Group #30685828 — subgroups

Subgroups — C₂×C₃×C₅×D₅×C₁₉⋊C₃ #30685828

Order 17100.

288 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 112 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	C₂×C₃×C₅²×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₅×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅×D₅×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₅²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃×C₅×C₁₉⋊C₃	—	5	1	no	maximal
7	C₂×C₃×D₅×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₃×C₅×D₅×C₁₉	C₂×C₃	1	2	yes	complemented
9	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
10	C₅×D₅×C₁₉⋊C₃	C₂×C₃	1	6	yes	direct product factor
11	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₅×D₅×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅×C₁₉⋊C₃	—	2	2	no	—
14	C₂×C₃×C₅×C₁₉⋊C₃	—	5	2	no	—
15	C₂×C₃×C₅×C₁₉⋊C₃	D₅	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×D₅×C₁₉⋊C₃	C₂×C₅	1	2	yes	direct product factor
18	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₅²×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
20	C₂²×C₃×C₅×C₁₉	—	5	1	no	—
21	C₂×C₃×D₅×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented
22	C₂²×C₅×C₁₉⋊C₃	—	5	3	no	—
23	C₂×D₅×C₁₉⋊C₃	C₃×C₅	1	3	yes	direct product factor
24	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
25	C₅×D₅×C₁₉	C₂×C₃²	1	2	yes	complemented
26	C₂×C₃²×C₅×D₅	—	19	1	no	maximal, Hall
27	C₃×C₅×C₁₉⋊C₃	—	2	2	no	—
28	C₃×C₅×C₁₉⋊C₃	C₂×D₅	1	1	yes	characteristic, direct product factor
29	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented
30	C₂²×C₃×C₁₉⋊C₃	—	5	1	no	Hall
31	C₂×C₃×C₅×C₁₉	—	2	2	no	—
32	C₂×C₃×C₅×C₁₉	—	5	2	no	—
33	C₂×C₃×C₅×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
35	C₃×D₅×C₁₉	C₂×C₃×C₅	1	2	yes	complemented
36	C₂×C₅×C₁₉⋊C₃	—	2	6	no	—
37	C₂×C₅×C₁₉⋊C₃	—	5	6	no	—
38	C₂×C₅×C₁₉⋊C₃	C₃×D₅	1	3	yes	direct product factor
39	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	1	3	yes	complemented
40	D₅×C₁₉⋊C₃	C₂×C₃×C₅	1	6	yes	direct product factor
41	C₅²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃²×C₅²	—	19	1	no	—
43	C₃²×C₅×D₅	—	19	2	no	—
44	C₂²×C₅×C₁₉	—	5	1	no	—
45	C₂×D₅×C₁₉	C₃²×C₅	1	1	yes	characteristic, complemented
46	C₂×C₃×C₁₉⋊C₃	—	5	2	no	—
47	C₂×C₃×C₁₉⋊C₃	C₅×D₅	1	1	yes	characteristic, direct product factor
48	C₂×C₃×C₅×D₅	—	19	3	no	—
49	C₂×C₃×C₅×D₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
50	C₃×C₅×C₁₉	—	2	2	no	—
51	C₃×C₅×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
52	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
53	C₅×C₁₉⋊C₃	—	2	6	no	—
54	C₅×C₁₉⋊C₃	C₂×C₃×D₅	1	3	yes	direct product factor
55	C₅×C₁₉⋊C₃	C₂²×C₃×C₅	1	3	yes	complemented
56	C₂²×C₃×C₁₉	—	5	1	no	—
57	C₂²×C₁₉⋊C₃	—	5	3	no	—
58	C₃²×C₅²	—	19	1	no	Hall
59	C₂×C₅×C₁₉	—	2	2	no	—
60	C₂×C₅×C₁₉	—	5	2	no	—
61	C₂×C₅×C₁₉	C₃²×D₅	1	1	yes	characteristic, complemented
62	C₂×C₅×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
63	D₅×C₁₉	C₂×C₃²×C₅	1	2	yes	complemented
64	C₂²×C₃²×C₅	—	95	1	no	—
65	C₂×C₃²×D₅	—	19	1	no	—
66	C₃×C₁₉⋊C₃	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
