Group #14559932 — subgroups

Subgroups — C₁₉×#2075 #14559932

Order 2432.

256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 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×#107	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#380	C₂	1	2	yes	maximal
4	C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#340	C₂	1	2	yes	maximal, complemented
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
12	C₁₉×#107	—	2	2	no	—
13	C₁₉×C₂²⋊C₈	—	2	2	no	—
14	C₁₉×#95	—	2	2	no	—
15	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	—	2	1	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂²⋊C₄×C₁₉	—	4	4	no	—
33	C₂³×C₁₉	—	2	1	no	—
34	C₂³×C₁₉	—	2	2	no	—
35	C₂³×C₁₉	—	2	1	no	—
36	C₂³×C₁₉	—	2	2	no	—
37	C₂³×C₁₉	D₈	1	2	yes	—
38	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#41	1	2	yes	—
52	C₂×C₄×C₁₉	#41	1	2	yes	—
53	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	—	4	1	no	—
56	#2075	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂²×C₁₉	—	2	2	no	—
58	C₂²×C₁₉	—	2	4	no	—
59	C₂²×C₁₉	—	4	1	no	—
60	C₂²×C₁₉	—	4	1	no	—
61	C₂²×C₁₉	—	4	2	no	—
62	C₂²×C₁₉	#121	1	1	yes	characteristic
63	C₂²×C₁₉	#123	1	2	yes	—
64	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
65	C₂²×C₁₉	#135	1	1	yes	characteristic
66	C₂²×C₁₉	#137	1	2	yes	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	—	8	2	no	—
69	C₄×C₁₉	—	8	2	no	—
70	C₄×C₁₉	#123	1	1	yes	characteristic
71	C₄×C₁₉	#124	1	1	yes	characteristic
72	C₄×C₁₉	#126	1	2	yes	—
73	C₂×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
75	#380	C₂×C₁₉	1	2	yes	—
76	#340	C₂×C₁₉	1	1	yes	characteristic, complemented
77	#340	C₂×C₁₉	1	2	yes	complemented
78	C₂×C₁₉	—	4	2	no	—
79	C₂×C₁₉	#397	1	1	yes	characteristic
80	C₂×C₁₉	#466	1	1	yes	characteristic
81	C₂×C₁₉	#470	1	1	yes	characteristic
82	C₂×C₁₉	#480	1	2	yes	—
83	C₂×C₁₉	#485	1	2	yes	—
84	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
85	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
86	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
88	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
89	C₂×C₂²⋊C₄	—	2	2	no	—
90	#107	—	2	2	no	—
91	C₂²⋊C₈	—	2	2	no	—
92	#95	—	2	2	no	—
93	C₁₉	#2075	1	1	yes	characteristic, direct product factor, Sylow
94	C₂⁴	D₄×C₁₉	1	1	yes	characteristic
95	C₂²×C₄	—	2	1	no	—
96	C₂²×C₄	—	2	1	no	—
97	C₂²×C₄	—	2	2	no	—
98	C₂²×C₄	—	2	2	no	—
99	C₂²×C₄	—	2	2	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
102	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	D₄×C₁₉	1	2	yes	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	2	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₂²⋊C₄	—	4	4	no	—
112	C₂³	—	2	1	no	—
113	C₂³	—	2	2	no	—
114	C₂³	—	2	1	no	—
115	C₂³	—	2	2	no	—
116	C₂³	D₈×C₁₉	1	2	yes	—
117	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	2	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
130	C₂×C₄	#41×C₁₉	1	2	yes	—
131	C₂×C₄	#41×C₁₉	1	2	yes	—
132	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	4	1	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	4	no	—
137	C₂²	—	4	1	no	—
138	C₂²	—	4	1	no	—
139	C₂²	—	4	2	no	—
140	C₂²	C₁₉×#121	1	1	yes	characteristic
141	C₂²	C₁₉×#123	1	2	yes	—
142	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
143	C₂²	C₁₉×#135	1	1	yes	characteristic
144	C₂²	C₁₉×#137	1	2	yes	—
145	C₄	—	4	1	no	—
146	C₄	—	8	2	no	—
147	C₄	—	8	2	no	—
148	C₄	C₁₉×#123	1	1	yes	characteristic
149	C₄	C₁₉×#124	1	1	yes	characteristic
150	C₄	C₁₉×#126	1	2	yes	—
151	C₂	—	4	2	no	—
152	C₂	C₁₉×#397	1	1	yes	characteristic
153	C₂	C₁₉×#466	1	1	yes	characteristic
154	C₂	C₁₉×#470	1	1	yes	characteristic
155	C₂	C₁₉×#480	1	2	yes	—
156	C₂	C₁₉×#485	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#107

