Group #44394671 — subgroups

Subgroups — C₂×C₃×C₅×C₂₃×D₂₁ #44394671

Order 28980.

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×C₂₃×D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₇×C₂₃	—	3	1	no	maximal
4	C₂×C₅×C₂₃×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₂₃×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₂₃×D₂₁	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₅×D₇×C₂₃	—	3	2	no	—
9	C₂×C₃×C₅×C₇×C₂₃	—	2	1	no	—
10	C₂×C₃×C₅×C₇×C₂₃	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×D₃×C₂₃	—	7	1	no	maximal, Hall
13	C₂×C₅×D₇×C₂₃	—	3	1	no	Hall
14	C₃×C₂₃×D₂₁	C₂×C₅	1	2	yes	direct product factor
15	C₂×C₃²×C₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
16	C₃×C₅×C₇×C₂₃	—	2	1	no	—
17	C₃×C₅×C₇×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₅×C₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₃×C₅×D₃×C₂₃	—	7	2	no	—
20	C₂×C₃²×C₅×C₂₃	D₇	1	1	yes	characteristic, complemented
21	C₂×C₂₃×D₂₁	C₃×C₅	1	1	yes	characteristic, direct product factor
22	C₂×C₃×D₇×C₂₃	—	3	1	no	—
23	C₂×C₅×C₇×C₂₃	C₃×D₃	1	1	yes	characteristic, complemented
24	C₅×D₇×C₂₃	—	3	2	no	—
25	C₃²×C₇×C₂₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₃×C₅×C₂₃	—	21	1	no	—
27	C₂×C₅×D₃×C₂₃	—	7	1	no	—
28	C₂×C₃×C₅×D₂₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₃²×C₅×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇×C₂₃	—	2	1	no	—
31	C₂×C₃×C₇×C₂₃	C₅×D₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₇×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
33	C₂₃×D₂₁	C₂×C₃×C₅	1	2	yes	direct product factor
34	C₃×D₇×C₂₃	—	3	2	no	—
35	C₂×C₃×D₃×C₂₃	—	7	1	no	Hall
36	C₅×C₇×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₂₃	—	2	1	no	—
38	C₂×C₃×C₅×C₂₃	—	21	2	no	—
39	C₂×C₃×C₅×C₂₃	C₃×D₇	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×C₂₃	D₂₁	1	1	yes	characteristic, direct product factor
41	C₅×D₃×C₂₃	—	7	2	no	—
42	C₂×D₇×C₂₃	—	3	1	no	Hall
43	C₂×C₃²×C₅×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
44	C₃×C₅×D₂₁	C₂×C₂₃	1	2	yes	direct product factor
45	C₃×C₇×C₂₃	—	2	1	no	—
46	C₃×C₇×C₂₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
47	C₃×C₇×C₂₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
48	C₂²×C₅×C₂₃	—	21	1	no	Hall
49	C₂×C₅×D₂₁	C₃×C₂₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₅×D₇	—	3	1	no	—
51	C₂×C₃²×C₂₃	C₅×D₇	1	1	yes	characteristic, complemented
52	C₃×D₃×C₂₃	—	7	2	no	—
53	C₃×C₅×C₂₃	—	2	1	no	—
54	C₃×C₅×C₂₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented
55	C₃×C₅×C₂₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor
56	C₂×C₇×C₂₃	C₃×C₅×D₃	1	1	yes	characteristic, complemented
57	D₇×C₂₃	—	3	2	no	—
58	C₃²×C₅×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₃×C₂₃	—	21	1	no	—
60	C₂×D₃×C₂₃	—	7	1	no	—
61	C₂×C₃×D₂₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
62	C₂×C₅×C₂₃	—	21	2	no	—
63	C₂×C₅×C₂₃	C₃×D₂₁	1	1	yes	characteristic, direct product factor
64	C₂×C₃×C₅×C₇	—	2	1	no	—
65	C₂×C₃×C₅×C₇	D₃×C₂₃	1	1	yes	characteristic, complemented
66	C₂×C₃×C₅×C₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
67	C₅×D₂₁	C₂×C₃×C₂₃	1	2	yes	direct product factor
68	C₃×C₅×D₇	—	3	2	no	—
69	C₃²×C₂₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
70	C₂×C₃×C₅×D₃	—	7	1	no	Hall
