Group #14560025 — subgroups

Subgroups — C₁₉×#2168 #14560025

Order 2432.

164 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 100 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×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
11	C₁₉×M₃₂	—	2	2	no	—
12	C₂×C₁₆×C₁₉	—	2	2	no	—
13	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
18	C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
19	C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×D₄×C₁₉	C₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	C₈	1	1	yes	characteristic
33	C₂²⋊C₄×C₁₉	C₈	1	1	yes	characteristic
34	C₂²⋊C₄×C₁₉	C₈	1	1	yes	characteristic
35	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₁₆×C₁₉	—	2	1	no	—
37	C₁₆×C₁₉	—	2	1	no	—
38	C₁₆×C₁₉	—	2	1	no	—
39	C₁₆×C₁₉	D₄	1	2	yes	complemented
40	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
41	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
42	D₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₈×C₁₉	—	2	1	no	—
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	—	2	1	no	—
55	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₁₉	#41	1	1	yes	characteristic
57	#2168	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	M₃₂	1	2	yes	complemented
64	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
70	C₄×C₁₉	#131	1	1	yes	characteristic
71	C₂×M₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
72	C₂²×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
73	C₈×D₄	C₂×C₁₉	1	1	yes	characteristic
74	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
75	C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
76	C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
77	#346	C₂×C₁₉	1	1	yes	characteristic, complemented
78	C₂×C₁₉	—	2	2	no	—
79	C₂×C₁₉	—	4	1	no	—
80	C₂×C₁₉	C₈×D₄	1	1	yes	characteristic
81	C₂×C₁₉	C₂×M₃₂	1	1	yes	characteristic
82	C₂×C₁₉	#504	1	1	yes	characteristic
83	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
84	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
85	C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
86	M₃₂	—	2	2	no	—
87	C₂×C₁₆	—	2	2	no	—
88	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
89	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
90	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
91	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
92	C₄⋊C₈	C₄×C₁₉	1	1	yes	characteristic
93	C₂²⋊C₈	C₄×C₁₉	1	1	yes	characteristic
94	C₂²⋊C₈	C₄×C₁₉	1	1	yes	characteristic
95	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
96	C₁₉	#2168	1	1	yes	characteristic, direct product factor, Sylow
97	C₂×D₄	C₈×C₁₉	1	1	yes	characteristic
98	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
99	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
105	C₂×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
106	C₂×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
107	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
108	C₄⋊C₄	C₈×C₁₉	1	1	yes	characteristic
109	C₂²⋊C₄	C₈×C₁₉	1	1	yes	characteristic
110	C₂²⋊C₄	C₈×C₁₉	1	1	yes	characteristic
111	C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
112	C₁₆	—	2	1	no	—
113	C₁₆	—	2	1	no	—
114	C₁₆	—	2	1	no	—
115	C₁₆	D₄×C₁₉	1	2	yes	complemented
116	C₂³	C₂×C₈×C₁₉	1	1	yes	characteristic
117	C₂³	C₂×C₈×C₁₉	1	1	yes	characteristic
118	D₄	—	2	2	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
124	C₂×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
125	C₂×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
126	C₂×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
127	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
128	C₈	—	2	1	no	—
129	C₈	—	2	1	no	—
130	C₈	—	2	1	no	—
131	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
132	C₈	#41×C₁₉	1	1	yes	characteristic
133	C₂²	—	2	1	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	C₁₉×M₃₂	1	2	yes	complemented
139	C₂²	C₂²×C₈×C₁₉	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
145	C₄	C₁₉×#131	1	1	yes	characteristic
146	C₂	—	2	2	no	—
147	C₂	—	4	1	no	—
148	C₂	C₈×D₄×C₁₉	1	1	yes	characteristic
149	C₂	C₂×C₁₉×M₃₂	1	1	yes	characteristic
150	C₂	C₁₉×#504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×M₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₈×D₄×C₁₉

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#346

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×D₄×C₁₉

C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₈

yes

characteristic

C₂²⋊C₄×C₁₉

C₈

yes

characteristic

C₂²⋊C₄×C₁₉

C₈

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

complemented

C₂³×C₁₉

C₂×C₈

yes

characteristic

C₂³×C₁₉

C₂×C₈

yes

characteristic

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

M₃₂

yes

complemented

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

#131

yes

characteristic

C₂×M₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₈×D₄

C₂×C₁₉

yes

characteristic

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂²⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂²⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

