Group #18013313 — subgroups

Subgroups — C₁₉×#7354 #18013313

Order 4864.

268 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 50 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	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1325	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
4	C₂×C₁₉×#102	—	2	2	no	—
5	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×#384	C₂²	1	1	yes	characteristic
7	C₁₉×#324	—	2	2	no	—
8	C₂²×D₄×C₁₉	—	2	1	no	—
9	C₂²×D₄×C₁₉	—	4	1	no	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₁₉×#127	—	2	1	no	—
12	C₁₉×#127	—	4	1	no	—
13	C₁₉×#127	C₈	1	2	yes	complemented
14	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#102	—	4	4	no	—
18	C₁₉×C₂²⋊C₈	—	4	2	no	—
19	C₄×C₈×C₁₉	—	4	1	no	—
20	C₂⁴×C₁₉	—	4	1	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	4	2	no	—
23	C₂×D₄×C₁₉	—	4	2	no	—
24	C₂×D₄×C₁₉	—	4	2	no	—
25	C₂×D₄×C₁₉	—	4	2	no	—
26	C₂×D₄×C₁₉	—	4	1	no	—
27	C₂×D₄×C₁₉	—	8	2	no	—
28	C₂×D₄×C₁₉	—	8	2	no	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₂×C₈×C₁₉	—	8	2	no	—
36	C₄⋊C₄×C₁₉	—	4	2	no	—
37	C₄⋊C₄×C₁₉	—	8	2	no	—
38	C₄²×C₁₉	—	2	1	no	—
39	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
40	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
41	#7354	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂³×C₁₉	—	4	2	no	—
43	C₂³×C₁₉	—	8	2	no	—
44	C₂³×C₁₉	—	8	2	no	—
45	C₂³×C₁₉	—	8	1	no	—
46	C₂³×C₁₉	—	8	1	no	—
47	C₂³×C₁₉	#99	1	1	yes	characteristic
48	D₄×C₁₉	—	4	4	no	—
49	D₄×C₁₉	—	8	2	no	—
50	D₄×C₁₉	—	8	4	no	—
51	D₄×C₁₉	—	8	4	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	—	8	2	no	—
60	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
62	C₈×C₁₉	—	4	2	no	—
63	C₈×C₁₉	—	16	2	no	—
64	#1957	C₂×C₁₉	1	1	yes	characteristic
65	#1325	C₂×C₁₉	1	2	yes	complemented
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	8	4	no	—
69	C₂²×C₁₉	—	8	2	no	—
70	C₂²×C₁₉	—	16	2	no	—
71	C₂²×C₁₉	—	16	1	no	—
72	C₂²×C₁₉	—	16	1	no	—
73	C₂²×C₁₉	#323	1	1	yes	characteristic
74	C₂²×C₁₉	#353	1	1	yes	characteristic
75	C₂²×C₁₉	#355	1	1	yes	characteristic
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	8	2	no	—
81	C₂×#127	C₄×C₁₉	1	1	yes	characteristic
82	C₂×#102	—	2	2	no	—
83	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
84	#384	C₂²×C₁₉	1	1	yes	characteristic
85	#324	—	2	2	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	2	1	no	—
88	C₂×C₁₉	—	16	2	no	—
89	C₂×C₁₉	#1318	1	1	yes	characteristic
90	C₂×C₁₉	#1408	1	1	yes	characteristic
91	C₂×C₁₉	#1410	1	1	yes	characteristic
92	C₂²×D₄	—	2	1	no	—
93	C₂²×D₄	—	4	1	no	—
94	C₂²×C₈	—	2	1	no	—
95	#127	—	2	1	no	—
96	#127	—	4	1	no	—
97	#127	C₈×C₁₉	1	2	yes	complemented
98	C₂×C₄⋊C₄	—	4	1	no	—
99	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
100	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
101	#102	—	4	4	no	—
102	C₂²⋊C₈	—	4	2	no	—
103	C₄×C₈	—	4	1	no	—
104	C₁₉	#7354	1	1	yes	characteristic, direct product factor, Sylow
105	C₂⁴	—	4	1	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	4	2	no	—
108	C₂×D₄	—	4	2	no	—
109	C₂×D₄	—	4	2	no	—
110	C₂×D₄	—	4	2	no	—
111	C₂×D₄	—	4	1	no	—
112	C₂×D₄	—	8	2	no	—
113	C₂×D₄	—	8	2	no	—
114	C₂²×C₄	—	2	1	no	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	4	1	no	—
119	C₂×C₈	—	4	1	no	—
120	C₂×C₈	—	8	2	no	—
121	C₄⋊C₄	—	4	2	no	—
122	C₄⋊C₄	—	8	2	no	—
123	C₄²	—	2	1	no	—
124	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
125	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
126	C₂³	—	4	2	no	—
127	C₂³	—	8	2	no	—
128	C₂³	—	8	2	no	—
129	C₂³	—	8	1	no	—
130	C₂³	—	8	1	no	—
131	C₂³	C₁₉×#99	1	1	yes	characteristic
132	D₄	—	4	4	no	—
133	D₄	—	8	2	no	—
134	D₄	—	8	4	no	—
135	D₄	—	8	4	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	8	2	no	—
144	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
145	C₂×C₄	C₁₉×#100	1	1	yes	characteristic
146	C₈	—	4	2	no	—
147	C₈	—	16	2	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	8	4	no	—
151	C₂²	—	8	2	no	—
152	C₂²	—	16	2	no	—
153	C₂²	—	16	1	no	—
154	C₂²	—	16	1	no	—
155	C₂²	C₁₉×#323	1	1	yes	characteristic
156	C₂²	C₁₉×#353	1	1	yes	characteristic
157	C₂²	C₁₉×#355	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	2	2	no	—
160	C₄	—	2	1	no	—
161	C₄	—	2	1	no	—
162	C₄	—	8	2	no	—
163	C₂	—	2	1	no	—
164	C₂	—	2	1	no	—
165	C₂	—	16	2	no	—
166	C₂	C₁₉×#1318	1	1	yes	characteristic
167	C₂	C₁₉×#1408	1	1	yes	characteristic
168	C₂	C₁₉×#1410	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1957