71	C₇×C₂₃	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
72	C₂×C₅×D₇	—	3	1	no	Hall
73	C₂×C₃×C₂₃	—	2	1	no	—
74	C₂×C₃×C₂₃	—	21	2	no	—
75	C₂×C₃×C₂₃	C₃×C₅×D₇	1	1	yes	characteristic, complemented
76	C₂×C₃×C₂₃	C₅×D₂₁	1	1	yes	characteristic, direct product factor
77	D₃×C₂₃	—	7	2	no	—
78	C₂×C₃²×C₇	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
79	C₃×D₂₁	C₂×C₅×C₂₃	1	2	yes	direct product factor
80	C₅×C₂₃	C₂×C₃×D₂₁	1	1	yes	characteristic, direct product factor, Hall
81	C₃×C₅×C₇	—	2	1	no	—
82	C₃×C₅×C₇	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
83	C₃×C₅×C₇	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
84	C₂²×C₂₃	—	21	1	no	Hall
85	C₂×C₃²×C₅	D₇×C₂₃	1	1	yes	characteristic, complemented
86	C₃×C₅×D₃	—	7	2	no	—
87	C₂×D₂₁	C₃×C₅×C₂₃	1	1	yes	characteristic, direct product factor
88	C₂×C₃×D₇	—	3	1	no	—
89	C₂×C₅×C₇	C₃×D₃×C₂₃	1	1	yes	characteristic, complemented
90	C₅×D₇	—	3	2	no	—
91	C₃×C₂₃	—	2	1	no	—
92	C₃×C₂₃	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented
93	C₃×C₂₃	C₂×C₅×D₂₁	1	1	yes	characteristic, direct product factor
94	C₃²×C₇	C₂²×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
95	C₂²×C₃×C₅	—	21	1	no	—
96	C₂×C₅×D₃	—	7	1	no	—
97	C₂×C₂₃	—	21	2	no	—
98	C₂×C₂₃	C₃×C₅×D₂₁	1	1	yes	characteristic, direct product factor
99	C₃²×C₅	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
100	C₂×C₃×C₇	—	2	1	no	—
101	C₂×C₃×C₇	C₅×D₃×C₂₃	1	1	yes	characteristic, complemented
102	C₂×C₃×C₇	C₂×C₃×C₅×C₂₃	1	1	yes	characteristic, complemented
103	D₂₁	C₂×C₃×C₅×C₂₃	1	2	yes	direct product factor
104	C₃×D₇	—	3	2	no	—
105	C₂×C₃×D₃	—	7	1	no	Hall
106	C₅×C₇	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
107	C₂×C₃×C₅	—	2	1	no	—
108	C₂×C₃×C₅	—	21	2	no	—
109	C₂×C₃×C₅	C₃×D₇×C₂₃	1	1	yes	characteristic, complemented
110	C₂×C₃×C₅	C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
111	C₅×D₃	—	7	2	no	—
112	C₂×D₇	—	3	1	no	Hall
113	C₂₃	C₂×C₃×C₅×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
114	C₃×C₇	—	2	1	no	—
115	C₃×C₇	C₂×C₅×D₃×C₂₃	1	1	yes	characteristic, complemented
116	C₃×C₇	C₂²×C₃×C₅×C₂₃	1	1	yes	characteristic, complemented
117	C₂²×C₅	—	21	1	no	Hall
118	C₂×C₃²	C₅×D₇×C₂₃	1	1	yes	characteristic, complemented
119	C₃×D₃	—	7	2	no	—
120	C₃×C₅	—	2	1	no	—
121	C₃×C₅	C₂×C₃×D₇×C₂₃	1	1	yes	characteristic, complemented
122	C₃×C₅	C₂×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
123	C₂×C₇	C₃×C₅×D₃×C₂₃	1	1	yes	characteristic, complemented
124	D₇	—	3	2	no	—
125	C₂²×C₃	—	21	1	no	—
126	C₂×D₃	—	7	1	no	—
127	C₂×C₅	—	21	2	no	—
128	C₂×C₅	C₃×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
129	C₃²	C₂×C₅×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
130	C₇	C₂×C₃×C₅×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
131	C₂×C₃	—	2	1	no	—
132	C₂×C₃	—	21	2	no	—
133	C₂×C₃	C₃×C₅×D₇×C₂₃	1	1	yes	characteristic, complemented
134	C₂×C₃	C₅×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
135	D₃	—	7	2	no	—
136	C₅	C₂×C₃×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	—	21	1	no	Sylow
138	C₃	—	2	1	no	—
139	C₃	C₂×C₅×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor
140	C₃	C₂×C₃×C₅×D₇×C₂₃	1	1	yes	characteristic, complemented
141	C₂	—	21	2	no	—
142	C₂	C₃×C₅×C₂₃×D₂₁	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×C₂₃×D₂₁

