Group #18016298 — subgroups

Subgroups — C₁₉×#10339 #18016298

Order 4864.

738 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2483	C₂	1	3	yes	maximal
2	C₁₉×#1819	C₂	1	3	yes	maximal
3	C₁₉×#1304	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
5	C₁₉×#397	—	2	6	no	—
6	C₁₉×#385	—	2	6	no	—
7	C₁₉×#381	—	2	6	no	—
8	C₁₉×#379	C₂²	1	1	yes	characteristic
9	C₁₉×#379	C₂²	1	3	yes	—
10	C₁₉×#342	—	2	6	no	—
11	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
12	C₂³×C₄×C₁₉	D₄	1	6	yes	—
13	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
14	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
15	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
16	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
17	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
18	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
19	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
20	C₂×C₂²⋊C₄×C₁₉	D₄	1	6	yes	—
21	C₁₉×#95	—	2	6	no	—
22	C₁₉×#95	—	2	12	no	—
23	C₂⁴×C₁₉	—	4	6	no	—
24	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
25	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
26	C₂⁴×C₁₉	#41	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	—	2	6	no	—
28	C₂²×C₄×C₁₉	—	2	6	no	—
29	C₂²×C₄×C₁₉	—	2	6	no	—
30	C₂²×C₄×C₁₉	—	2	6	no	—
31	C₂²×C₄×C₁₉	—	4	12	no	—
32	C₂²×C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	8	6	no	—
34	C₂²⋊C₄×C₁₉	—	4	12	no	—
35	C₂²⋊C₄×C₁₉	—	4	3	no	—
36	C₂²⋊C₄×C₁₉	—	4	6	no	—
37	C₂²⋊C₄×C₁₉	—	4	3	no	—
38	C₂²⋊C₄×C₁₉	—	4	6	no	—
39	C₂²⋊C₄×C₁₉	—	4	6	no	—
40	#10339	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂³×C₁₉	—	2	12	no	—
42	C₂³×C₁₉	—	2	6	no	—
43	C₂³×C₁₉	—	4	3	no	—
44	C₂³×C₁₉	—	4	6	no	—
45	C₂³×C₁₉	—	4	3	no	—
46	C₂³×C₁₉	—	8	8	no	—
47	C₂³×C₁₉	#120	1	3	yes	—
48	C₂³×C₁₉	#121	1	3	yes	—
49	C₂³×C₁₉	#127	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	4	12	no	—
51	C₂×C₄×C₁₉	—	4	12	no	—
52	C₂×C₄×C₁₉	—	4	6	no	—
53	C₂×C₄×C₁₉	—	4	6	no	—
54	C₂×C₄×C₁₉	—	4	12	no	—
55	C₂×C₄×C₁₉	—	8	6	no	—
56	C₂×C₄×C₁₉	—	8	3	no	—
57	#2483	C₂×C₁₉	1	3	yes	—
58	#1819	C₂×C₁₉	1	3	yes	—
59	#1304	C₂×C₁₉	1	1	yes	characteristic
60	C₂²×C₁₉	—	2	6	no	—
61	C₂²×C₁₉	—	2	6	no	—
62	C₂²×C₁₉	—	2	3	no	—
63	C₂²×C₁₉	—	2	3	no	—
64	C₂²×C₁₉	—	4	12	no	—
65	C₂²×C₁₉	—	8	6	no	—
66	C₂²×C₁₉	—	8	2	no	—
67	C₂²×C₁₉	#392	1	1	yes	characteristic
68	C₂²×C₁₉	#458	1	6	yes	—
69	C₄×C₁₉	—	8	6	no	—
70	C₄×C₁₉	—	8	6	no	—
71	C₄×C₁₉	—	16	1	no	—
72	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
73	#397	—	2	6	no	—
74	#385	—	2	6	no	—
75	#381	—	2	6	no	—
76	#379	C₂²×C₁₉	1	1	yes	characteristic
77	#379	C₂²×C₁₉	1	3	yes	—
78	#342	—	2	6	no	—
79	C₂×C₁₉	—	2	6	no	—
80	C₂×C₁₉	—	4	1	no	—
81	C₂×C₁₉	—	4	3	no	—
82	C₂×C₁₉	#2022	1	3	yes	—
83	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
84	C₂³×C₄	D₄×C₁₉	1	6	yes	—
85	C₂×C₄⋊C₄	—	2	6	no	—
86	C₂×C₂²⋊C₄	—	2	3	no	—
87	C₂×C₂²⋊C₄	—	2	6	no	—
88	C₂×C₂²⋊C₄	—	2	6	no	—
89	C₂×C₂²⋊C₄	—	2	6	no	—
90	C₂×C₂²⋊C₄	—	2	3	no	—
91	C₂×C₂²⋊C₄	—	2	3	no	—
92	C₂×C₂²⋊C₄	D₄×C₁₉	1	6	yes	—
93	#95	—	2	6	no	—
94	#95	—	2	12	no	—
95	C₁₉	#10339	1	1	yes	characteristic, direct product factor, Sylow
96	C₂⁴	—	4	6	no	—
97	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
98	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
99	C₂⁴	#41×C₁₉	1	1	yes	characteristic
100	C₂²×C₄	—	2	6	no	—
101	C₂²×C₄	—	2	6	no	—
102	C₂²×C₄	—	2	6	no	—
103	C₂²×C₄	—	2	6	no	—
104	C₂²×C₄	—	4	12	no	—
105	C₂²×C₄	—	4	1	no	—
106	C₄⋊C₄	—	8	6	no	—
107	C₂²⋊C₄	—	4	12	no	—
108	C₂²⋊C₄	—	4	3	no	—
109	C₂²⋊C₄	—	4	6	no	—
110	C₂²⋊C₄	—	4	3	no	—
111	C₂²⋊C₄	—	4	6	no	—
112	C₂²⋊C₄	—	4	6	no	—
113	C₂³	—	2	12	no	—
114	C₂³	—	2	6	no	—
115	C₂³	—	4	3	no	—
116	C₂³	—	4	6	no	—
117	C₂³	—	4	3	no	—
118	C₂³	—	8	8	no	—
119	C₂³	C₁₉×#120	1	3	yes	—
120	C₂³	C₁₉×#121	1	3	yes	—
121	C₂³	C₁₉×#127	1	1	yes	characteristic
122	C₂×C₄	—	4	12	no	—
123	C₂×C₄	—	4	12	no	—
124	C₂×C₄	—	4	6	no	—
125	C₂×C₄	—	4	6	no	—
126	C₂×C₄	—	4	12	no	—
127	C₂×C₄	—	8	6	no	—
128	C₂×C₄	—	8	3	no	—
129	C₂²	—	2	6	no	—
130	C₂²	—	2	6	no	—
131	C₂²	—	2	3	no	—
132	C₂²	—	2	3	no	—
133	C₂²	—	4	12	no	—
134	C₂²	—	8	6	no	—
135	C₂²	—	8	2	no	—
136	C₂²	C₁₉×#392	1	1	yes	characteristic
137	C₂²	C₁₉×#458	1	6	yes	—
138	C₄	—	8	6	no	—
139	C₄	—	8	6	no	—
140	C₄	—	16	1	no	—
141	C₂	—	2	6	no	—
142	C₂	—	4	1	no	—
143	C₂	—	4	3	no	—
144	C₂	C₁₉×#2022	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2483