67	C₂×C₃×C₅²	—	19	3	no	—
68	C₂×C₃×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
69	C₃×C₅×D₅	—	19	6	no	—
70	C₃×C₅×D₅	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
71	C₂×C₃×C₁₉	—	5	2	no	—
72	C₂×C₃×C₁₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented
73	C₂×C₁₉⋊C₃	—	5	6	no	—
74	C₂×C₁₉⋊C₃	C₃×C₅×D₅	1	3	yes	direct product factor
75	C₂×C₅×D₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
76	C₅×C₁₉	—	2	2	no	—
77	C₅×C₁₉	C₂×C₃²×D₅	1	1	yes	characteristic, complemented
78	C₅×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented
79	C₂×C₃²×C₅	—	19	1	no	—
80	C₂×C₃²×C₅	—	19	1	no	—
81	C₂×C₃²×C₅	—	38	2	no	—
82	C₂×C₃²×C₅	—	95	2	no	—
83	C₃²×D₅	—	19	2	no	—
84	C₂²×C₁₉	—	5	1	no	Hall
85	C₃×C₅²	—	19	3	no	—
86	C₃×C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
87	C₂²×C₃×C₅	—	5	1	no	—
88	C₂²×C₃×C₅	—	95	3	no	—
89	C₂×C₃×D₅	—	19	3	no	—
90	C₂×C₃×D₅	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
91	C₃×C₁₉	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented
92	C₁₉⋊C₃	C₂×C₃×C₅×D₅	1	3	yes	direct product factor
93	C₂×C₅²	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
94	C₅×D₅	C₂×C₃×C₁₉⋊C₃	1	2	yes	direct product factor
95	C₃²×C₅	—	19	1	no	—
96	C₃²×C₅	—	19	1	no	—
97	C₃²×C₅	—	38	2	no	—
98	C₂×C₁₉	—	5	2	no	—
99	C₂×C₁₉	C₃²×C₅×D₅	1	1	yes	characteristic, complemented
100	C₂²×C₃²	—	95	1	no	Hall
101	C₂×C₃×C₅	—	2	2	no	—
102	C₂×C₃×C₅	—	5	2	no	—
103	C₂×C₃×C₅	—	19	3	no	—
104	C₂×C₃×C₅	—	19	3	no	—
105	C₂×C₃×C₅	—	38	6	no	—
106	C₂×C₃×C₅	—	95	6	no	—
107	C₂×C₃×C₅	D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
108	C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
109	C₃×D₅	—	19	6	no	—
110	C₃×D₅	C₂×C₅×C₁₉⋊C₃	1	2	yes	direct product factor
111	C₅²	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
112	C₂²×C₅	—	5	1	no	—
113	C₂×D₅	C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
114	C₁₉	C₂×C₃²×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
115	C₂×C₃²	—	19	1	no	—
116	C₂×C₃²	—	95	2	no	—
117	C₃×C₅	—	2	2	no	—
118	C₃×C₅	—	19	3	no	—
119	C₃×C₅	—	19	3	no	—
120	C₃×C₅	—	38	6	no	—
121	C₃×C₅	C₂×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
122	C₃×C₅	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
123	C₂²×C₃	—	5	1	no	—
124	C₂²×C₃	—	95	3	no	—
125	C₂×C₅	—	2	2	no	—
126	C₂×C₅	—	5	2	no	—
127	C₂×C₅	C₃×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
128	C₂×C₅	C₂×C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
129	D₅	C₂×C₃×C₅×C₁₉⋊C₃	1	2	yes	direct product factor
130	C₃²	—	19	1	no	Sylow
131	C₂×C₃	—	5	2	no	—
132	C₂×C₃	—	19	3	no	—
133	C₂×C₃	—	95	6	no	—
134	C₂×C₃	C₅×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
135	C₅	—	2	2	no	—
136	C₅	C₂×C₃×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
137	C₅	C₂²×C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
138	C₂²	—	5	1	no	Sylow
139	C₃	—	19	3	no	—
140	C₃	C₂×C₅×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
141	C₂	—	5	2	no	—
142	C₂	C₃×C₅×D₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅²×C₁₉⋊C₃

