Group #30685842 — subgroups

Subgroups — C₂×C₅×D₁₅×C₁₉⋊C₃ #30685842

Order 17100.

224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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	C₅×D₁₅×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₉×D₁₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅×C₁₉⋊C₃	—	3	1	no	maximal
5	C₃×C₅²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₅×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅×D₃×C₁₉⋊C₃	—	5	1	no	maximal
8	C₅×C₁₉×D₁₅	C₂×C₃	1	2	yes	complemented
9	C₂×C₅²×C₁₉⋊C₃	—	2	1	no	—
10	C₂×C₅²×C₁₉⋊C₃	D₃	1	1	yes	characteristic, complemented
11	C₅×D₅×C₁₉⋊C₃	—	3	2	no	—
12	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₅×D₅×C₁₉	—	3	1	no	Hall
14	C₂×C₃×C₅×C₁₉⋊C₃	—	2	2	no	—
15	C₂×C₃×C₅×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
17	D₁₅×C₁₉⋊C₃	C₂×C₅	1	2	yes	direct product factor
18	C₅×D₃×C₁₉⋊C₃	—	5	2	no	—
19	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
20	C₅²×C₁₉⋊C₃	—	2	1	no	—
21	C₅²×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×C₁₉×D₁₅	C₃×C₅	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×C₁₉	—	5	1	no	—
24	C₂²×C₅×C₁₉⋊C₃	—	15	1	no	—
25	C₂×D₅×C₁₉⋊C₃	—	3	1	no	—
26	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
27	C₅×D₅×C₁₉	—	3	2	no	—
28	C₂×C₃×C₅×D₁₅	—	19	1	no	maximal, Hall
29	C₃×C₅×C₁₉⋊C₃	—	2	2	no	—
30	C₃×C₅×C₁₉⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented
31	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented
32	C₂×D₃×C₁₉⋊C₃	—	5	1	no	Hall
33	C₂×C₃×C₅×C₁₉	—	2	2	no	—
34	C₂×C₃×C₅×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
36	C₁₉×D₁₅	C₂×C₃×C₅	1	2	yes	complemented
37	C₅×D₃×C₁₉	—	5	2	no	—
38	C₂×C₅×C₁₉⋊C₃	—	2	4	no	—
39	C₂×C₅×C₁₉⋊C₃	—	2	2	no	—
40	C₂×C₅×C₁₉⋊C₃	—	2	1	no	—
41	C₂×C₅×C₁₉⋊C₃	—	2	1	no	—
42	C₂×C₅×C₁₉⋊C₃	—	15	2	no	—
43	C₂×C₅×C₁₉⋊C₃	C₅×D₃	1	1	yes	characteristic, complemented
44	C₂×C₅×C₁₉⋊C₃	D₁₅	1	1	yes	characteristic, direct product factor
45	D₅×C₁₉⋊C₃	—	3	2	no	—
46	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃²×C₅²	—	19	1	no	—
48	C₃×C₅×D₁₅	—	19	2	no	—
49	C₂²×C₅×C₁₉	—	15	1	no	—
50	C₂×D₅×C₁₉	—	3	1	no	—
51	C₂×C₃×C₁₉⋊C₃	C₅×D₅	1	1	yes	characteristic, complemented
52	D₃×C₁₉⋊C₃	—	5	2	no	—
53	C₂×C₅×D₁₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
54	C₂×C₃×C₅×D₅	—	57	1	no	—
55	C₃×C₅×C₁₉	—	2	2	no	—
56	C₃×C₅×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
57	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
58	C₅×C₁₉⋊C₃	—	2	4	no	—
59	C₅×C₁₉⋊C₃	—	2	2	no	—
60	C₅×C₁₉⋊C₃	—	2	1	no	—
61	C₅×C₁₉⋊C₃	—	2	1	no	—
62	C₅×C₁₉⋊C₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
63	C₅×C₁₉⋊C₃	C₂×D₁₅	1	1	yes	characteristic, direct product factor
64	C₂×D₃×C₁₉	—	5	1	no	—
65	C₂²×C₁₉⋊C₃	—	15	1	no	—
66	C₃²×C₅²	—	19	1	no	Hall
67	C₂×C₅×C₁₉	—	2	2	no	—
68	C₂×C₅×C₁₉	—	15	2	no	—
69	C₂×C₅×C₁₉	C₃×C₅×D₃	1	1	yes	characteristic, complemented
70	C₂×C₅×C₁₉	C₃×D₁₅	1	1	yes	characteristic, complemented
71	D₅×C₁₉	—	3	2	no	—
72	C₂×C₃×D₁₅	—	19	1	no	—
73	C₂×C₃×C₅×D₃	—	95	1	no	—
74	C₃×C₁₉⋊C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
75	C₂×C₃×C₅²	—	19	1	no	—
76	C₂×C₃×C₅²	—	38	1	no	—