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×C₂²⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#380

C₂

yes

maximal

C₁₉×#340

C₂

yes

maximal, characteristic, complemented

C₁₉×#340

C₂

yes

maximal, complemented

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₁₉×#107

—

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

D₈

yes

—

C₂³×C₁₉

C₂×D₄

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

#2075

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

C₂×D₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×#107

C₂×C₁₉

yes

characteristic, complemented

C₂×C₂²⋊C₈

C₂×C₁₉

yes

characteristic

#380

C₂×C₁₉

yes

—

#340

C₂×C₁₉

yes

characteristic, complemented

#340

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#485

yes

—

C₂³×C₄

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂×C₂²⋊C₄

—

#107

—

C₂²⋊C₈

—

#95

—

C₁₉

#2075

yes

characteristic, direct product factor, Sylow

C₂⁴

D₄×C₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

D₄×C₁₉

yes

characteristic

102

C₂²×C₄

C₂³×C₁₉

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

D₄×C₁₉

yes

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

D₈×C₁₉

yes

—

117

C₂³

C₂×D₄×C₁₉

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

130

C₂×C₄

#41×C₁₉

yes

—

131

C₂×C₄

#41×C₁₉

yes

—

132

C₂×C₄

#41×C₁₉

yes

characteristic

133

C₈

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₁₉×#121

yes

characteristic

141

C₂²

C₁₉×#123

yes

—

142

C₂²

C₂×D₈×C₁₉

yes

characteristic

143

C₂²

C₁₉×#135

yes

characteristic

144

C₂²

C₁₉×#137

yes

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

C₁₉×#123

yes

characteristic

149

C₄

C₁₉×#124

yes

characteristic

150

C₄

C₁₉×#126

yes

—

151

C₂

—

152

C₂

C₁₉×#397

yes

characteristic

153

C₂

C₁₉×#466

yes

characteristic

154

C₂

C₁₉×#470

yes

characteristic

155

C₂

C₁₉×#480

yes

—

156

C₂

C₁₉×#485

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

D₄

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×#107	C₂	semidirect
4. C₁₉×#340	C₂	semidirect
5. C₁₉×#340	C₂	semidirect
56. #2075	C₁₉	direct (N × H)
73. C₂×#107	C₂×C₁₉	semidirect
76. #340	C₂×C₁₉	semidirect
77. #340	C₂×C₁₉	semidirect
93. C₁₉	#2075	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×#107

C₂

semidirect

4. C₁₉×#340

C₂

semidirect

5. C₁₉×#340

C₂

semidirect

56. #2075

C₁₉

direct (N × H)

73. C₂×#107

C₂×C₁₉

semidirect

76. #340

C₂×C₁₉

semidirect

77. #340

C₂×C₁₉

semidirect

93. C₁₉

#2075

direct (N × H)

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

subgroup	index
C₂×C₁₉×#107	2
C₂×C₁₉×C₂²⋊C₈	2
C₁₉×#380	2
C₁₉×#340	2
#2075	19

subgroup

index

C₂×C₁₉×#107

C₂×C₁₉×C₂²⋊C₈

C₁₉×#380

C₁₉×#340

#2075

Subgroups — C₁₉×#2075 #14559932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2075 #14559932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2075 #14559932