₂×C₃×C₅×C₁₃×D₇

semidirect

140. C₃

C₂×C₅×C₁₃×D₂₁

direct (N × H)

142. C₂

C₃×C₅×C₁₃×D₂₁

direct (N × H)

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

subgroup	index
C₃×C₅×C₁₃×D₂₁	2
C₂×C₃²×C₅×C₇×C₁₃	2
C₂×C₅×C₁₃×D₂₁	3
C₂×C₃×C₅×C₁₃×D₇	3
C₂×C₃×C₁₃×D₂₁	5
C₂×C₃×C₅×D₃×C₁₃	7
C₂×C₃×C₅×D₂₁	13

subgroup

index

C₃×C₅×C₁₃×D₂₁

C₂×C₃²×C₅×C₇×C₁₃

C₂×C₅×C₁₃×D₂₁

C₂×C₃×C₅×C₁₃×D₇

C₂×C₃×C₁₃×D₂₁

C₂×C₃×C₅×D₃×C₁₃

C₂×C₃×C₅×D₂₁

Subgroups — C₂×C₃×C₅×C₁₃×D₂₁ #30655792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C5×C13×D21 #30655792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₃×D₂₁ #30655792