Group #18014754 — subgroups

Subgroups — C₁₉×#8795 #18014754

Order 4864.

270 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 126 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×#1846	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1286	C₂	1	2	yes	maximal
5	C₁₉×#1286	C₂	1	2	yes	maximal
6	C₁₉×#431	C₂²	1	2	yes	—
7	C₂×C₁₉×#107	—	2	1	no	—
8	C₂×C₁₉×#106	—	2	1	no	—
9	C₁₉×#423	C₂²	1	1	yes	characteristic
10	C₁₉×#423	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#382	C₂²	1	2	yes	—
13	C₁₉×#341	—	2	1	no	—
14	C₁₉×#341	—	2	1	no	—
15	C₁₉×#322	C₄	1	4	yes	complemented
16	C₂×M₁₆×C₁₉	—	2	1	no	—
17	C₂×M₁₆×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₁₉×#107	—	4	2	no	—
23	C₁₉×#106	—	4	2	no	—
24	C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₁₉×C₂²⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
29	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₉	Q₈	1	2	yes	—
31	C₁₉×#95	—	2	4	no	—
32	C₂²×C₄×C₁₉	—	4	2	no	—
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	#41	1	2	yes	—
35	M₁₆×C₁₉	—	4	1	no	—
36	M₁₆×C₁₉	—	4	1	no	—
37	M₁₆×C₁₉	—	4	1	no	—
38	M₁₆×C₁₉	—	4	1	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	—	2	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	4	no	—
44	C₂×C₈×C₁₉	—	4	1	no	—
45	C₂×C₈×C₁₉	—	4	1	no	—
46	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₄²×C₁₉	#41	1	2	yes	—
53	#8795	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂³×C₁₉	#124	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	—	8	4	no	—
57	C₂×C₄×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#117	1	2	yes	—
60	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#125	1	2	yes	—
62	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
66	C₈×C₁₉	—	2	2	no	—
67	C₈×C₁₉	—	2	2	no	—
68	C₈×C₁₉	—	4	4	no	—
69	C₈×C₁₉	—	8	1	no	—
70	C₈×C₁₉	—	8	1	no	—
71	#1846	C₂×C₁₉	1	1	yes	characteristic
72	#1837	C₂×C₁₉	1	1	yes	characteristic
73	#1452	C₂×C₁₉	1	1	yes	characteristic
74	#1286	C₂×C₁₉	1	2	yes	—
75	#1286	C₂×C₁₉	1	2	yes	—
76	C₂²×C₁₉	—	2	2	no	—
77	C₂²×C₁₉	#382	1	1	yes	characteristic
78	C₂²×C₁₉	#490	1	1	yes	characteristic
79	C₂²×C₁₉	#491	1	1	yes	characteristic
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	—	16	2	no	—
83	C₄×C₁₉	#428	1	1	yes	characteristic
84	C₄×C₁₉	#428	1	1	yes	characteristic
85	C₄×C₁₉	#489	1	1	yes	characteristic
86	C₄×C₁₉	#489	1	1	yes	characteristic
87	#431	C₂²×C₁₉	1	2	yes	—
88	C₂×#107	—	2	1	no	—
89	C₂×#106	—	2	1	no	—
90	#423	C₂²×C₁₉	1	1	yes	characteristic
91	#423	C₂²×C₁₉	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
93	#382	C₂²×C₁₉	1	2	yes	—
94	#341	—	2	1	no	—
95	#341	—	2	1	no	—
96	#322	C₄×C₁₉	1	4	yes	complemented
97	C₂×C₁₉	—	2	1	no	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	#1833	1	2	yes	—
100	C₂×C₁₉	#1836	1	1	yes	characteristic
101	C₂×M₁₆	—	2	1	no	—
102	C₂×M₁₆	—	2	1	no	—
103	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
104	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
107	#107	—	4	2	no	—
108	#106	—	4	2	no	—
109	C₄⋊C₈	—	2	2	no	—
110	C₄⋊C₈	—	2	2	no	—
111	C₄⋊C₈	—	2	2	no	—
112	C₂²⋊C₈	—	2	2	no	—
113	C₄×C₈	C₂×C₄×C₁₉	1	4	yes	—
114	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
115	C₄×C₈	Q₈×C₁₉	1	2	yes	—
116	#95	—	2	4	no	—
117	C₁₉	#8795	1	1	yes	characteristic, direct product factor, Sylow
118	C₂²×C₄	—	4	2	no	—
119	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
120	C₂²×C₄	#41×C₁₉	1	2	yes	—
121	M₁₆	—	4	1	no	—
122	M₁₆	—	4	1	no	—
123	M₁₆	—	4	1	no	—
124	M₁₆	—	4	1	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	4	no	—
130	C₂×C₈	—	4	1	no	—
131	C₂×C₈	—	4	1	no	—
132	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
133	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
134	C₄⋊C₄	—	4	2	no	—
135	C₄⋊C₄	—	4	2	no	—
136	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
137	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
138	C₄²	#41×C₁₉	1	2	yes	—
139	C₂³	C₁₉×#124	1	1	yes	characteristic
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	8	4	no	—
142	C₂×C₄	—	8	2	no	—
143	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
144	C₂×C₄	C₁₉×#117	1	2	yes	—
145	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
146	C₂×C₄	C₁₉×#125	1	2	yes	—
147	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
150	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
151	C₈	—	2	2	no	—
152	C₈	—	2	2	no	—
153	C₈	—	4	4	no	—
154	C₈	—	8	1	no	—
155	C₈	—	8	1	no	—
156	C₂²	—	2	2	no	—
157	C₂²	C₁₉×#382	1	1	yes	characteristic
158	C₂²	C₁₉×#490	1	1	yes	characteristic
159	C₂²	C₁₉×#491	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	2	2	no	—
162	C₄	—	16	2	no	—
163	C₄	C₁₉×#428	1	1	yes	characteristic
164	C₄	C₁₉×#428	1	1	yes	characteristic
165	C₄	C₁₉×#489	1	1	yes	characteristic
166	C₄	C₁₉×#489	1	1	yes	characteristic
167	C₂	—	2	1	no	—
168	C₂	—	2	1	no	—
169	C₂	C₁₉×#1833	1	2	yes	—
170	C₂	C₁₉×#1836	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1846