C₂

yes

maximal, characteristic, complemented

C₃×C₅×D₅×C₁₉⋊C₃

C₂

yes

maximal, direct product factor

C₂×C₃×C₅×D₅×C₁₉

C₃

yes

maximal, characteristic, complemented

C₂×C₅×D₅×C₁₉⋊C₃

C₃

yes

maximal, direct product factor

C₃×C₅²×C₁₉⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂²×C₃×C₅×C₁₉⋊C₃

—

maximal

C₂×C₃×D₅×C₁₉⋊C₃

C₅

yes

maximal, characteristic, direct product factor

C₃×C₅×D₅×C₁₉

C₂×C₃

yes

complemented

C₂×C₅²×C₁₉⋊C₃

C₂×C₃

yes

complemented

C₅×D₅×C₁₉⋊C₃

C₂×C₃

yes

direct product factor

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₅×D₅×C₁₉

C₃²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₁₉⋊C₃

—

C₂×C₃×C₅×C₁₉⋊C₃

—

C₂×C₃×C₅×C₁₉⋊C₃

D₅

yes

characteristic, direct product factor

C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

yes

characteristic, complemented

C₃×D₅×C₁₉⋊C₃

C₂×C₅

yes

direct product factor

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₅²×C₁₉⋊C₃

C₂²×C₃

yes

complemented

C₂²×C₃×C₅×C₁₉

—

C₂×C₃×D₅×C₁₉

C₃×C₅

yes

characteristic, complemented

C₂²×C₅×C₁₉⋊C₃

—

C₂×D₅×C₁₉⋊C₃

C₃×C₅

yes

direct product factor

C₂×C₅²×C₁₉

C₂×C₃²

yes

characteristic, complemented

C₅×D₅×C₁₉

C₂×C₃²

yes

complemented

C₂×C₃²×C₅×D₅

—

maximal, Hall

C₃×C₅×C₁₉⋊C₃

—

C₃×C₅×C₁₉⋊C₃

C₂×D₅

yes

characteristic, direct product factor

C₃×C₅×C₁₉⋊C₃

C₂²×C₅

yes

characteristic, complemented

C₂²×C₃×C₁₉⋊C₃

—

Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₃×D₅

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

characteristic, complemented

C₃×D₅×C₁₉

C₂×C₃×C₅

yes

complemented

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

C₃×D₅

yes

direct product factor

C₂×C₅×C₁₉⋊C₃

C₂×C₃×C₅

yes

complemented

D₅×C₁₉⋊C₃

C₂×C₃×C₅

yes

direct product factor

C₅²×C₁₉

C₂²×C₃²

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

—

C₃²×C₅×D₅

—

C₂²×C₅×C₁₉

—

C₂×D₅×C₁₉

C₃²×C₅

yes

characteristic, complemented

C₂×C₃×C₁₉⋊C₃

—

C₂×C₃×C₁₉⋊C₃

C₅×D₅

yes

characteristic, direct product factor

C₂×C₃×C₅×D₅

—

C₂×C₃×C₅×D₅

C₁₉⋊C₃

yes

characteristic, direct product factor

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₃×D₅

yes

characteristic, complemented

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

characteristic, complemented

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

C₂×C₃×D₅

yes

direct product factor

C₅×C₁₉⋊C₃

C₂²×C₃×C₅

yes

complemented

C₂²×C₃×C₁₉

—

C₂²×C₁₉⋊C₃

—

C₃²×C₅²

—

Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃²×D₅

yes

characteristic, complemented

C₂×C₅×C₁₉

C₂×C₃²×C₅

yes

characteristic, complemented

D₅×C₁₉

C₂×C₃²×C₅

yes

complemented

C₂²×C₃²×C₅

—

C₂×C₃²×D₅

—

C₃×C₁₉⋊C₃

C₂×C₅×D₅

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅²

—

C₂×C₃×C₅²

C₂×C₁₉⋊C₃

yes

characteristic, complemented

C₃×C₅×D₅

—

C₃×C₅×D₅

C₂×C₁₉⋊C₃

yes

direct product factor

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₃×C₅×D₅

yes

characteristic, complemented

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

C₃×C₅×D₅

yes

direct product factor

C₂×C₅×D₅

C₃×C₁₉⋊C₃

yes

characteristic, direct product factor, Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₃²×D₅