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅×C₇×C₂₃

C₂

yes

maximal, characteristic, complemented

C₂×C₃×C₅×D₇×C₂₃

—

maximal

C₂×C₅×C₂₃×D₂₁

C₃

yes

maximal, characteristic, direct product factor

C₃²×C₅×C₇×C₂₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×C₂₃×D₂₁

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₂₃×D₂₁

C₂×C₃

yes

direct product factor

C₃×C₅×D₇×C₂₃

—

C₂×C₃×C₅×C₇×C₂₃

—

C₂×C₃×C₅×C₇×C₂₃

D₃

yes

characteristic, complemented

C₂×C₃×C₅×C₇×C₂₃

C₂×C₃

yes

characteristic, complemented

C₂×C₃×C₅×D₃×C₂₃

—

maximal, Hall

C₂×C₅×D₇×C₂₃

—

Hall

C₃×C₂₃×D₂₁

C₂×C₅

yes

direct product factor

C₂×C₃²×C₇×C₂₃

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₇×C₂₃

—

C₃×C₅×C₇×C₂₃

C₂×D₃

yes

characteristic, complemented

C₃×C₅×C₇×C₂₃

C₂²×C₃

yes

characteristic, complemented

C₃×C₅×D₃×C₂₃

—

C₂×C₃²×C₅×C₂₃

D₇

yes

characteristic, complemented

C₂×C₂₃×D₂₁

C₃×C₅

yes

characteristic, direct product factor

C₂×C₃×D₇×C₂₃

—

C₂×C₅×C₇×C₂₃

C₃×D₃

yes

characteristic, complemented

C₅×D₇×C₂₃

—

C₃²×C₇×C₂₃

C₂²×C₅

yes

characteristic, complemented, Hall

C₂²×C₃×C₅×C₂₃

—

C₂×C₅×D₃×C₂₃

—

C₂×C₃×C₅×D₂₁

C₂₃

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₅×C₂₃

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₂₃

—

C₂×C₃×C₇×C₂₃

C₅×D₃

yes

characteristic, complemented

C₂×C₃×C₇×C₂₃

C₂×C₃×C₅

yes

characteristic, complemented

C₂₃×D₂₁

C₂×C₃×C₅

yes

direct product factor

C₃×D₇×C₂₃

—

C₂×C₃×D₃×C₂₃

—

Hall

C₅×C₇×C₂₃

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₂₃

—

C₂×C₃×C₅×C₂₃

—

C₂×C₃×C₅×C₂₃

C₃×D₇

yes

characteristic, complemented

C₂×C₃×C₅×C₂₃

D₂₁

yes

characteristic, direct product factor

C₅×D₃×C₂₃

—

C₂×D₇×C₂₃

—

Hall

C₂×C₃²×C₅×C₇

C₂×C₂₃

yes

characteristic, complemented

C₃×C₅×D₂₁

C₂×C₂₃

yes

direct product factor

C₃×C₇×C₂₃

—

C₃×C₇×C₂₃

C₂×C₅×D₃

yes

characteristic, complemented

C₃×C₇×C₂₃

C₂²×C₃×C₅

yes

characteristic, complemented

C₂²×C₅×C₂₃

—

Hall

C₂×C₅×D₂₁

C₃×C₂₃

yes

characteristic, direct product factor

C₂×C₃×C₅×D₇

—

C₂×C₃²×C₂₃

C₅×D₇

yes

characteristic, complemented

C₃×D₃×C₂₃

—

C₃×C₅×C₂₃

—

C₃×C₅×C₂₃

C₂×C₃×D₇

yes

characteristic, complemented

C₃×C₅×C₂₃

C₂×D₂₁

yes

characteristic, direct product factor

C₂×C₇×C₂₃

C₃×C₅×D₃

yes

characteristic, complemented

D₇×C₂₃

—

C₃²×C₅×C₇

C₂²×C₂₃

yes

characteristic, complemented, Hall

C₂²×C₃×C₂₃

—

C₂×D₃×C₂₃

—

C₂×C₃×D₂₁

C₅×C₂₃

yes

characteristic, direct product factor, Hall

C₂×C₅×C₂₃

—

C₂×C₅×C₂₃

C₃×D₂₁

yes

characteristic, direct product factor

C₂×C₃×C₅×C₇

—

C₂×C₃×C₅×C₇

D₃×C₂₃

yes

characteristic, complemented

C₂×C₃×C₅×C₇

C₂×C₃×C₂₃

yes

characteristic, complemented

C₅×D₂₁

C₂×C₃×C₂₃

yes

direct product factor

C₃×C₅×D₇

—

C₃²×C₂₃

C₂×C₅×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₅×D₃

—

Hall

C₇×C₂₃

C₂×C₃×C₅×D₃

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