77	C₂×C₃×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
78	C₅×D₁₅	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
79	C₃×C₅×D₅	—	57	2	no	—
80	C₂×C₃×C₁₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented
81	D₃×C₁₉	—	5	2	no	—
82	C₂×C₁₉⋊C₃	—	2	1	no	—
83	C₂×C₁₉⋊C₃	—	15	2	no	—
84	C₂×C₁₉⋊C₃	C₅×D₁₅	1	1	yes	characteristic, direct product factor
85	C₂×C₅×D₅	—	3	1	no	Hall
86	C₅×C₁₉	—	2	2	no	—
87	C₅×C₁₉	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented
88	C₅×C₁₉	C₂×C₃×D₁₅	1	1	yes	characteristic, complemented
89	C₂×C₃²×C₅	—	19	1	no	—
90	C₂×C₃²×C₅	—	19	1	no	—
91	C₂×C₃²×C₅	—	38	2	no	—
92	C₃×D₁₅	—	19	2	no	—
93	C₃×C₅×D₃	—	95	2	no	—
94	C₂²×C₁₉	—	15	1	no	Hall
95	C₃×C₅²	—	19	1	no	—
96	C₃×C₅²	—	38	1	no	—
97	C₃×C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
98	C₂²×C₃×C₅	—	285	1	no	—
99	C₂×D₁₅	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
100	C₂×C₅×D₃	—	5	1	no	—
101	C₂×C₃×D₅	—	57	1	no	—
102	C₃×C₁₉	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented
103	C₁₉⋊C₃	—	2	1	no	—
104	C₁₉⋊C₃	C₂×C₅×D₁₅	1	1	yes	characteristic, direct product factor
105	C₂×C₅²	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
106	C₅×D₅	—	3	2	no	—
107	C₃²×C₅	—	19	1	no	—
108	C₃²×C₅	—	19	1	no	—
109	C₃²×C₅	—	38	2	no	—
110	C₂×C₁₉	—	15	2	no	—
111	C₂×C₁₉	C₃×C₅×D₁₅	1	1	yes	characteristic, complemented
112	C₂×C₃×D₃	—	95	1	no	Hall
113	C₂×C₃×C₅	—	2	2	no	—
114	C₂×C₃×C₅	—	19	1	no	—
115	C₂×C₃×C₅	—	19	1	no	—
116	C₂×C₃×C₅	—	285	2	no	—
117	C₂×C₃×C₅	—	38	2	no	—
118	C₂×C₃×C₅	—	38	4	no	—
119	C₂×C₃×C₅	—	38	1	no	—
120	C₂×C₃×C₅	—	38	1	no	—
121	C₂×C₃×C₅	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
122	C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
123	D₁₅	C₂×C₅×C₁₉⋊C₃	1	2	yes	direct product factor
124	C₃×D₅	—	57	2	no	—
125	C₅×D₃	—	5	2	no	—
126	C₅²	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
127	C₂²×C₅	—	15	1	no	—
128	C₂×D₅	—	3	1	no	—
129	C₁₉	C₂×C₃×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
130	C₂×C₃²	—	19	1	no	—
131	C₃×D₃	—	95	2	no	—
132	C₃×C₅	—	2	2	no	—
133	C₃×C₅	—	19	1	no	—
134	C₃×C₅	—	19	1	no	—
135	C₃×C₅	—	38	2	no	—
136	C₃×C₅	—	38	4	no	—
137	C₃×C₅	—	38	1	no	—
138	C₃×C₅	—	38	1	no	—
139	C₃×C₅	C₂×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
140	C₃×C₅	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
141	C₂²×C₃	—	285	1	no	—
142	C₂×D₃	—	5	1	no	—
143	C₂×C₅	—	2	2	no	—
144	C₂×C₅	—	15	2	no	—
145	C₂×C₅	C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
146	C₂×C₅	D₁₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
147	D₅	—	3	2	no	—
148	C₃²	—	19	1	no	Sylow
149	C₂×C₃	—	19	1	no	—
150	C₂×C₃	—	285	2	no	—
151	C₂×C₃	—	38	1	no	—
152	C₂×C₃	C₅×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
153	D₃	—	5	2	no	—
154	C₅	—	2	2	no	—
155	C₅	C₂×C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
156	C₅	C₂×D₁₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
157	C₂²	—	15	1	no	Sylow
158	C₃	—	19	1	no	—
159	C₃	—	38	1	no	—
160	C₃	C₂×C₅×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
161	C₂	—	15	2	no	—
162	C₂	C₅×D₁₅×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