#346

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₈×D₄

yes

characteristic

C₂×C₁₉

C₂×M₃₂

yes

characteristic

C₂×C₁₉

#504

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

C₄×D₄

C₄×C₁₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₄×C₁₉

yes

characteristic

C₂²⋊C₈

C₄×C₁₉

yes

characteristic

C₂²⋊C₈

C₄×C₁₉

yes

characteristic

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2168

yes

characteristic, direct product factor, Sylow

C₂×D₄

C₈×C₁₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₁₉

yes

characteristic

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×C₄×C₁₉

yes

characteristic

105

C₂×C₈

C₂×C₄×C₁₉

yes

characteristic

106

C₂×C₈

C₂×C₄×C₁₉

yes

characteristic

107

C₂×C₈

C₂³×C₁₉

yes

characteristic

108

C₄⋊C₄

C₈×C₁₉

yes

characteristic

109

C₂²⋊C₄

C₈×C₁₉

yes

characteristic

110

C₂²⋊C₄

C₈×C₁₉

yes

characteristic

111

C₄²

C₂×C₄×C₁₉

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

115

C₁₆

D₄×C₁₉

yes

complemented

116

C₂³

C₂×C₈×C₁₉

yes

characteristic

117

C₂³

C₂×C₈×C₁₉

yes

characteristic

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₂×C₈×C₁₉

yes

characteristic

124

C₂×C₄

C₂×C₈×C₁₉

yes

characteristic

125

C₂×C₄

C₂×C₈×C₁₉

yes

characteristic

126

C₂×C₄

C₂×C₈×C₁₉

yes

characteristic

127

C₂×C₄

C₂²×C₄×C₁₉

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

C₂×D₄×C₁₉

yes

characteristic

132

C₈

#41×C₁₉

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₁₉×M₃₂

yes

complemented

139

C₂²

C₂²×C₈×C₁₉

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

C₄×D₄×C₁₉

yes

characteristic

145

C₄

C₁₉×#131

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

C₈×D₄×C₁₉

yes

characteristic

149

C₂

C₂×C₁₉×M₃₂

yes

characteristic

150

C₂

C₁₉×#504

yes

characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂²×C₈
prime radical	C₂×D₄×C₁₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₈×C₁₉

C₂³

commutator

C₂²

C₂²×C₈×C₁₉

Frattini, cosocle

C₂×C₈

C₂³×C₁₉

socle

C₂²×C₁₉

C₂²×C₈

prime radical

C₂×D₄×C₁₉

C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×M₃₂	C₂	semidirect
2. C₂²×C₁₆×C₁₉	C₂	semidirect
4. C₁₉×C₄⋊C₁₆	C₂	semidirect
5. C₁₉×C₂²⋊C₁₆	C₂	semidirect
6. C₁₉×C₂²⋊C₁₆	C₂	semidirect
7. C₁₉×#346	C₂	semidirect
39. C₁₆×C₁₉	D₄	semidirect
57. #2168	C₁₉	direct (N × H)
63. C₂²×C₁₉	M₃₂	semidirect
71. C₂×M₃₂	C₂×C₁₉	semidirect
72. C₂²×C₁₆	C₂×C₁₉	semidirect
74. C₄⋊C₁₆	C₂×C₁₉	semidirect
75. C₂²⋊C₁₆	C₂×C₁₉	semidirect
76. C₂²⋊C₁₆	C₂×C₁₉	semidirect
77. #346	C₂×C₁₉	semidirect
96. C₁₉	#2168	direct (N × H)
115. C₁₆	D₄×C₁₉	semidirect
138. C₂²	C₁₉×M₃₂	semidirect

H ≅ G/N

type

1. C₂×C₁₉×M₃₂

C₂

semidirect

2. C₂²×C₁₆×C₁₉

C₂

semidirect

4. C₁₉×C₄⋊C₁₆

C₂

semidirect

5. C₁₉×C₂²⋊C₁₆

C₂

semidirect

6. C₁₉×C₂²⋊C₁₆

C₂

semidirect

7. C₁₉×#346

C₂

semidirect

39. C₁₆×C₁₉

D₄

semidirect

57. #2168

C₁₉

direct (N × H)

63. C₂²×C₁₉

M₃₂

semidirect

71. C₂×M₃₂

C₂×C₁₉

semidirect

72. C₂²×C₁₆

C₂×C₁₉

semidirect

74. C₄⋊C₁₆

C₂×C₁₉

semidirect

75. C₂²⋊C₁₆

C₂×C₁₉

semidirect

76. C₂²⋊C₁₆

C₂×C₁₉

semidirect

77. #346

C₂×C₁₉

semidirect

96. C₁₉

#2168

direct (N × H)

115. C₁₆

D₄×C₁₉

semidirect

138. C₂²

C₁₉×M₃₂

semidirect

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

subgroup	index
C₂×C₁₉×M₃₂	2
C₂²×C₁₆×C₁₉	2
C₈×D₄×C₁₉	2
C₁₉×C₄⋊C₁₆	2
C₁₉×C₂²⋊C₁₆	2
C₁₉×#346	2
#2168	19

subgroup

index

C₂×C₁₉×M₃₂

C₂²×C₁₆×C₁₉

C₈×D₄×C₁₉

C₁₉×C₄⋊C₁₆

C₁₉×C₂²⋊C₁₆

C₁₉×#346

#2168

Subgroups — C₁₉×#2168 #14560025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2168 #14560025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2168 #14560025