Subgroups — D 19 ⋊( C 3 ⋊#64425 ) #45692471

C₃⋊#19150290

C₂

yes

C₃×D₁₉⋊#3862

C₂

yes

D₁₉×C₃⋊(C₇⋊D₇)

C₃

yes

—

maximal

C₃×C₁₉⋊#3862

C₂²

yes

characteristic, complemented, Hall

C₃⋊(C₇⋊D₁₃₃)

C₂×C₃

yes

C₁₉×C₃⋊(C₇⋊D₇)

C₂×C₃

yes

C₃×C₇²×D₁₉

C₂×C₃

yes

D₁₉⋊#3862

—

D₁₉⋊#3862

D₃

yes

—

—

—

—

D₁₉×C₇⋊D₇

—

C₁₉⋊#3862

—

C₁₉⋊#3862

C₂×D₃

yes

C₃×C₇²×C₁₉

C₂²×C₃

yes

—

—

—

—

—

—

C₇⋊D₁₃₃

—

C₁₉×C₇⋊D₇

—

C₇²×D₁₉

C₃×D₃

yes

—

maximal, Hall

D₁₉×D₂₁

—

D₁₉×D₂₁

—

D₁₉×D₂₁

—

—

—

—

—

C₇²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃×#3862

—

—

—

D₃₉₉

—

D₃₉₉

—

D₃₉₉

—

C₁₉×D₂₁

—

C₁₉×D₂₁

—

C₁₉×D₂₁

—

C₃×C₇×D₁₉

—

C₃×C₇×D₁₉

yes

C₃×C₇×D₁₉

yes

—

—

—

—

—

—

—

—

D₃×D₁₉⋊C₃

—

C₂×C₃⋊(C₇⋊D₇)

—

C₂×#64425

—

D₇×D₁₉

—

D₇×D₁₉

—

D₇×D₁₉

—

C₃×#3862

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

yes

C₃×C₇×C₁₉

yes

—

—

—

—

C₃⋊(D₁₉⋊C₃)

—

D₃×C₁₉⋊C₃

—

C₃×D₁₉⋊C₃

—

C₂×C₃×C₇²

—

C₃⋊(C₇⋊D₇)

—

C₃⋊(C₇⋊D₇)

D₁₉⋊C₃

yes

—

—

—

—

D₁₃₃

—

D₁₃₃

—

D₁₃₃

—

C₇×D₁₉

—

C₇×D₁₉

yes

C₇×D₁₉

yes

D₇×C₁₉

—

D₇×C₁₉

—

D₇×C₁₉

—

—

133

—

—

133

—

D₃×D₁₉

—

C₂×D₁₉⋊C₃

—

147

—

C₂×C₇⋊D₇

—

C₃×C₁₉⋊C₃

—

C₃×C₇²

C₂×D₁₉⋊C₃

yes

#3862

—

#3862

—

100

C₇×C₁₉

—

101

C₇×C₁₉

yes

102

C₇×C₁₉

yes

103

C₂×C₃×ΓL(1,𝔽₈)

—

133

—

104

C₂×C₃×ΓL(1,𝔽₈)

—

133

—

105

—

133

—

106

—

133

—

107

—

133

—

108

—

133

—

109

D₅₇

—

110

C₃×D₁₉

#64425

yes

111

D₃×C₁₉

—

112

C₂×C₁₉⋊C₃

—

147

—

113

D₁₉⋊C₃

—

114

D₁₉⋊C₃

—

115

D₁₉⋊C₃

—

147

—

116

C₂×C₇²

—

117

C₇⋊D₇

—

118

C₇⋊D₇

—

119

C₂×D₂₁

—

133

—

120

C₂×D₂₁

—

133

—

121

C₂×D₂₁

—

399

—

122

—

399

—

123

—

399

—

124

C₂×D₁₉

—

147

125

C₃×ΓL(1,𝔽₈)

—

133

—

126

C₃×ΓL(1,𝔽₈)