C₂

yes

maximal, characteristic

C₁₉×#1837

C₂

yes

maximal, characteristic

C₁₉×#1452

C₂

yes

maximal, characteristic

C₁₉×#1286

C₂

yes

maximal

C₁₉×#1286

C₂

yes

maximal

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#107

—

C₂×C₁₉×#106

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#382

C₂²

yes

—

C₁₉×#341

—

C₁₉×#341

—

C₁₉×#322

C₄

yes

complemented

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₁₉×#95

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

#8795

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1846

C₂×C₁₉

yes

characteristic

#1837

C₂×C₁₉

yes

characteristic

#1452

C₂×C₁₉

yes

characteristic

#1286

C₂×C₁₉

yes

—

#1286

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×#107

—

C₂×#106

—

#423

C₂²×C₁₉

yes

characteristic

#423

C₂²×C₁₉

yes

characteristic

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

#382

C₂²×C₁₉

yes

—

#341

—

#341

—

#322

C₄×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1833

yes

—

100

C₂×C₁₉

#1836

yes

characteristic

101

C₂×M₁₆

—

102

C₂×M₁₆

—

103

C₂²×C₈

D₄×C₁₉

yes

characteristic

104

C₂²×C₈

D₄×C₁₉

yes

characteristic

105

C₂×C₄⋊C₄

—

106

C₂×C₄²

C₂³×C₁₉

yes

characteristic

107

#107

—

108

#106

—

109

C₄⋊C₈

—

110

C₄⋊C₈

—

111

C₄⋊C₈

—

112

C₂²⋊C₈

—

113

C₄×C₈

C₂×C₄×C₁₉

yes

—

114

C₄×C₈

C₂×C₄×C₁₉

yes

—

115

C₄×C₈

Q₈×C₁₉

yes

—

116

#95

—

117

C₁₉

#8795

yes

characteristic, direct product factor, Sylow

118

C₂²×C₄

—

119

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

120

C₂²×C₄

#41×C₁₉

yes

—

121

M₁₆

—

122

M₁₆

—

123

M₁₆

—

124

M₁₆

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

133

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄²

C₂²×C₄×C₁₉

yes

characteristic

137

C₄²

C₂×Q₈×C₁₉

yes

characteristic

138

C₄²

#41×C₁₉

yes

—

139

C₂³

C₁₉×#124

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂×C₄⋊C₄×C₁₉

yes

characteristic

144

C₂×C₄

C₁₉×#117

yes

—

145

C₂×C₄

C₁₉×#124

yes

characteristic

146

C₂×C₄

C₁₉×#125

yes

—

147

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

148

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

149

C₂×C₄

C₁₉×#137

yes

characteristic

150

C₂×C₄

C₁₉×#137

yes

characteristic

151

C₈

—

152

C₈

—

153

C₈

—

154

C₈

—

155

C₈

—

156

C₂²

—

157

C₂²

C₁₉×#382

yes

characteristic

158

C₂²

C₁₉×#490

yes

characteristic

159

C₂²

C₁₉×#491

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

C₁₉×#428

yes

characteristic

164

C₄

C₁₉×#428

yes

characteristic

165

C₄

C₁₉×#489

yes

characteristic

166

C₄

C₁₉×#489

yes

characteristic

167

C₂

—

168

C₂

—

169

C₂

C₁₉×#1833

yes

—

170

C₂

C₁₉×#1836

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#382
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#382

commutator

C₄²

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

C₂³×C₁₉

G ▷ C₄² ▷ C₂² ▷ C₁

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
15. C₁₉×#322	C₄	semidirect
53. #8795	C₁₉	direct (N × H)
96. #322	C₄×C₁₉	semidirect
117. C₁₉	#8795	direct (N × H)

H ≅ G/N

type

15. C₁₉×#322

C₄

semidirect

53. #8795

C₁₉

direct (N × H)

96. #322

C₄×C₁₉

semidirect

117. C₁₉

#8795

direct (N × H)

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

subgroup	index
C₁₉×#1846	2
C₁₉×#1837	2
C₁₉×#1452	2
C₁₉×#1286	2
#8795	19

subgroup

index

C₁₉×#1846

C₁₉×#1837

C₁₉×#1452

C₁₉×#1286

#8795

Subgroups — C₁₉×#8795 #18014754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8795 #18014754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8795 #18014754