yes

characteristic, complemented

C₅×C₁₉

C₂²×C₃²×C₅

yes

characteristic, complemented

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₃²×D₅

—

C₂²×C₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

C₂²×C₁₉⋊C₃

yes

characteristic, complemented

C₂²×C₃×C₅

—

C₂²×C₃×C₅

—

C₂×C₃×D₅

—

C₂×C₃×D₅

C₅×C₁₉⋊C₃

yes

characteristic, direct product factor

C₃×C₁₉

C₂×C₃×C₅×D₅

yes

characteristic, complemented

C₁₉⋊C₃

C₂×C₃×C₅×D₅

yes

direct product factor

C₂×C₅²

C₂×C₃×C₁₉⋊C₃

yes

characteristic, complemented

C₅×D₅

C₂×C₃×C₁₉⋊C₃

yes

direct product factor

C₃²×C₅

—

C₃²×C₅

—

C₃²×C₅

—

C₂×C₁₉

—

C₂×C₁₉

C₃²×C₅×D₅

yes

characteristic, complemented

100

C₂²×C₃²

—

Hall

101

C₂×C₃×C₅

—

102

C₂×C₃×C₅

—

103

C₂×C₃×C₅

—

104

C₂×C₃×C₅

—

105

C₂×C₃×C₅

—

106

C₂×C₃×C₅

—

107

C₂×C₃×C₅

D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

108

C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

yes

characteristic, complemented

109

C₃×D₅

—

110

C₃×D₅

C₂×C₅×C₁₉⋊C₃

yes

direct product factor

111

C₅²

C₂²×C₃×C₁₉⋊C₃

yes

characteristic, complemented, Sylow

112

C₂²×C₅

—

113

C₂×D₅

C₃×C₅×C₁₉⋊C₃

yes

characteristic, direct product factor

114

C₁₉

C₂×C₃²×C₅×D₅

yes

characteristic, complemented, Sylow

115

C₂×C₃²

—

116

C₂×C₃²

—

117

C₃×C₅

—

118

C₃×C₅

—

119

C₃×C₅

—

120

C₃×C₅

—

121

C₃×C₅

C₂×D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

122

C₃×C₅

C₂²×C₅×C₁₉⋊C₃

yes

characteristic, complemented

123

C₂²×C₃

—

124

C₂²×C₃

—

125

C₂×C₅

—

126

C₂×C₅

—

127

C₂×C₅

C₃×D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

128

C₂×C₅

C₂×C₃×C₅×C₁₉⋊C₃

yes

characteristic, complemented

129

D₅

C₂×C₃×C₅×C₁₉⋊C₃

yes

direct product factor

130

C₃²

—

Sylow

131

C₂×C₃

—

132

C₂×C₃

—

133

C₂×C₃

—

134

C₂×C₃

C₅×D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

135

C₅

—

136

C₅

C₂×C₃×D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

137

C₅

C₂²×C₃×C₅×C₁₉⋊C₃

yes

characteristic, complemented

138

C₂²

—

Sylow

139

C₃

—

140

C₃

C₂×C₅×D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

141

C₂

—

142

C₂

C₃×C₅×D₅×C₁₉⋊C₃

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅

subgroup

G/H

center, hypercenter

C₂×C₃×C₅

D₅×C₁₉⋊C₃

commutator, cosocle, hypocenter

C₅×C₁₉

C₂²×C₃²×C₅

Frattini

C₁

Fitting, socle

C₂×C₃×C₅²×C₁₉

C₂×C₃

LCS

G ▷ C₅×C₁₉

UCS

C₁ ◁ C₂×C₃×C₅

N	H ≅ G/N	type
1. C₂×C₃×C₅²×C₁₉⋊C₃	C₂	semidirect
2. C₃×C₅×D₅×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₅×D₅×C₁₉	C₃	semidirect
4. C₂×C₅×D₅×C₁₉⋊C₃	C₃	direct (N × H)