Hall

C₂×C₃×C₂₃

—

C₂×C₃×C₂₃

—

C₂×C₃×C₂₃

C₃×C₅×D₇

yes

characteristic, complemented

C₂×C₃×C₂₃

C₅×D₂₁

yes

characteristic, direct product factor

D₃×C₂₃

—

C₂×C₃²×C₇

C₂×C₅×C₂₃

yes

characteristic, complemented

C₃×D₂₁

C₂×C₅×C₂₃

yes

direct product factor

C₅×C₂₃

C₂×C₃×D₂₁

yes

characteristic, direct product factor, Hall

C₃×C₅×C₇

—

C₃×C₅×C₇

C₂×D₃×C₂₃

yes

characteristic, complemented

C₃×C₅×C₇

C₂²×C₃×C₂₃

yes

characteristic, complemented

C₂²×C₂₃

—

Hall

C₂×C₃²×C₅

D₇×C₂₃

yes

characteristic, complemented

C₃×C₅×D₃

—

C₂×D₂₁

C₃×C₅×C₂₃

yes

characteristic, direct product factor

C₂×C₃×D₇

—

C₂×C₅×C₇

C₃×D₃×C₂₃

yes

characteristic, complemented

C₅×D₇

—

C₃×C₂₃

—

C₃×C₂₃

C₂×C₃×C₅×D₇

yes

characteristic, complemented

C₃×C₂₃

C₂×C₅×D₂₁

yes

characteristic, direct product factor

C₃²×C₇

C₂²×C₅×C₂₃

yes

characteristic, complemented, Hall

C₂²×C₃×C₅

—

C₂×C₅×D₃

—

C₂×C₂₃

—

C₂×C₂₃

C₃×C₅×D₂₁

yes

characteristic, direct product factor

C₃²×C₅

C₂×D₇×C₂₃

yes

characteristic, complemented, Hall

100

C₂×C₃×C₇

—

101

C₂×C₃×C₇

C₅×D₃×C₂₃

yes

characteristic, complemented

102

C₂×C₃×C₇

C₂×C₃×C₅×C₂₃

yes

characteristic, complemented

103

D₂₁

C₂×C₃×C₅×C₂₃

yes

direct product factor

104

C₃×D₇

—

105

C₂×C₃×D₃

—

Hall

106

C₅×C₇

C₂×C₃×D₃×C₂₃

yes

characteristic, complemented, Hall

107

C₂×C₃×C₅

—

108

C₂×C₃×C₅

—

109

C₂×C₃×C₅

C₃×D₇×C₂₃

yes

characteristic, complemented

110

C₂×C₃×C₅

C₂₃×D₂₁

yes

characteristic, direct product factor

111

C₅×D₃

—

112

C₂×D₇

—

Hall

113

C₂₃

C₂×C₃×C₅×D₂₁

yes

characteristic, direct product factor, Sylow

114

C₃×C₇

—

115

C₃×C₇

C₂×C₅×D₃×C₂₃

yes

characteristic, complemented

116

C₃×C₇

C₂²×C₃×C₅×C₂₃

yes

characteristic, complemented

117

C₂²×C₅

—

Hall

118

C₂×C₃²

C₅×D₇×C₂₃

yes

characteristic, complemented

119

C₃×D₃

—

120

C₃×C₅

—

121

C₃×C₅

C₂×C₃×D₇×C₂₃

yes

characteristic, complemented

122

C₃×C₅

C₂×C₂₃×D₂₁

yes

characteristic, direct product factor

123

C₂×C₇

C₃×C₅×D₃×C₂₃

yes

characteristic, complemented

124

D₇

—

125

C₂²×C₃

—

126

C₂×D₃

—

127

C₂×C₅

—

128

C₂×C₅

C₃×C₂₃×D₂₁

yes

characteristic, direct product factor

129

C₃²

C₂×C₅×D₇×C₂₃

yes

characteristic, complemented, Sylow

130

C₇

C₂×C₃×C₅×D₃×C₂₃

yes

characteristic, complemented, Sylow

131

C₂×C₃

—

132

C₂×C₃

—

133

C₂×C₃

C₃×C₅×D₇×C₂₃

yes

characteristic, complemented

134

C₂×C₃

C₅×C₂₃×D₂₁

yes

characteristic, direct product factor

135

D₃

—

136

C₅

C₂×C₃×C₂₃×D₂₁

yes

characteristic, direct product factor, Sylow

137

C₂²

—

Sylow

138

C₃

—

139

C₃

C₂×C₅×C₂₃×D₂₁

yes

characteristic, direct product factor

140

C₃

C₂×C₃×C₅×D₇×C₂₃

yes

characteristic, complemented

141

C₂

—

142

C₂

C₃×C₅×C₂₃×D₂₁

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₂₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃×C₅×C₂₃

