Group #18070857 — subgroups

Subgroups — #18070857

Order 4864.

384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14563778	C₂	1	2	yes	maximal
2	#14561458	C₂	1	4	yes	maximal
3	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
4	#11926299	—	2	2	no	—
5	#11926299	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
8	C₁₉×#389	C₂²	1	2	yes	—
9	C₁₉×#387	—	2	2	no	—
10	C₁₉×#382	C₄	1	1	yes	characteristic
11	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
12	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#125	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	—	2	4	no	—
26	C₁₉×#95	—	2	2	no	—
27	C₁₉×#95	—	2	2	no	—
28	C₁₉×#95	—	2	2	no	—
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
36	C₄⋊C₄×C₁₉	—	2	8	no	—
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄⋊C₄×C₁₉	—	4	2	no	—
39	C₄⋊C₄×C₁₉	—	4	4	no	—
40	C₄⋊C₄×C₁₉	M₁₆	1	4	yes	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	C₄²×C₁₉	—	2	4	no	—
44	C₄²×C₁₉	—	4	2	no	—
45	C₄²×C₁₉	—	4	1	no	—
46	C₄²×C₁₉	—	4	4	no	—
47	C₂×C₁₉⋊C₈	—	4	4	no	—
48	C₂×C₁₉⋊C₈	—	4	4	no	—
49	C₂×C₁₉⋊C₈	—	4	4	no	—
50	#7650	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	4	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	#101	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
70	C₂×C₄×C₁₉	#135	1	4	yes	—
71	C₁₉⋊C₈	—	8	4	no	—
72	C₄×#125	D₁₉	1	1	yes	characteristic
73	#1839	—	19	2	no	—
74	#1271	—	19	4	no	—
75	C₂²×C₁₉	#407	1	1	yes	characteristic
76	C₂²×C₁₉	#410	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
78	C₂²×C₁₉	#416	1	2	yes	—
79	C₂²×C₁₉	#421	1	2	yes	—
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	4	no	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	4	1	no	—
84	C₄×C₁₉	—	4	2	no	—
85	C₄×C₁₉	—	4	4	no	—
86	C₄×C₁₉	—	8	2	no	—
87	C₂×#125	Dic₁₉	1	1	yes	characteristic
88	#389	C₂×D₁₉	1	2	yes	—
89	#387	—	2	2	no	—
90	#382	Dic₁₉	1	1	yes	characteristic
91	C₄×C₄⋊C₄	—	2	2	no	—
92	C₄×C₄⋊C₄	Dic₁₉	1	2	yes	—
93	C₄³	C₂×D₁₉	1	1	yes	characteristic
94	#336	—	19	4	no	—
95	#336	—	38	2	no	—
96	#336	—	38	2	no	—
97	C₂×C₁₉	#1467	1	1	yes	characteristic
98	C₂×C₁₉	#1488	1	2	yes	—
99	C₂×C₁₉	#1521	1	2	yes	—
100	C₂×C₁₉	#1534	1	1	yes	characteristic
101	C₂×C₁₉	#1544	1	1	yes	characteristic
102	C₂²×C₈	—	38	4	no	—
103	#125	—	2	4	no	—
104	C₂×C₄⋊C₄	—	2	2	no	—
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
107	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
108	C₂×C₄²	—	2	2	no	—
109	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
110	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
111	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
112	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
113	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
114	#95	—	2	2	no	—
115	#95	—	2	2	no	—
116	#95	—	2	2	no	—
117	C₁₉	#7650	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₄	—	2	2	no	—
119	C₂²×C₄	—	2	2	no	—
120	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
121	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
122	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
123	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
124	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
125	C₂×C₈	—	76	4	no	—
126	C₂×C₈	—	76	4	no	—
127	C₂×C₈	—	76	4	no	—
128	C₄⋊C₄	—	2	8	no	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	4	2	no	—
131	C₄⋊C₄	—	4	4	no	—
132	C₄⋊C₄	#64520	1	4	yes	—
133	C₄²	—	2	4	no	—
134	C₄²	—	2	2	no	—
135	C₄²	—	2	2	no	—
136	C₄²	—	4	2	no	—
137	C₄²	—	4	1	no	—
138	C₄²	—	4	4	no	—
139	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	#10597293	1	2	yes	—
157	C₂×C₄	C₂×#64520	1	2	yes	—
158	C₂×C₄	#10597396	1	4	yes	—
159	C₈	—	152	4	no	—
160	C₂²	#11926508	1	1	yes	characteristic
161	C₂²	#11926518	1	1	yes	characteristic
162	C₂²	C₂×#10597293	1	1	yes	characteristic
163	C₂²	#11926540	1	2	yes	—
164	C₂²	#11926561	1	2	yes	—
165	C₄	—	2	4	no	—
166	C₄	—	2	2	no	—
167	C₄	—	2	2	no	—
168	C₄	—	4	2	no	—
169	C₄	—	4	4	no	—
170	C₄	—	4	1	no	—
171	C₄	—	8	2	no	—
172	C₂	#14561979	1	1	yes	characteristic
173	C₂	#14562069	1	2	yes	—
174	C₂	#14562212	1	2	yes	—
175	C₂	#14562262	1	1	yes	characteristic
176	C₂	#14562300	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563778