C₅×D₁₅×C₁₉⋊C₃

C₂

yes

maximal, direct product factor

C₂×C₅×C₁₉×D₁₅

C₃

yes

maximal, characteristic, complemented

C₂×C₅×D₅×C₁₉⋊C₃

—

maximal

C₃×C₅²×C₁₉⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂×D₁₅×C₁₉⋊C₃

C₅

yes

maximal, characteristic, direct product factor

C₂×C₅×D₃×C₁₉⋊C₃

—

maximal

C₅×C₁₉×D₁₅

C₂×C₃

yes

complemented

C₂×C₅²×C₁₉⋊C₃

—

C₂×C₅²×C₁₉⋊C₃

D₃

yes

characteristic, complemented

C₅×D₅×C₁₉⋊C₃

—

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₅×D₅×C₁₉

—

Hall

C₂×C₃×C₅×C₁₉⋊C₃

—

C₂×C₃×C₅×C₁₉⋊C₃

D₅

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

yes

characteristic, complemented

D₁₅×C₁₉⋊C₃

C₂×C₅

yes

direct product factor

C₅×D₃×C₁₉⋊C₃

—

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₅²×C₁₉⋊C₃

—

C₅²×C₁₉⋊C₃

C₂×D₃

yes

characteristic, complemented

C₂×C₁₉×D₁₅

C₃×C₅

yes

characteristic, complemented

C₂×C₅×D₃×C₁₉

—

C₂²×C₅×C₁₉⋊C₃

—

C₂×D₅×C₁₉⋊C₃

—

C₂×C₅²×C₁₉

C₃×D₃

yes

characteristic, complemented

C₅×D₅×C₁₉

—

C₂×C₃×C₅×D₁₅

—

maximal, Hall

C₃×C₅×C₁₉⋊C₃

—

C₃×C₅×C₁₉⋊C₃

C₂×D₅

yes

characteristic, complemented

C₃×C₅×C₁₉⋊C₃

C₂²×C₅

yes

characteristic, complemented

C₂×D₃×C₁₉⋊C₃

—

Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₃×D₅

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

characteristic, complemented

C₁₉×D₁₅

C₂×C₃×C₅

yes

complemented

C₅×D₃×C₁₉

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

C₅×D₃

yes

characteristic, complemented

C₂×C₅×C₁₉⋊C₃

D₁₅

yes

characteristic, direct product factor

D₅×C₁₉⋊C₃

—

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

—

C₃×C₅×D₁₅

—

C₂²×C₅×C₁₉

—

C₂×D₅×C₁₉

—

C₂×C₃×C₁₉⋊C₃

C₅×D₅

yes

characteristic, complemented

D₃×C₁₉⋊C₃

—

C₂×C₅×D₁₅

C₁₉⋊C₃

yes

characteristic, direct product factor

C₂×C₃×C₅×D₅

—

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

—

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

C₂×C₅×D₃

yes

characteristic, complemented

C₅×C₁₉⋊C₃

C₂×D₁₅

yes

characteristic, direct product factor

C₂×D₃×C₁₉

—

C₂²×C₁₉⋊C₃

—

C₃²×C₅²

—

Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×C₅×D₃

yes

characteristic, complemented

C₂×C₅×C₁₉

C₃×D₁₅

yes

characteristic, complemented

D₅×C₁₉

—

C₂×C₃×D₁₅

—

C₂×C₃×C₅×D₃

—

C₃×C₁₉⋊C₃

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₂×C₃×C₅²

—

C₂×C₃×C₅²

C₂×C₁₉⋊C₃

yes

characteristic, complemented

C₅×D₁₅

C₂×C₁₉⋊C₃

yes

direct product factor

C₃×C₅×D₅

—

C₂×C₃×C₁₉

C₃×C₅×D₅

yes

characteristic, complemented

D₃×C₁₉

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

C₅×D₁₅

yes

characteristic, direct product factor

C₂×C₅×D₅

—

Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₃×C₅×D₃

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃×D₁₅

yes

characteristic, complemented

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₃×D₁₅

—

C₃×C₅×D₃

—

C₂²×C₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

—

C₃×C₅²

C₂²×C₁₉⋊C₃

yes

characteristic, complemented

C₂²×C₃×C₅

—

285

—

C₂×D₁₅

C₅×C₁₉⋊C₃

yes

characteristic, direct product factor

100

C₂×C₅×D₃

—

101

C₂×C₃×D₅

—

102

C₃×C₁₉

C₂×C₃×C₅×D₅

yes

characteristic, complemented

103

C₁₉⋊C₃

—

104

C₁₉⋊C₃

C₂×C₅×D₁₅

yes

characteristic, direct product factor

105

C₂×C₅²

D₃×C₁₉⋊C₃

yes

characteristic, complemented

106

C₅×D₅

—

107

C₃²×C₅

—

108

C₃²×C₅

—

109

C₃²×C₅

—

110

C₂×C₁₉

—

111

C₂×C₁₉

C₃×C₅×D₁₅

yes

characteristic, complemented

112

C₂×C₃×D₃

—

Hall

113

C₂×C₃×C₅

—

114

C₂×C₃×C₅

—

115

C₂×C₃×C₅

—

116

C₂×C₃×C₅

—

285

—

117

C₂×C₃×C₅

—

118

C₂×C₃×C₅

—

119

C₂×C₃×C₅

—

120

C₂×C₃×C₅

—

121

C₂×C₃×C₅

D₅×C₁₉⋊C₃

yes

characteristic, complemented

122

C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

yes

characteristic, complemented

123

D₁₅

C₂×C₅×C₁₉⋊C₃

yes

direct product factor

124

C₃×D₅

—

125

C₅×D₃

—

126

C₅²

C₂×D₃×C₁₉⋊C₃

yes

characteristic, complemented, Sylow

127

C₂²×C₅

—

128

C₂×D₅

—

129

C₁₉

C₂×C₃×C₅×D₁₅

yes

characteristic, complemented, Sylow

130

C₂×C₃²

—

131

C₃×D₃

—

132

C₃×C₅

—

133

C₃×C₅

—

134

C₃×C₅

—

135

C₃×C₅

—

136

C₃×C₅

—

137

C₃×C₅

—

138

