Group #18013245 — subgroups

Subgroups — C₁₉×#7286 #18013245

Order 4864.

250 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1985	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1461	C₂	1	2	yes	maximal
3	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
4	C₁₉×#431	—	2	2	no	—
5	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
7	C₁₉×#336	—	2	2	no	—
8	C₁₉×#324	—	2	2	no	—
9	C₁₉×#324	C₄	1	4	yes	—
10	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	—	2	1	no	—
13	C₄×Q₈×C₁₉	—	4	1	no	—
14	C₄×Q₈×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	2	yes	—
19	C₁₉×C₄⋊C₈	—	4	2	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₁₉×C₂²⋊C₈	—	2	4	no	—
22	C₁₉×#97	—	4	1	no	—
23	C₄×C₈×C₁₉	—	4	2	no	—
24	C₂×Q₈×C₁₉	—	2	4	no	—
25	C₂×Q₈×C₁₉	—	4	1	no	—
26	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	—	4	4	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₄⋊C₄×C₁₉	—	4	2	no	—
38	C₄⋊C₄×C₁₉	—	4	1	no	—
39	C₄²×C₁₉	—	2	1	no	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	#7286	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₁₉	#95	1	1	yes	characteristic
45	Q₈×C₁₉	—	4	4	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#108	1	4	yes	—
59	C₈×C₁₉	—	4	2	no	—
60	C₈×C₁₉	—	8	4	no	—
61	C₈×C₁₉	—	8	1	no	—
62	#1985	C₂×C₁₉	1	1	yes	characteristic
63	#1461	C₂×C₁₉	1	2	yes	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	#341	1	2	yes	—
67	C₂²×C₁₉	#342	1	1	yes	characteristic
68	C₄×C₁₉	—	2	4	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	4	1	no	—
71	C₄×C₁₉	—	4	2	no	—
72	C₄×C₁₉	—	4	1	no	—
73	C₄×C₁₉	#355	1	1	yes	characteristic
74	C₄×C₁₉	#356	1	1	yes	characteristic
75	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
76	#431	—	2	2	no	—
77	C₂×C₄⋊C₈	C₄×C₁₉	1	1	yes	characteristic
78	C₂×#97	C₄×C₁₉	1	1	yes	characteristic
79	#336	—	2	2	no	—
80	#324	—	2	2	no	—
81	#324	C₄×C₁₉	1	4	yes	—
82	C₂×C₁₉	—	2	2	no	—
83	C₂×C₁₉	#1298	1	1	yes	characteristic
84	C₂×C₁₉	#1391	1	1	yes	characteristic
85	C₂×C₁₉	#1394	1	1	yes	characteristic
86	C₂²×Q₈	Q₈×C₁₉	1	1	yes	characteristic
87	C₂²×C₈	—	2	1	no	—
88	C₂²×C₈	—	2	1	no	—
89	C₄×Q₈	—	4	1	no	—
90	C₄×Q₈	—	4	1	no	—
91	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
92	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
93	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
94	C₂×C₄²	D₄×C₁₉	1	2	yes	—
95	C₄⋊C₈	—	4	1	no	—
96	C₄⋊C₈	—	4	2	no	—
97	C₂²⋊C₈	—	2	4	no	—
98	#97	—	4	1	no	—
99	C₄×C₈	—	4	2	no	—
100	C₁₉	#7286	1	1	yes	characteristic, direct product factor, Sylow
101	C₂×Q₈	—	2	4	no	—
102	C₂×Q₈	—	4	1	no	—
103	C₂²×C₄	C₄²×C₁₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
106	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
107	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	4	1	no	—
110	C₂×C₈	—	4	1	no	—
111	C₂×C₈	—	4	4	no	—
112	C₂×C₈	—	4	2	no	—
113	C₂×C₈	—	4	1	no	—
114	C₄⋊C₄	—	4	2	no	—
115	C₄⋊C₄	—	4	1	no	—
116	C₄²	—	2	2	no	—
117	C₄²	—	2	1	no	—
118	C₄²	—	2	1	no	—
119	C₄²	—	2	2	no	—
120	C₂³	C₁₉×#95	1	1	yes	characteristic
121	Q₈	—	4	4	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
133	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
134	C₂×C₄	C₁₉×#108	1	4	yes	—
135	C₈	—	4	2	no	—
136	C₈	—	8	4	no	—
137	C₈	—	8	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₁₉×#341	1	2	yes	—
141	C₂²	C₁₉×#342	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	4	no	—
144	C₄	—	4	2	no	—
145	C₄	—	4	1	no	—
146	C₄	—	4	1	no	—
147	C₄	C₁₉×#355	1	1	yes	characteristic
148	C₄	C₁₉×#356	1	1	yes	characteristic
149	C₂	—	2	2	no	—
150	C₂	C₁₉×#1298	1	1	yes	characteristic
151	C₂	C₁₉×#1391	1	1	yes	characteristic
152	C₂	C₁₉×#1394	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1985

C₂

yes

maximal, characteristic

C₁₉×#1461

C₂

yes

maximal

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#336

—

C₁₉×#324

—

C₁₉×#324

C₄

yes

—

C₂²×Q₈×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#7286

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#95

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1985

C₂×C₁₉

yes

characteristic

#1461

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#341

yes

—

C₂²×C₁₉

#342

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄×Q₈

C₂²×C₁₉

yes

characteristic

#431

—

C₂×C₄⋊C₈

C₄×C₁₉

yes

characteristic

C₂×#97

C₄×C₁₉

yes

—

—

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

Q₈×C₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

C₂×C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

C₂×C₄²

D₄×C₁₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

100

C₁₉

#7286

yes

characteristic, direct product factor, Sylow

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂²×C₄

C₄²×C₁₉

yes

characteristic

104

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

105

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

106

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

107

C₂²×C₄

C₄⋊C₄×C₁₉

yes

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₂³

C₁₉×#95

yes

characteristic

121

Q₈

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₁₉×#99

yes

characteristic

133

C₂×C₄

C₁₉×#99

yes

characteristic

134

C₂×C₄

C₁₉×#108

yes

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₁₉×#341

yes

—

141

C₂²

C₁₉×#342

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

C₁₉×#355

yes

characteristic

148

C₄

C₁₉×#356

yes

characteristic

149

C₂

—

150

C₂

C₁₉×#1298

yes

characteristic

151

C₂

C₁₉×#1391

yes

characteristic

152

C₂

C₁₉×#1394

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#99
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₉
socle	C₂²×C₁₉	#342
prime radical	C₂³×C₁₉	#95
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#99

commutator

C₂²×C₄

C₄²×C₁₉

Frattini, cosocle

C₂×C₄×Q₈

C₂²×C₁₉

C₂²×C₁₉

C₂³×C₁₉

G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

N	H ≅ G/N	type
43. #7286	C₁₉	direct (N × H)
100. C₁₉	#7286	direct (N × H)

H ≅ G/N

type

43. #7286

C₁₉

direct (N × H)

100. C₁₉

#7286

direct (N × H)

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

subgroup	index
C₁₉×#1985	2
C₁₉×#1461	2
#7286	19

subgroup

index

C₁₉×#1985

C₁₉×#1461

#7286

Subgroups — C₁₉×#7286 #18013245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7286 #18013245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7286 #18013245