subgroup

G/H

center, hypercenter

C₂×C₃×C₅×C₂₃

D₂₁

commutator, cosocle, hypocenter

C₃×C₇

C₂²×C₃×C₅×C₂₃

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅×C₇×C₂₃

C₂

LCS

G ▷ C₃×C₇

UCS

C₁ ◁ C₂×C₃×C₅×C₂₃

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₂₃	C₂	semidirect
4. C₂×C₅×C₂₃×D₂₁	C₃	direct (N × H)
5. C₃²×C₅×C₇×C₂₃	C₂²	semidirect
6. C₂×C₃×C₂₃×D₂₁	C₅	direct (N × H)
7. C₅×C₂₃×D₂₁	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₇×C₂₃	D₃	semidirect
11. C₂×C₃×C₅×C₇×C₂₃	C₂×C₃	semidirect
14. C₃×C₂₃×D₂₁	C₂×C₅	direct (N × H)
15. C₂×C₃²×C₇×C₂₃	C₂×C₅	semidirect
17. C₃×C₅×C₇×C₂₃	C₂×D₃	semidirect
18. C₃×C₅×C₇×C₂₃	C₂²×C₃	semidirect
20. C₂×C₃²×C₅×C₂₃	D₇	semidirect
21. C₂×C₂₃×D₂₁	C₃×C₅	direct (N × H)
23. C₂×C₅×C₇×C₂₃	C₃×D₃	semidirect
25. C₃²×C₇×C₂₃	C₂²×C₅	semidirect
28. C₂×C₃×C₅×D₂₁	C₂₃	direct (N × H)
29. C₃²×C₅×C₂₃	C₂×D₇	semidirect
31. C₂×C₃×C₇×C₂₃	C₅×D₃	semidirect
32. C₂×C₃×C₇×C₂₃	C₂×C₃×C₅	semidirect
33. C₂₃×D₂₁	C₂×C₃×C₅	direct (N × H)
36. C₅×C₇×C₂₃	C₂×C₃×D₃	semidirect
39. C₂×C₃×C₅×C₂₃	C₃×D₇	semidirect
40. C₂×C₃×C₅×C₂₃	D₂₁	direct (N × H)
43. C₂×C₃²×C₅×C₇	C₂×C₂₃	semidirect
44. C₃×C₅×D₂₁	C₂×C₂₃	direct (N × H)
46. C₃×C₇×C₂₃	C₂×C₅×D₃	semidirect
47. C₃×C₇×C₂₃	C₂²×C₃×C₅	semidirect
49. C₂×C₅×D₂₁	C₃×C₂₃	direct (N × H)
51. C₂×C₃²×C₂₃	C₅×D₇	semidirect
54. C₃×C₅×C₂₃	C₂×C₃×D₇	semidirect
55. C₃×C₅×C₂₃	C₂×D₂₁	direct (N × H)
56. C₂×C₇×C₂₃	C₃×C₅×D₃	semidirect
58. C₃²×C₅×C₇	C₂²×C₂₃	semidirect
61. C₂×C₃×D₂₁	C₅×C₂₃	direct (N × H)
63. C₂×C₅×C₂₃	C₃×D₂₁	direct (N × H)