C₃×C₅

—

139

C₃×C₅

C₂×D₅×C₁₉⋊C₃

yes

characteristic, complemented

140

C₃×C₅

C₂²×C₅×C₁₉⋊C₃

yes

characteristic, complemented

141

C₂²×C₃

—

285

—

142

C₂×D₃

—

143

C₂×C₅

—

144

C₂×C₅

—

145

C₂×C₅

C₅×D₃×C₁₉⋊C₃

yes

characteristic, complemented

146

C₂×C₅

D₁₅×C₁₉⋊C₃

yes

characteristic, direct product factor

147

D₅

—

148

C₃²

—

Sylow

149

C₂×C₃

—

150

C₂×C₃

—

285

—

151

C₂×C₃

—

152

C₂×C₃

C₅×D₅×C₁₉⋊C₃

yes

characteristic, complemented

153

D₃

—

154

C₅

—

155

C₅

C₂×C₅×D₃×C₁₉⋊C₃

yes

characteristic, complemented

156

C₅

C₂×D₁₅×C₁₉⋊C₃

yes

characteristic, direct product factor

157

C₂²

—

Sylow

158

C₃

—

159

C₃

—

160

C₃

C₂×C₅×D₅×C₁₉⋊C₃

yes

characteristic, complemented

161

C₂

—

162

C₂

C₅×D₁₅×C₁₉⋊C₃

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₂×C₅

subgroup

G/H

center, hypercenter

C₂×C₅

D₁₅×C₁₉⋊C₃

commutator, cosocle, hypocenter

C₃×C₅×C₁₉

C₂²×C₃×C₅

Frattini

C₁

Fitting, socle

C₂×C₃×C₅²×C₁₉

C₂×C₃

LCS

G ▷ C₃×C₅×C₁₉

UCS

C₁ ◁ C₂×C₅

N	H ≅ G/N	type
1. C₂×C₃×C₅²×C₁₉⋊C₃	C₂	semidirect
2. C₅×D₁₅×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₅×C₁₉×D₁₅	C₃	semidirect
5. C₃×C₅²×C₁₉⋊C₃	C₂²	semidirect
6. C₂×D₁₅×C₁₉⋊C₃	C₅	direct (N × H)
8. C₅×C₁₉×D₁₅	C₂×C₃	semidirect
10. C₂×C₅²×C₁₉⋊C₃	D₃	semidirect
12. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
15. C₂×C₃×C₅×C₁₉⋊C₃	D₅	semidirect
16. C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	semidirect
17. D₁₅×C₁₉⋊C₃	C₂×C₅	direct (N × H)
19. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
21. C₅²×C₁₉⋊C₃	C₂×D₃	semidirect
22. C₂×C₁₉×D₁₅	C₃×C₅	semidirect
26. C₂×C₅²×C₁₉	C₃×D₃	semidirect
30. C₃×C₅×C₁₉⋊C₃	C₂×D₅	semidirect
31. C₃×C₅×C₁₉⋊C₃	C₂²×C₅	semidirect
34. C₂×C₃×C₅×C₁₉	C₃×D₅	semidirect
35. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
36. C₁₉×D₁₅	C₂×C₃×C₅	semidirect
43. C₂×C₅×C₁₉⋊C₃	C₅×D₃	semidirect
44. C₂×C₅×C₁₉⋊C₃	D₁₅	direct (N × H)
46. C₅²×C₁₉	C₂×C₃×D₃	semidirect
51. C₂×C₃×C₁₉⋊C₃	C₅×D₅	semidirect
53. C₂×C₅×D₁₅	C₁₉⋊C₃	direct (N × H)
56. C₃×C₅×C₁₉	C₂×C₃×D₅	semidirect
57. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