5. C₃×C₅²×C₁₉⋊C₃	C₂²	semidirect
7. C₂×C₃×D₅×C₁₉⋊C₃	C₅	direct (N × H)
8. C₃×C₅×D₅×C₁₉	C₂×C₃	semidirect
9. C₂×C₅²×C₁₉⋊C₃	C₂×C₃	semidirect
10. C₅×D₅×C₁₉⋊C₃	C₂×C₃	direct (N × H)
11. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
12. C₂×C₅×D₅×C₁₉	C₃²	semidirect
15. C₂×C₃×C₅×C₁₉⋊C₃	D₅	direct (N × H)
16. C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	semidirect
17. C₃×D₅×C₁₉⋊C₃	C₂×C₅	direct (N × H)
18. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
19. C₅²×C₁₉⋊C₃	C₂²×C₃	semidirect
21. C₂×C₃×D₅×C₁₉	C₃×C₅	semidirect
23. C₂×D₅×C₁₉⋊C₃	C₃×C₅	direct (N × H)
24. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
25. C₅×D₅×C₁₉	C₂×C₃²	semidirect
28. C₃×C₅×C₁₉⋊C₃	C₂×D₅	direct (N × H)
29. C₃×C₅×C₁₉⋊C₃	C₂²×C₅	semidirect
33. C₂×C₃×C₅×C₁₉	C₃×D₅	semidirect
34. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
35. C₃×D₅×C₁₉	C₂×C₃×C₅	semidirect
38. C₂×C₅×C₁₉⋊C₃	C₃×D₅	direct (N × H)
39. C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
40. D₅×C₁₉⋊C₃	C₂×C₃×C₅	direct (N × H)
41. C₅²×C₁₉	C₂²×C₃²	semidirect
45. C₂×D₅×C₁₉	C₃²×C₅	semidirect
47. C₂×C₃×C₁₉⋊C₃	C₅×D₅	direct (N × H)
49. C₂×C₃×C₅×D₅	C₁₉⋊C₃	direct (N × H)
51. C₃×C₅×C₁₉	C₂×C₃×D₅	semidirect
52. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
54. C₅×C₁₉⋊C₃	C₂×C₃×D₅	direct (N × H)
55. C₅×C₁₉⋊C₃	C₂²×C₃×C₅	semidirect
61. C₂×C₅×C₁₉	C₃²×D₅	semidirect
62. C₂×C₅×C₁₉	C₂×C₃²×C₅	semidirect
63. D₅×C₁₉	C₂×C₃²×C₅	semidirect
66. C₃×C₁₉⋊C₃	C₂×C₅×D₅	direct (N × H)
68. C₂×C₃×C₅²	C₂×C₁₉⋊C₃	semidirect
70. C₃×C₅×D₅	C₂×C₁₉⋊C₃	direct (N × H)
72. C₂×C₃×C₁₉	C₃×C₅×D₅	semidirect
74. C₂×C₁₉⋊C₃	C₃×C₅×D₅	direct (N × H)
75. C₂×C₅×D₅	C₃×C₁₉⋊C₃	direct (N × H)
77. C₅×C₁₉	C₂×C₃²×D₅	semidirect
78. C₅×C₁₉	C₂²×C₃²×C₅	semidirect
86. C₃×C₅²	C₂²×C₁₉⋊C₃	semidirect
90. C₂×C₃×D₅	C₅×C₁₉⋊C₃	direct (N × H)
91. C₃×C₁₉	C₂×C₃×C₅×D₅	semidirect
92. C₁₉⋊C₃	C₂×C₃×C₅×D₅	direct (N × H)
93. C₂×C₅²	C₂×C₃×C₁₉⋊C₃	semidirect
94. C₅×D₅	C₂×C₃×C₁₉⋊C₃	direct (N × H)
99. C₂×C₁₉	C₃²×C₅×D₅	semidirect
107. C₂×C₃×C₅	D₅×C₁₉⋊C₃	direct (N × H)
108. C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	semidirect
110. C₃×D₅	C₂×C₅×C₁₉⋊C₃	direct (N × H)
111. C₅²	C₂²×C₃×C₁₉⋊C₃	semidirect
113. C₂×D₅	C₃×C₅×C₁₉⋊C₃	direct (N × H)
114. C₁₉	C₂×C₃²×C₅×D₅	semidirect
121. C₃×C₅	C₂×D₅×C₁₉⋊C₃	direct (N × H)
122. C₃×C₅	C₂²×C₅×C₁₉⋊C₃	semidirect
127. C₂×C₅	C₃×D₅×C₁₉⋊C₃	direct (N × H)
128. C₂×C₅	C₂×C₃×C₅×C₁₉⋊C₃	semidirect
129. D₅	C₂×C₃×C₅×C₁₉⋊C₃	direct (N × H)
134. C₂×C₃	C₅×D₅×C₁₉⋊C₃	direct (N × H)
136. C₅	C₂×C₃×D₅×C₁₉⋊C₃	direct (N × H)
137. C₅	C₂²×C₃×C₅×C₁₉⋊C₃	semidirect
140. C₃	C₂×C₅×D₅×C₁₉⋊C₃	direct (N × H)
142. C₂	C₃×C₅×D₅×C₁₉⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₂×C₃×C₅²×C₁₉⋊C₃