65. C₂×C₃×C₅×C₇	D₃×C₂₃	semidirect
66. C₂×C₃×C₅×C₇	C₂×C₃×C₂₃	semidirect
67. C₅×D₂₁	C₂×C₃×C₂₃	direct (N × H)
69. C₃²×C₂₃	C₂×C₅×D₇	semidirect
71. C₇×C₂₃	C₂×C₃×C₅×D₃	semidirect
75. C₂×C₃×C₂₃	C₃×C₅×D₇	semidirect
76. C₂×C₃×C₂₃	C₅×D₂₁	direct (N × H)
78. C₂×C₃²×C₇	C₂×C₅×C₂₃	semidirect
79. C₃×D₂₁	C₂×C₅×C₂₃	direct (N × H)
80. C₅×C₂₃	C₂×C₃×D₂₁	direct (N × H)
82. C₃×C₅×C₇	C₂×D₃×C₂₃	semidirect
83. C₃×C₅×C₇	C₂²×C₃×C₂₃	semidirect
85. C₂×C₃²×C₅	D₇×C₂₃	semidirect
87. C₂×D₂₁	C₃×C₅×C₂₃	direct (N × H)
89. C₂×C₅×C₇	C₃×D₃×C₂₃	semidirect
92. C₃×C₂₃	C₂×C₃×C₅×D₇	semidirect
93. C₃×C₂₃	C₂×C₅×D₂₁	direct (N × H)
94. C₃²×C₇	C₂²×C₅×C₂₃	semidirect
98. C₂×C₂₃	C₃×C₅×D₂₁	direct (N × H)
99. C₃²×C₅	C₂×D₇×C₂₃	semidirect
101. C₂×C₃×C₇	C₅×D₃×C₂₃	semidirect
102. C₂×C₃×C₇	C₂×C₃×C₅×C₂₃	semidirect
103. D₂₁	C₂×C₃×C₅×C₂₃	direct (N × H)
106. C₅×C₇	C₂×C₃×D₃×C₂₃	semidirect
109. C₂×C₃×C₅	C₃×D₇×C₂₃	semidirect
110. C₂×C₃×C₅	C₂₃×D₂₁	direct (N × H)
113. C₂₃	C₂×C₃×C₅×D₂₁	direct (N × H)
115. C₃×C₇	C₂×C₅×D₃×C₂₃	semidirect
116. C₃×C₇	C₂²×C₃×C₅×C₂₃	semidirect
118. C₂×C₃²	C₅×D₇×C₂₃	semidirect
121. C₃×C₅	C₂×C₃×D₇×C₂₃	semidirect
122. C₃×C₅	C₂×C₂₃×D₂₁	direct (N × H)
123. C₂×C₇	C₃×C₅×D₃×C₂₃	semidirect
128. C₂×C₅	C₃×C₂₃×D₂₁	direct (N × H)
129. C₃²	C₂×C₅×D₇×C₂₃	semidirect
130. C₇	C₂×C₃×C₅×D₃×C₂₃	semidirect
133. C₂×C₃	C₃×C₅×D₇×C₂₃	semidirect
134. C₂×C₃	C₅×C₂₃×D₂₁	direct (N × H)
136. C₅	C₂×C₃×C₂₃×D₂₁	direct (N × H)
139. C₃	C₂×C₅×C₂₃×D₂₁	direct (N × H)
140. C₃	C₂×C₃×C₅×D₇×C₂₃	semidirect
142. C₂	C₃×C₅×C₂₃×D₂₁	direct (N × H)

