Group #18013293 — subgroups

Subgroups — C₁₉×#7334 #18013293

Order 4864.

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

normal subgroups only

This group has 182 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×C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₂²⋊C₃₂	C₂	1	2	yes	maximal, complemented
3	C₂³×C₈×C₁₉	C₄	1	1	yes	characteristic
4	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₉×C₃₂	—	2	2	no	—
7	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
8	C₂³×C₄×C₁₉	C₈	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	—	2	1	no	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂²×C₈×C₁₉	—	4	1	no	—
12	C₂²×C₈×C₁₉	—	4	1	no	—
13	C₂²×C₈×C₁₉	C₈	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₁₉	—	2	1	no	—
16	C₂×C₁₆×C₁₉	—	4	1	no	—
17	C₂×C₁₆×C₁₉	—	4	1	no	—
18	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
19	C₁₉×C₃₂	—	4	2	no	—
20	C₂⁴×C₁₉	C₁₆	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	4	1	no	—
25	C₂²×C₄×C₁₉	C₁₆	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
36	C₁₆×C₁₉	—	2	2	no	—
37	C₁₆×C₁₉	—	4	1	no	—
38	#7334	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂³×C₁₉	—	2	1	no	—
40	C₂³×C₁₉	—	2	1	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	C₃₂	1	2	yes	complemented
44	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
54	C₈×C₁₉	—	2	1	no	—
55	C₈×C₁₉	—	4	1	no	—
56	C₈×C₁₉	#99	1	1	yes	characteristic
57	C₈×C₁₉	#100	1	1	yes	characteristic
58	C₂×C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
59	C₂²⋊C₃₂	C₂×C₁₉	1	2	yes	complemented
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	4	2	no	—
64	C₂²×C₁₉	—	4	2	no	—
65	C₂²×C₁₉	—	4	1	no	—
66	C₂²×C₁₉	—	4	1	no	—
67	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
68	C₂²×C₁₉	C₂×C₃₂	1	1	yes	characteristic
69	C₂²×C₁₉	M₆₄	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	4	1	no	—
72	C₄×C₁₉	#323	1	1	yes	characteristic
73	C₄×C₁₉	#349	1	1	yes	characteristic
74	C₂³×C₈	C₄×C₁₉	1	1	yes	characteristic
75	C₂²×C₁₆	C₄×C₁₉	1	1	yes	characteristic
76	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
77	C₂×C₃₂	—	2	2	no	—
78	C₂²⋊C₁₆	—	2	2	no	—
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	4	2	no	—
82	C₂×C₁₉	#1314	1	1	yes	characteristic
83	C₂×C₁₉	C₂²⋊C₃₂	1	1	yes	characteristic
84	C₂×C₁₉	#1400	1	1	yes	characteristic
85	C₂³×C₄	C₈×C₁₉	1	1	yes	characteristic
86	C₂²×C₈	—	2	1	no	—
87	C₂²×C₈	—	2	1	no	—
88	C₂²×C₈	—	4	1	no	—
89	C₂²×C₈	—	4	1	no	—
90	C₂²×C₈	C₈×C₁₉	1	1	yes	characteristic
91	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
92	C₂×C₁₆	—	2	1	no	—
93	C₂×C₁₆	—	4	1	no	—
94	C₂×C₁₆	—	4	1	no	—
95	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
96	C₃₂	—	4	2	no	—
97	C₁₉	#7334	1	1	yes	characteristic, direct product factor, Sylow
98	C₂⁴	C₁₆×C₁₉	1	1	yes	characteristic
99	C₂²×C₄	—	2	1	no	—
100	C₂²×C₄	—	2	1	no	—
101	C₂²×C₄	—	4	1	no	—
102	C₂²×C₄	—	4	1	no	—
103	C₂²×C₄	C₁₆×C₁₉	1	1	yes	characteristic
104	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	4	2	no	—
109	C₂×C₈	—	4	1	no	—
110	C₂×C₈	—	4	1	no	—
111	C₂×C₈	—	4	1	no	—
112	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
113	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
114	C₁₆	—	2	2	no	—
115	C₁₆	—	4	1	no	—
116	C₂³	—	2	1	no	—
117	C₂³	—	2	1	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	4	1	no	—
120	C₂³	C₁₉×C₃₂	1	2	yes	complemented
121	C₂³	C₂×C₁₆×C₁₉	1	1	yes	characteristic
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
130	C₂×C₄	C₁₉×M₃₂	1	1	yes	characteristic
131	C₈	—	2	1	no	—
132	C₈	—	4	1	no	—
133	C₈	C₁₉×#99	1	1	yes	characteristic
134	C₈	C₁₉×#100	1	1	yes	characteristic
135	C₂²	—	2	1	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	2	no	—
138	C₂²	—	4	2	no	—
139	C₂²	—	4	2	no	—
140	C₂²	—	4	1	no	—
141	C₂²	—	4	1	no	—
142	C₂²	C₁₉×C₂²⋊C₁₆	1	1	yes	characteristic
143	C₂²	C₂×C₁₉×C₃₂	1	1	yes	characteristic
144	C₂²	C₁₉×M₆₄	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	4	1	no	—
147	C₄	C₁₉×#323	1	1	yes	characteristic
148	C₄	C₁₉×#349	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	—	4	2	no	—
152	C₂	C₁₉×#1314	1	1	yes	characteristic
153	C₂	C₁₉×C₂²⋊C₃₂	1	1	yes	characteristic
154	C₂	C₁₉×#1400	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₁₉×C₂²⋊C₃₂