C₂

semidirect

2. C₃×C₅×D₅×C₁₉⋊C₃

C₂

direct (N × H)

3. C₂×C₃×C₅×D₅×C₁₉

C₃

semidirect

4. C₂×C₅×D₅×C₁₉⋊C₃

C₃

direct (N × H)

5. C₃×C₅²×C₁₉⋊C₃

C₂²

semidirect

7. C₂×C₃×D₅×C₁₉⋊C₃

C₅

direct (N × H)

8. C₃×C₅×D₅×C₁₉

C₂×C₃

semidirect

9. C₂×C₅²×C₁₉⋊C₃

C₂×C₃

semidirect

10. C₅×D₅×C₁₉⋊C₃

C₂×C₃

direct (N × H)

11. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

12. C₂×C₅×D₅×C₁₉

C₃²

semidirect

15. C₂×C₃×C₅×C₁₉⋊C₃

D₅

direct (N × H)

16. C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

semidirect

17. C₃×D₅×C₁₉⋊C₃

C₂×C₅

direct (N × H)

18. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

19. C₅²×C₁₉⋊C₃

C₂²×C₃

semidirect

21. C₂×C₃×D₅×C₁₉

C₃×C₅

semidirect

23. C₂×D₅×C₁₉⋊C₃

C₃×C₅

direct (N × H)

24. C₂×C₅²×C₁₉

C₂×C₃²

semidirect

25. C₅×D₅×C₁₉

C₂×C₃²

semidirect

28. C₃×C₅×C₁₉⋊C₃

C₂×D₅

direct (N × H)

29. C₃×C₅×C₁₉⋊C₃

C₂²×C₅

semidirect

33. C₂×C₃×C₅×C₁₉

C₃×D₅

semidirect

34. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

35. C₃×D₅×C₁₉

C₂×C₃×C₅

semidirect

38. C₂×C₅×C₁₉⋊C₃

C₃×D₅

direct (N × H)

39. C₂×C₅×C₁₉⋊C₃

C₂×C₃×C₅

semidirect

40. D₅×C₁₉⋊C₃

C₂×C₃×C₅

direct (N × H)

41. C₅²×C₁₉

C₂²×C₃²

semidirect

45. C₂×D₅×C₁₉

C₃²×C₅

semidirect

47. C₂×C₃×C₁₉⋊C₃

C₅×D₅

direct (N × H)

49. C₂×C₃×C₅×D₅

C₁₉⋊C₃

direct (N × H)

51. C₃×C₅×C₁₉

C₂×C₃×D₅

semidirect

52. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

54. C₅×C₁₉⋊C₃

C₂×C₃×D₅

direct (N × H)