C₂

yes

maximal, characteristic

C₁₉×#1325

C₂

yes

maximal, complemented

C₂×C₁₉×#127

C₄

yes

characteristic

C₂×C₁₉×#102

—

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#324

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

C₈

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#102

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

#7354

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

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

#100

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

#1957

C₂×C₁₉

yes

characteristic

#1325

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#127

C₄×C₁₉

yes

characteristic

C₂×#102

—

C₂×C₄×C₈

C₄×C₁₉

yes

characteristic

#384

C₂²×C₁₉

yes

characteristic

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

—

#127

C₈×C₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

100

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

101

#102

—

102

C₂²⋊C₈

—

103

C₄×C₈

—

104

C₁₉

#7354

yes

characteristic, direct product factor, Sylow

105

C₂⁴

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄²

—

124

C₄²

C₂×C₈×C₁₉

yes

characteristic

125

C₄²

M₁₆×C₁₉

yes

characteristic

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

C₁₉×#99

yes

characteristic

132

D₄

—

133

D₄

—

134

D₄

—

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

145

C₂×C₄

C₁₉×#100

yes

characteristic

146

C₈

—

147

C₈

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

C₁₉×#323

yes

characteristic

156

C₂²

C₁₉×#353

yes

characteristic

157

C₂²

C₁₉×#355

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₂

—

164

C₂

—

165

C₂

—

166

C₂

C₁₉×#1318

yes

characteristic

167

C₂

C₁₉×#1408

yes

characteristic

168

C₂

C₁₉×#1410

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#353
commutator	C₄²	C₂×C₈×C₁₉
Frattini, cosocle	#384	C₂²×C₁₉
prime radical	C₂×C₁₉×#127	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#384 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#353

commutator

C₄²

C₂×C₈×C₁₉

Frattini, cosocle

#384

C₂²×C₁₉

prime radical

C₂×C₁₉×#127

C₄

LCS

G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#384 ◁ G

N	H ≅ G/N	type
2. C₁₉×#1325	C₂	semidirect
13. C₁₉×#127	C₈	semidirect
41. #7354	C₁₉	direct (N × H)
65. #1325	C₂×C₁₉	semidirect
97. #127	C₈×C₁₉	semidirect
104. C₁₉	#7354	direct (N × H)

H ≅ G/N

type

2. C₁₉×#1325

C₂

semidirect

13. C₁₉×#127

C₈

semidirect

41. #7354

C₁₉

direct (N × H)

65. #1325

C₂×C₁₉

semidirect

97. #127

C₈×C₁₉

semidirect

104. C₁₉

#7354

direct (N × H)

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

subgroup	index
C₁₉×#1957	2
C₁₉×#1325	2
#7354	19

subgroup

index

C₁₉×#1957

C₁₉×#1325

#7354

Subgroups — C₁₉×#7354 #18013313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7354 #18013313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7354 #18013313