C₂

yes

maximal, complemented

C₂³×C₈×C₁₉

C₄

yes

characteristic

C₂²×C₁₆×C₁₉

C₄

yes

characteristic

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₃₂

—

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

—

C₁₉×C₃₂

—

C₂⁴×C₁₉

C₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₁₆

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7334

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₃₂

yes

complemented

C₂³×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₂²⋊C₁₆

C₂×C₁₉

yes

characteristic

C₂²⋊C₃₂

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₂²×C₁₉

C₂×C₃₂

yes

characteristic

C₂²×C₁₉

M₆₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂³×C₈

C₄×C₁₉

yes

characteristic

C₂²×C₁₆

C₄×C₁₉

yes

characteristic

C₂²×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₃₂

—

C₂²⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1314

yes

characteristic

C₂×C₁₉

C₂²⋊C₃₂

yes

characteristic

C₂×C₁₉

#1400

yes

characteristic

C₂³×C₄

C₈×C₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₈×C₁₉

yes

characteristic

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

—

C₃₂

—

C₁₉

#7334

yes

characteristic, direct product factor, Sylow

C₂⁴

C₁₆×C₁₉

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₁₆×C₁₉

yes

characteristic

104

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

113

C₂×C₈

M₁₆×C₁₉

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₁₉×C₃₂

yes

complemented

121

C₂³

C₂×C₁₆×C₁₉

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

130

C₂×C₄

C₁₉×M₃₂

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

C₁₉×#99

yes

characteristic

134

C₈

C₁₉×#100

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₁₉×C₂²⋊C₁₆

yes

characteristic

143

C₂²

C₂×C₁₉×C₃₂

yes

characteristic

144

C₂²

C₁₉×M₆₄

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

C₁₉×#323

yes

characteristic

148

C₄

C₁₉×#349

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

—

152

C₂

C₁₉×#1314

yes

characteristic

153

C₂

C₁₉×C₂²⋊C₃₂

yes

characteristic

154

C₂

C₁₉×#1400

yes

characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂×C₁₉×C₃₂
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
socle	C₂²×C₁₉	C₂²⋊C₁₆
prime radical	C₂⁴×C₁₉	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₈×C₁₉

C₂²⋊C₄

commutator

C₂²

C₂×C₁₉×C₃₂

Frattini, cosocle

C₂²×C₁₆

C₂²×C₁₉

socle

C₂²×C₁₉

C₂²⋊C₁₆

prime radical

C₂⁴×C₁₉

C₁₆

LCS

G ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×C₂²⋊C₃₂	C₂	semidirect
38. #7334	C₁₉	direct (N × H)
43. C₂³×C₁₉	C₃₂	semidirect
59. C₂²⋊C₃₂	C₂×C₁₉	semidirect
97. C₁₉	#7334	direct (N × H)
120. C₂³	C₁₉×C₃₂	semidirect

H ≅ G/N

type

2. C₁₉×C₂²⋊C₃₂

C₂

semidirect

38. #7334

C₁₉

direct (N × H)

43. C₂³×C₁₉

C₃₂

semidirect

59. C₂²⋊C₃₂

C₂×C₁₉

semidirect

97. C₁₉

#7334

direct (N × H)

120. C₂³

C₁₉×C₃₂

semidirect

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

subgroup	index
C₂×C₁₉×C₂²⋊C₁₆	2
C₁₉×C₂²⋊C₃₂	2
#7334	19

subgroup

index

C₂×C₁₉×C₂²⋊C₁₆

C₁₉×C₂²⋊C₃₂

#7334

Subgroups — C₁₉×#7334 #18013293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7334 #18013293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7334 #18013293