Group #18017875 — subgroups

Subgroups — C₁₉×#11916 #18017875

Order 4864.

274 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3139	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2165	C₂	1	2	yes	maximal
3	C₁₉×#1356	C₂	1	4	yes	maximal, complemented
4	C₁₉×#533	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₁₉×#491	C₄	1	2	yes	—
7	C₁₉×#491	C₂²	1	2	yes	—
8	C₁₉×#487	—	2	2	no	—
9	C₁₉×#419	—	2	2	no	—
10	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#364	—	2	2	no	—
12	C₁₉×#349	—	2	2	no	—
13	C₁₉×#347	C₂²	1	4	yes	—
14	C₂²×Q₈×C₁₉	—	2	1	no	—
15	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
16	C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₁₉×C₄⋊Q₈	—	2	1	no	—
18	C₁₉×C₄⋊Q₈	—	4	1	no	—
19	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
20	C₁₉×#125	C₂×C₄	1	2	yes	—
21	C₁₉×C₂²⋊Q₈	—	4	1	no	—
22	C₄×Q₈×C₁₉	—	4	1	no	—
23	C₁₉×#117	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₁₉×M₃₂	—	2	4	no	—
27	C₁₉×#103	—	2	4	no	—
28	C₁₉×#103	—	2	4	no	—
29	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
30	C₁₉×#97	C₂³	1	1	yes	characteristic
31	C₄×C₈×C₁₉	D₄	1	2	yes	—
32	C₂×Q₈×C₁₉	—	2	2	no	—
33	C₂×Q₈×C₁₉	—	4	1	no	—
34	C₂×Q₈×C₁₉	—	4	4	no	—
35	C₂×Q₈×C₁₉	—	4	1	no	—
36	C₂²×C₄×C₁₉	—	2	1	no	—
37	C₂²×C₄×C₁₉	—	4	1	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	M₁₆×C₁₉	—	4	2	no	—
40	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
42	C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₄⋊C₄×C₁₉	—	4	2	no	—
44	C₄⋊C₄×C₁₉	—	4	2	no	—
45	C₄⋊C₄×C₁₉	—	4	2	no	—
46	C₄⋊C₄×C₁₉	—	4	1	no	—
47	C₂²⋊C₄×C₁₉	—	4	1	no	—
48	C₄²×C₁₉	—	2	1	no	—
49	C₄²×C₁₉	—	4	1	no	—
50	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₁₆×C₁₉	—	4	4	no	—
53	#11916	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂³×C₁₉	#100	1	1	yes	characteristic
55	Q₈×C₁₉	—	4	4	no	—
56	Q₈×C₁₉	—	8	2	no	—
57	Q₈×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	4	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	8	2	no	—
65	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₈×C₁₉	—	2	2	no	—
68	C₈×C₁₉	—	2	2	no	—
69	#3139	C₂×C₁₉	1	1	yes	characteristic
70	#2165	C₂×C₁₉	1	2	yes	—
71	#1356	C₂×C₁₉	1	4	yes	complemented
72	C₂²×C₁₉	—	2	1	no	—
73	C₂²×C₁₉	—	4	1	no	—
74	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	4	1	no	—
78	C₄×C₁₉	—	8	2	no	—
79	C₄×C₁₉	—	8	2	no	—
80	C₄×C₁₉	#421	1	2	yes	—
81	#533	C₄×C₁₉	1	1	yes	characteristic
82	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
83	#491	C₄×C₁₉	1	2	yes	—
84	#491	C₂²×C₁₉	1	2	yes	—
85	#487	—	2	2	no	—
86	#419	—	2	2	no	—
87	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
88	#364	—	2	2	no	—
89	#349	—	2	2	no	—
90	#347	C₂²×C₁₉	1	4	yes	—
91	C₂×C₁₉	—	2	1	no	—
92	C₂×C₁₉	—	4	1	no	—
93	C₂×C₁₉	#1533	1	1	yes	characteristic
94	C₂²×Q₈	—	2	1	no	—
95	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
96	C₄⋊Q₈	—	2	1	no	—
97	C₄⋊Q₈	—	2	1	no	—
98	C₄⋊Q₈	—	4	1	no	—
99	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
100	#125	C₂×C₄×C₁₉	1	2	yes	—
101	C₂²⋊Q₈	—	4	1	no	—
102	C₄×Q₈	—	4	1	no	—
103	#117	—	2	1	no	—
104	C₂×C₄⋊C₄	—	4	1	no	—
105	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
106	M₃₂	—	2	4	no	—
107	#103	—	2	4	no	—
108	#103	—	2	4	no	—
109	#97	C₂×C₄×C₁₉	1	1	yes	characteristic
110	#97	C₂³×C₁₉	1	1	yes	characteristic
111	C₄×C₈	D₄×C₁₉	1	2	yes	—
112	C₁₉	#11916	1	1	yes	characteristic, direct product factor, Sylow
113	C₂×Q₈	—	2	2	no	—
114	C₂×Q₈	—	4	1	no	—
115	C₂×Q₈	—	4	4	no	—
116	C₂×Q₈	—	4	1	no	—
117	C₂²×C₄	—	2	1	no	—
118	C₂²×C₄	—	4	1	no	—
119	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
120	M₁₆	—	4	2	no	—
121	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
122	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	—	4	2	no	—
125	C₄⋊C₄	—	4	2	no	—
126	C₄⋊C₄	—	4	2	no	—
127	C₄⋊C₄	—	4	1	no	—
128	C₂²⋊C₄	—	4	1	no	—
129	C₄²	—	2	1	no	—
130	C₄²	—	4	1	no	—
131	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
132	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
133	C₁₆	—	4	4	no	—
134	C₂³	C₁₉×#100	1	1	yes	characteristic
135	Q₈	—	4	4	no	—
136	Q₈	—	8	2	no	—
137	Q₈	—	8	2	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	4	2	no	—
144	C₂×C₄	—	8	2	no	—
145	C₂×C₄	C₁₉×#100	1	1	yes	characteristic
146	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
147	C₈	—	2	2	no	—
148	C₈	—	2	2	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	4	1	no	—
151	C₂²	C₂×C₁₉×#100	1	1	yes	characteristic
152	C₄	—	2	2	no	—
153	C₄	—	2	1	no	—
154	C₄	—	4	1	no	—
155	C₄	—	8	2	no	—
156	C₄	—	8	2	no	—
157	C₄	C₁₉×#421	1	2	yes	—
158	C₂	—	2	1	no	—
159	C₂	—	4	1	no	—
160	C₂	C₁₉×#1533	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3139