62. C₅×C₁₉⋊C₃	C₂×C₅×D₃	semidirect
63. C₅×C₁₉⋊C₃	C₂×D₁₅	direct (N × H)
69. C₂×C₅×C₁₉	C₃×C₅×D₃	semidirect
70. C₂×C₅×C₁₉	C₃×D₁₅	semidirect
74. C₃×C₁₉⋊C₃	C₂×C₅×D₅	semidirect
77. C₂×C₃×C₅²	C₂×C₁₉⋊C₃	semidirect
78. C₅×D₁₅	C₂×C₁₉⋊C₃	direct (N × H)
80. C₂×C₃×C₁₉	C₃×C₅×D₅	semidirect
84. C₂×C₁₉⋊C₃	C₅×D₁₅	direct (N × H)
87. C₅×C₁₉	C₂×C₃×C₅×D₃	semidirect
88. C₅×C₁₉	C₂×C₃×D₁₅	semidirect
97. C₃×C₅²	C₂²×C₁₉⋊C₃	semidirect
99. C₂×D₁₅	C₅×C₁₉⋊C₃	direct (N × H)
102. C₃×C₁₉	C₂×C₃×C₅×D₅	semidirect
104. C₁₉⋊C₃	C₂×C₅×D₁₅	direct (N × H)
105. C₂×C₅²	D₃×C₁₉⋊C₃	semidirect
111. C₂×C₁₉	C₃×C₅×D₁₅	semidirect
121. C₂×C₃×C₅	D₅×C₁₉⋊C₃	semidirect
122. C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	semidirect
123. D₁₅	C₂×C₅×C₁₉⋊C₃	direct (N × H)
126. C₅²	C₂×D₃×C₁₉⋊C₃	semidirect
129. C₁₉	C₂×C₃×C₅×D₁₅	semidirect
139. C₃×C₅	C₂×D₅×C₁₉⋊C₃	semidirect
140. C₃×C₅	C₂²×C₅×C₁₉⋊C₃	semidirect
145. C₂×C₅	C₅×D₃×C₁₉⋊C₃	semidirect
146. C₂×C₅	D₁₅×C₁₉⋊C₃	direct (N × H)
152. C₂×C₃	C₅×D₅×C₁₉⋊C₃	semidirect
155. C₅	C₂×C₅×D₃×C₁₉⋊C₃	semidirect
156. C₅	C₂×D₁₅×C₁₉⋊C₃	direct (N × H)
160. C₃	C₂×C₅×D₅×C₁₉⋊C₃	semidirect
162. C₂	C₅×D₁₅×C₁₉⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₂×C₃×C₅²×C₁₉⋊C₃

C₂

semidirect

2. C₅×D₁₅×C₁₉⋊C₃

C₂

direct (N × H)

3. C₂×C₅×C₁₉×D₁₅

C₃

semidirect

5. C₃×C₅²×C₁₉⋊C₃

C₂²

semidirect

6. C₂×D₁₅×C₁₉⋊C₃

C₅

direct (N × H)

8. C₅×C₁₉×D₁₅

C₂×C₃

semidirect

10. C₂×C₅²×C₁₉⋊C₃

D₃

semidirect

12. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

15. C₂×C₃×C₅×C₁₉⋊C₃

D₅

semidirect

16. C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

semidirect

17. D₁₅×C₁₉⋊C₃

C₂×C₅

direct (N × H)

19. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

21. C₅²×C₁₉⋊C₃

C₂×D₃

semidirect

22. C₂×C₁₉×D₁₅

C₃×C₅

semidirect

26. C₂×C₅²×C₁₉

C₃×D₃

semidirect

30. C₃×C₅×C₁₉⋊C₃

C₂×D₅

semidirect

31. C₃×C₅×C₁₉⋊C₃

C₂²×C₅

semidirect

34. C₂×C₃×C₅×C₁₉

C₃×D₅

semidirect

35. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

36. C₁₉×D₁₅

C₂×C₃×C₅

semidirect

43. C₂×C₅×C₁₉⋊C₃

C₅×D₃

semidirect

44. C₂×C₅×C₁₉⋊C₃

D₁₅

direct (N × H)