C₂

yes

maximal

#14561458

C₂

yes

maximal

C₄×C₁₉×#125

C₂

yes

maximal, characteristic

#11926299

—

#11926299

—

#11926299

C₂²

yes

—

C₂×C₁₉×#125

C₄

yes

characteristic

C₁₉×#389

C₂²

yes

—

C₁₉×#387

—

C₁₉×#382

C₄

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7650

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₁₉⋊C₈

—

C₄×#125

D₁₉

yes

characteristic

#1839

—

#1271

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#421

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#125

Dic₁₉

yes

characteristic

#389

C₂×D₁₉

yes

—

#387

—

#382

Dic₁₉

yes

characteristic

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

Dic₁₉

yes

—

C₄³

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

#1467

yes

characteristic

C₂×C₁₉

#1488

yes

—

C₂×C₁₉

#1521

yes

—

100

C₂×C₁₉

#1534

yes

characteristic

101

C₂×C₁₉

#1544

yes

characteristic

102

C₂²×C₈

—

103

#125

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

107

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

108

C₂×C₄²

—

109

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

110

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

111

C₂×C₄²

C₂²⋊D₁₉

yes

—

112

C₂×C₄²

C₂²⋊D₁₉

yes

—

113

C₂×C₄²

C₂²×D₁₉

yes

characteristic

114

#95

—

115

#95

—

116

#95

—

117

C₁₉

#7650

yes

characteristic, complemented, Sylow

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

121

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

122

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

123

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

124

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

#64520

yes

—

133

C₄²

—

134

C₄²

—

135

C₄²

—

136

C₄²

—

137

C₄²

—

138

C₄²

—

139

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

#10597293

yes

—

157

C₂×C₄

C₂×#64520

yes

—

158

C₂×C₄

#10597396

yes

—

159

C₈

—

152

—

160

C₂²

#11926508

yes

characteristic

161

C₂²

#11926518

yes

characteristic

162

C₂²

C₂×#10597293

yes

characteristic

163

C₂²

#11926540

yes

—

164

C₂²

#11926561

yes

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₂

#14561979

yes

characteristic

173

C₂

#14562069

yes

—

174

C₂

#14562212

yes

—

175

C₂

#14562262

yes

characteristic

176

C₂

#14562300

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#125	D₁₉
hypocenter	C₁₉	#7650
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#125

N	H ≅ G/N	type
117. C₁₉	#7650	semidirect

H ≅ G/N

type

117. C₁₉

#7650

semidirect

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

subgroup	index
#14563778	2
#14561458	2
C₄×C₁₉×#125	2
#7650	19

subgroup

index

#14563778

#14561458

C₄×C₁₉×#125

#7650

Subgroups — #18070857

Conjugacy classes of subgroups

Complements

Maximal subgroups