C₂

yes

maximal, characteristic

C₁₉×#2165

C₂

yes

maximal

C₁₉×#1356

C₂

yes

maximal, complemented

C₁₉×#533

C₄

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×#491

C₄

yes

—

C₁₉×#491

C₂²

yes

—

C₁₉×#487

—

C₁₉×#419

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#364

—

C₁₉×#349

—

C₁₉×#347

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×M₃₂

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#97

C₂×C₄

yes

characteristic

C₁₉×#97

C₂³

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₁₆×C₁₉

—

#11916

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#100

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

#100

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

#3139

C₂×C₁₉

yes

characteristic

#2165

C₂×C₁₉

yes

—

#1356

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#100

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#421

yes

—

#533

C₄×C₁₉

yes

characteristic

C₂×C₄⋊Q₈

C₄×C₁₉

yes

characteristic

#491

C₄×C₁₉

yes

—

#491

C₂²×C₁₉

yes

—

#487

—

#419

—

C₄×M₁₆

C₂²×C₁₉

yes

—

—

C₂²×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1533

yes

characteristic

C₂²×Q₈

—

C₂×M₁₆

D₄×C₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×C₄×C₁₉

yes

—

100

#125

C₂×C₄×C₁₉

yes

—

101

C₂²⋊Q₈

—

102

C₄×Q₈

—

103

#117

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

106

M₃₂

—

107

#103

—

108

#103

—

109

#97

C₂×C₄×C₁₉

yes

characteristic

110

#97

C₂³×C₁₉

yes

characteristic

111

C₄×C₈

D₄×C₁₉

yes

—

112

C₁₉

#11916

yes

characteristic, direct product factor, Sylow

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

120

M₁₆

—

121

C₂×C₈

C₂²⋊C₄×C₁₉

yes

—

122

C₂×C₈

C₂×D₄×C₁₉

yes

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₂²⋊C₄

—

129

C₄²

—

130

C₄²

—

131

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

132

C₄²

C₂²×C₄×C₁₉

yes

characteristic

133

C₁₆

—

134

C₂³

C₁₉×#100

yes

characteristic

135

Q₈

—

136

Q₈

—

137

Q₈

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

C₁₉×#100

yes

characteristic

146

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

147

C₈

—

148

C₈

—

149

C₂²

—

150

C₂²

—

151

C₂²

C₂×C₁₉×#100

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

C₁₉×#421

yes

—

158

C₂

—

159

C₂

—

160

C₂

C₁₉×#1533

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1533
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#97	C₂³×C₁₉
prime radical	C₂³×C₁₉	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#1533

commutator

C₄²

C₂²×C₄×C₁₉

C₂³×C₁₉

C₂³×C₁₉

G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1356	C₂	semidirect
53. #11916	C₁₉	direct (N × H)
71. #1356	C₂×C₁₉	semidirect
112. C₁₉	#11916	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1356

C₂

semidirect

53. #11916

C₁₉

direct (N × H)

71. #1356

C₂×C₁₉

semidirect

112. C₁₉

#11916

direct (N × H)

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

subgroup	index
C₁₉×#3139	2
C₁₉×#2165	2
C₁₉×#1356	2
#11916	19

subgroup

index

C₁₉×#3139

C₁₉×#2165

C₁₉×#1356

#11916

Subgroups — C₁₉×#11916 #18017875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11916 #18017875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11916 #18017875