C₂

yes

maximal

C₁₉×#1819

C₂

yes

maximal

C₁₉×#1304

C₂

yes

maximal, characteristic

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#397

—

C₁₉×#385

—

C₁₉×#381

—

C₁₉×#379

C₂²

yes

characteristic

C₁₉×#379

C₂²

yes

—

C₁₉×#342

—

C₂⁵×C₁₉

C₂³

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

#41

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#10339

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

—

C₂³×C₁₉

#121

yes

—

C₂³×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

#2483

C₂×C₁₉

yes

—

#1819

C₂×C₁₉

yes

—

#1304

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#392

yes

characteristic

C₂²×C₁₉

#458

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

—

—

—

—

C₂²×C₁₉

yes

characteristic

#379

C₂²×C₁₉

yes

—

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2022

yes

—

C₂⁵

C₂³×C₁₉

yes

characteristic

C₂³×C₄

D₄×C₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

#95

—

#95

—

C₁₉

#10339

yes

characteristic, direct product factor, Sylow

C₂⁴

—

C₂⁴

C₂×D₄×C₁₉

yes

—

C₂⁴

C₂×D₄×C₁₉

yes

—

C₂⁴

#41×C₁₉

yes

characteristic

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

112

C₂²⋊C₄

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₁₉×#120

yes

—

120

C₂³

C₁₉×#121

yes

—

121

C₂³

C₁₉×#127

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

C₁₉×#392

yes

characteristic

137

C₂²

C₁₉×#458

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

C₁₉×#2022

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂⁵

C₂³×C₁₉

prime radical

C₂⁵×C₁₉

C₂³

LCS

G ▷ C₂⁵ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

N	H ≅ G/N	type
40. #10339	C₁₉	direct (N × H)
95. C₁₉	#10339	direct (N × H)

H ≅ G/N

type

40. #10339

C₁₉

direct (N × H)

95. C₁₉

#10339

direct (N × H)

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

subgroup	index
C₁₉×#2483	2
C₁₉×#1819	2
C₁₉×#1304	2
#10339	19

subgroup

index

C₁₉×#2483

C₁₉×#1819

C₁₉×#1304

#10339

Subgroups — C₁₉×#10339 #18016298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10339 #18016298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10339 #18016298