H ≅ G/N

type

1. C₃×C₅×C₂₃×D₂₁

C₂

direct (N × H)

2. C₂×C₃²×C₅×C₇×C₂₃

C₂

semidirect

4. C₂×C₅×C₂₃×D₂₁

C₃

direct (N × H)

5. C₃²×C₅×C₇×C₂₃

C₂²

semidirect

6. C₂×C₃×C₂₃×D₂₁

C₅

direct (N × H)

7. C₅×C₂₃×D₂₁

C₂×C₃

direct (N × H)

10. C₂×C₃×C₅×C₇×C₂₃

D₃

semidirect

11. C₂×C₃×C₅×C₇×C₂₃

C₂×C₃

semidirect

14. C₃×C₂₃×D₂₁

C₂×C₅

direct (N × H)

15. C₂×C₃²×C₇×C₂₃

C₂×C₅

semidirect

17. C₃×C₅×C₇×C₂₃

C₂×D₃

semidirect

18. C₃×C₅×C₇×C₂₃

C₂²×C₃

semidirect

20. C₂×C₃²×C₅×C₂₃

D₇

semidirect

21. C₂×C₂₃×D₂₁

C₃×C₅

direct (N × H)

23. C₂×C₅×C₇×C₂₃

C₃×D₃

semidirect

25. C₃²×C₇×C₂₃

C₂²×C₅

semidirect

28. C₂×C₃×C₅×D₂₁

C₂₃

direct (N × H)

29. C₃²×C₅×C₂₃

C₂×D₇

semidirect

31. C₂×C₃×C₇×C₂₃

C₅×D₃

semidirect

32. C₂×C₃×C₇×C₂₃

C₂×C₃×C₅

semidirect

33. C₂₃×D₂₁

C₂×C₃×C₅

direct (N × H)

36. C₅×C₇×C₂₃

C₂×C₃×D₃

semidirect

39. C₂×C₃×C₅×C₂₃

C₃×D₇

semidirect

40. C₂×C₃×C₅×C₂₃

D₂₁

direct (N × H)

43. C₂×C₃²×C₅×C₇

C₂×C₂₃

semidirect

44. C₃×C₅×D₂₁

C₂×C₂₃

direct (N × H)

46. C₃×C₇×C₂₃

C₂×C₅×D₃

semidirect

47. C₃×C₇×C₂₃

C₂²×C₃×C₅

semidirect

49. C₂×C₅×D₂₁

C₃×C₂₃

direct (N × H)

51. C₂×C₃²×C₂₃

C₅×D₇

semidirect

54. C₃×C₅×C₂₃

C₂×C₃×D₇

semidirect

55. C₃×C₅×C₂₃

C₂×D₂₁

direct (N × H)

56. C₂×C₇×C₂₃

C₃×C₅×D₃

semidirect

58. C₃²×C₅×C₇

C₂²×C₂₃

semidirect

61. C₂×C₃×D₂₁

C₅×C₂₃

direct (N × H)

63. C₂×C₅×C₂₃

C₃×D₂₁

direct (N × H)

65. C₂×C₃×C₅×C₇

D₃×C₂₃

semidirect

66. C₂×C₃×C₅×C₇

C₂×C₃×C₂₃

semidirect

67. C₅×D₂₁

C₂×C₃×C₂₃

direct (N × H)