46. C₅²×C₁₉

C₂×C₃×D₃

semidirect

51. C₂×C₃×C₁₉⋊C₃

C₅×D₅

semidirect

53. C₂×C₅×D₁₅

C₁₉⋊C₃

direct (N × H)

56. C₃×C₅×C₁₉

C₂×C₃×D₅

semidirect

57. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

62. C₅×C₁₉⋊C₃

C₂×C₅×D₃

semidirect

63. C₅×C₁₉⋊C₃

C₂×D₁₅

direct (N × H)

69. C₂×C₅×C₁₉

C₃×C₅×D₃

semidirect

70. C₂×C₅×C₁₉

C₃×D₁₅

semidirect

74. C₃×C₁₉⋊C₃

C₂×C₅×D₅

semidirect

77. C₂×C₃×C₅²

C₂×C₁₉⋊C₃

semidirect

78. C₅×D₁₅

C₂×C₁₉⋊C₃

direct (N × H)

80. C₂×C₃×C₁₉

C₃×C₅×D₅

semidirect

84. C₂×C₁₉⋊C₃

C₅×D₁₅

direct (N × H)

87. C₅×C₁₉

C₂×C₃×C₅×D₃

semidirect

88. C₅×C₁₉

C₂×C₃×D₁₅

semidirect

97. C₃×C₅²

C₂²×C₁₉⋊C₃

semidirect

99. C₂×D₁₅

C₅×C₁₉⋊C₃

direct (N × H)

102. C₃×C₁₉

C₂×C₃×C₅×D₅

semidirect

104. C₁₉⋊C₃

C₂×C₅×D₁₅

direct (N × H)

105. C₂×C₅²

D₃×C₁₉⋊C₃

semidirect

111. C₂×C₁₉

C₃×C₅×D₁₅

semidirect

121. C₂×C₃×C₅

D₅×C₁₉⋊C₃

semidirect

122. C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

semidirect

123. D₁₅

C₂×C₅×C₁₉⋊C₃

direct (N × H)

126. C₅²

C₂×D₃×C₁₉⋊C₃

semidirect

129. C₁₉

C₂×C₃×C₅×D₁₅

semidirect

139. C₃×C₅

C₂×D₅×C₁₉⋊C₃

semidirect

140. C₃×C₅

C₂²×C₅×C₁₉⋊C₃

semidirect

145. C₂×C₅

C₅×D₃×C₁₉⋊C₃

semidirect

146. C₂×C₅

D₁₅×C₁₉⋊C₃

direct (N × H)

152. C₂×C₃

C₅×D₅×C₁₉⋊C₃

semidirect

155. C₅

C₂×C₅×D₃×C₁₉⋊C₃

semidirect

156. C₅

C₂×D₁₅×C₁₉⋊C₃

direct (N × H)

160. C₃

C₂×C₅×D₅×C₁₉⋊C₃

semidirect

162. C₂

C₅×D₁₅×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
C₅×D₁₅×C₁₉⋊C₃	2
C₂×C₅×C₁₉×D₁₅	3
C₂×C₅×D₅×C₁₉⋊C₃	3
C₂×D₁₅×C₁₉⋊C₃	5
C₂×C₅×D₃×C₁₉⋊C₃	5
C₂×C₃×C₅×D₁₅	19

subgroup

index

C₂×C₃×C₅²×C₁₉⋊C₃

C₅×D₁₅×C₁₉⋊C₃

C₂×C₅×C₁₉×D₁₅

C₂×C₅×D₅×C₁₉⋊C₃

C₂×D₁₅×C₁₉⋊C₃

C₂×C₅×D₃×C₁₉⋊C₃

C₂×C₃×C₅×D₁₅

Subgroups — C₂×C₅×D₁₅×C₁₉⋊C₃ #30685842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C5×D15×C19⋊C3 #30685842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₅×C₁₉⋊C₃ #30685842