55. C₅×C₁₉⋊C₃

C₂²×C₃×C₅

semidirect

61. C₂×C₅×C₁₉

C₃²×D₅

semidirect

62. C₂×C₅×C₁₉

C₂×C₃²×C₅

semidirect

63. D₅×C₁₉

C₂×C₃²×C₅

semidirect

66. C₃×C₁₉⋊C₃

C₂×C₅×D₅

direct (N × H)

68. C₂×C₃×C₅²

C₂×C₁₉⋊C₃

semidirect

70. C₃×C₅×D₅

C₂×C₁₉⋊C₃

direct (N × H)

72. C₂×C₃×C₁₉

C₃×C₅×D₅

semidirect

74. C₂×C₁₉⋊C₃

C₃×C₅×D₅

direct (N × H)

75. C₂×C₅×D₅

C₃×C₁₉⋊C₃

direct (N × H)

77. C₅×C₁₉

C₂×C₃²×D₅

semidirect

78. C₅×C₁₉

C₂²×C₃²×C₅

semidirect

86. C₃×C₅²

C₂²×C₁₉⋊C₃

semidirect

90. C₂×C₃×D₅

C₅×C₁₉⋊C₃

direct (N × H)

91. C₃×C₁₉

C₂×C₃×C₅×D₅

semidirect

92. C₁₉⋊C₃

C₂×C₃×C₅×D₅

direct (N × H)

93. C₂×C₅²

C₂×C₃×C₁₉⋊C₃

semidirect

94. C₅×D₅

C₂×C₃×C₁₉⋊C₃

direct (N × H)

99. C₂×C₁₉

C₃²×C₅×D₅

semidirect

107. C₂×C₃×C₅

D₅×C₁₉⋊C₃

direct (N × H)

108. C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

semidirect

110. C₃×D₅

C₂×C₅×C₁₉⋊C₃

direct (N × H)

111. C₅²

C₂²×C₃×C₁₉⋊C₃

semidirect

113. C₂×D₅

C₃×C₅×C₁₉⋊C₃

direct (N × H)

114. C₁₉

C₂×C₃²×C₅×D₅

semidirect

121. C₃×C₅

C₂×D₅×C₁₉⋊C₃

direct (N × H)

122. C₃×C₅

C₂²×C₅×C₁₉⋊C₃

semidirect

127. C₂×C₅

C₃×D₅×C₁₉⋊C₃

direct (N × H)

128. C₂×C₅

C₂×C₃×C₅×C₁₉⋊C₃

semidirect

129. D₅

C₂×C₃×C₅×C₁₉⋊C₃

direct (N × H)

134. C₂×C₃

C₅×D₅×C₁₉⋊C₃

direct (N × H)

136. C₅

C₂×C₃×D₅×C₁₉⋊C₃

direct (N × H)

137. C₅

C₂²×C₃×C₅×C₁₉⋊C₃

semidirect

140. C₃

C₂×C₅×D₅×C₁₉⋊C₃

direct (N × H)

142. C₂

C₃×C₅×D₅×C₁₉⋊C₃

direct (N × H)

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

subgroup	index
C₂×C₃×C₅²×C₁₉⋊C₃	2
C₃×C₅×D₅×C₁₉⋊C₃	2
C₂×C₃×C₅×D₅×C₁₉	3
C₂×C₅×D₅×C₁₉⋊C₃	3
C₂²×C₃×C₅×C₁₉⋊C₃	5
C₂×C₃×D₅×C₁₉⋊C₃	5
C₂×C₃²×C₅×D₅	19

subgroup

index

C₂×C₃×C₅²×C₁₉⋊C₃

C₃×C₅×D₅×C₁₉⋊C₃

C₂×C₃×C₅×D₅×C₁₉

C₂×C₅×D₅×C₁₉⋊C₃

C₂²×C₃×C₅×C₁₉⋊C₃

C₂×C₃×D₅×C₁₉⋊C₃

C₂×C₃²×C₅×D₅

Subgroups — C₂×C₃×C₅×D₅×C₁₉⋊C₃ #30685828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C5×D5×C19⋊C3 #30685828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×D₅×C₁₉⋊C₃ #30685828