69. C₃²×C₂₃

C₂×C₅×D₇

semidirect

71. C₇×C₂₃

C₂×C₃×C₅×D₃

semidirect

75. C₂×C₃×C₂₃

C₃×C₅×D₇

semidirect

76. C₂×C₃×C₂₃

C₅×D₂₁

direct (N × H)

78. C₂×C₃²×C₇

C₂×C₅×C₂₃

semidirect

79. C₃×D₂₁

C₂×C₅×C₂₃

direct (N × H)

80. C₅×C₂₃

C₂×C₃×D₂₁

direct (N × H)

82. C₃×C₅×C₇

C₂×D₃×C₂₃

semidirect

83. C₃×C₅×C₇

C₂²×C₃×C₂₃

semidirect

85. C₂×C₃²×C₅

D₇×C₂₃

semidirect

87. C₂×D₂₁

C₃×C₅×C₂₃

direct (N × H)

89. C₂×C₅×C₇

C₃×D₃×C₂₃

semidirect

92. C₃×C₂₃

C₂×C₃×C₅×D₇

semidirect

93. C₃×C₂₃

C₂×C₅×D₂₁

direct (N × H)

94. C₃²×C₇

C₂²×C₅×C₂₃

semidirect

98. C₂×C₂₃

C₃×C₅×D₂₁

direct (N × H)

99. C₃²×C₅

C₂×D₇×C₂₃

semidirect

101. C₂×C₃×C₇

C₅×D₃×C₂₃

semidirect

102. C₂×C₃×C₇

C₂×C₃×C₅×C₂₃

semidirect

103. D₂₁

C₂×C₃×C₅×C₂₃

direct (N × H)

106. C₅×C₇

C₂×C₃×D₃×C₂₃

semidirect

109. C₂×C₃×C₅

C₃×D₇×C₂₃

semidirect

110. C₂×C₃×C₅

C₂₃×D₂₁

direct (N × H)

113. C₂₃

C₂×C₃×C₅×D₂₁

direct (N × H)

115. C₃×C₇

C₂×C₅×D₃×C₂₃

semidirect

116. C₃×C₇

C₂²×C₃×C₅×C₂₃

semidirect

118. C₂×C₃²

C₅×D₇×C₂₃

semidirect

121. C₃×C₅

C₂×C₃×D₇×C₂₃

semidirect

122. C₃×C₅

C₂×C₂₃×D₂₁

direct (N × H)

123. C₂×C₇

C₃×C₅×D₃×C₂₃

semidirect

128. C₂×C₅

C₃×C₂₃×D₂₁

direct (N × H)

129. C₃²

C₂×C₅×D₇×C₂₃

semidirect

130. C₇

C₂×C₃×C₅×D₃×C₂₃

semidirect

133. C₂×C₃

C₃×C₅×D₇×C₂₃

semidirect

134. C₂×C₃

C₅×C₂₃×D₂₁

direct (N × H)

136. C₅

C₂×C₃×C₂₃×D₂₁

direct (N × H)

139. C₃

C₂×C₅×C₂₃×D₂₁

direct (N × H)

140. C₃

C₂×C₃×C₅×D₇×C₂₃

semidirect

142. C₂

C₃×C₅×C₂₃×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×C₂₃×D₂₁	2
C₂×C₃²×C₅×C₇×C₂₃	2
C₂×C₃×C₅×D₇×C₂₃	3
C₂×C₅×C₂₃×D₂₁	3
C₂×C₃×C₂₃×D₂₁	5
C₂×C₃×C₅×D₃×C₂₃	7
C₂×C₃×C₅×D₂₁	23

subgroup

index

C₃×C₅×C₂₃×D₂₁

C₂×C₃²×C₅×C₇×C₂₃

C₂×C₃×C₅×D₇×C₂₃

C₂×C₅×C₂₃×D₂₁

C₂×C₃×C₂₃×D₂₁

C₂×C₃×C₅×D₃×C₂₃

C₂×C₃×C₅×D₂₁

Subgroups — C₂×C₃×C₅×C₂₃×D₂₁ #44394671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C5×C23×D21 #44394671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₂₃×D₂₁ #44394671