—

133

—

127

C₃×C₁₉

C₂×#64425

yes

128

C₁₉⋊C₃

—

129

C₁₉⋊C₃

—

130

C₇²

D₃×D₁₉⋊C₃

yes

characteristic, complemented, Sylow

131

C₂×C₃×C₇

—

132

C₂×C₃×C₇

—

133

C₂×C₃×C₇

—

134

D₂₁

—

135

D₂₁

—

136

D₂₁

—

137

D₂₁

—

133

—

138

D₂₁

—

133

—

139

D₂₁

—

399

—

140

—

266

—

141

—

266

—

142

—

133

—

143

—

133

—

144

—

399

—

145

—

399

—

146

—

399

—

147

—

399

—

148

C₂×C₁₉

—

147

—

149

D₁₉

—

147

—

150

D₁₉

yes

151

C₂×C₃×D₃

—

931

152

C₂×D₇

—

399

—

153

C₂×D₇

—

399

—

154

C₂×D₇

—

1197

—

155

C₃×C₇

—

156

C₃×C₇

#11716321⋊C₂

yes

157

C₃×C₇

#11716322⋊C₂

yes

158

—

266

—

159

—

266

—

160

—

133

—

161

—

133

—

162

C₁₉

yes

characteristic, complemented, Sylow

163

C₂×C₃²

—

931

—

164

C₃×D₃

—

931

—

165

C₃×D₃

—

931

—

166

C₂×C₇

—

167

C₂×C₇

—

168

C₂×C₇

—

169

D₇

—

170

D₇

—

171

D₇

—

172

D₇

—

399

—

173

D₇

—

399

—

174

D₇

—

1197

—

175

C₂²×C₃

—

2793

—

176

C₂×D₃

—

931

—

177

C₃²

—

931

Sylow

178

C₇

—

179

C₇

#11716321⋊D₃

yes

180

C₇

#11716322⋊D₃

yes

181

C₂×C₃

—

182

C₂×C₃

—

1862

—

183

C₂×C₃

—

931

—

184

C₂×C₃

—

2793

—

185

C₂×C₃

—

2793

—

186

D₃

—

187

D₃

—

931

—

188

C₂²

—

2793

Sylow

189

C₃

—

1862

—

190

C₃

—

931

—

191

C₃

yes

192

C₂

—

193

C₂

—

147

—

194

C₂

—

2793

—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₉	C₂²×C₃
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁

subgroup

G/H

center, Frattini, hypercenter

C₁

commutator, Fitting, socle, cosocle, hypocenter

C₃×C₇²×C₁₉

C₂²×C₃

LCS

G ▷ C₃×C₇²×C₁₉

UCS

C₁

N	H ≅ G/N	type
1. C₃⋊#19150291	C₂	semidirect
2. C₃⋊#19150290	C₂	semidirect
3. C₃×D₁₉⋊#3862	C₂	semidirect
4. D₁₉×C₃⋊(C₇⋊D₇)	C₃	semidirect
6. C₃×C₁₉⋊#3862	C₂²	semidirect
7. C₃⋊(C₇⋊D₁₃₃)	C₂×C₃	semidirect
8. C₁₉×C₃⋊(C₇⋊D₇)	C₂×C₃	semidirect
9. C₃×C₇²×D₁₉	C₂×C₃	semidirect
11. D₁₉⋊#3862	D₃	semidirect
18. C₁₉⋊#3862	C₂×D₃	semidirect
19. C₃×C₇²×C₁₉	C₂²×C₃	semidirect
28. C₇²×D₁₉	C₃×D₃	semidirect
37. C₇²×C₁₉	C₂×C₃×D₃	semidirect
48. C₃×C₇×D₁₉	AGL(1,𝔽₇)	semidirect
49. C₃×C₇×D₁₉	AGL(1,𝔽₇)	semidirect
66. C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
67. C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
77. C₃⋊(C₇⋊D₇)	D₁₉⋊C₃	semidirect
86. C₇×D₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
87. C₇×D₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
97. C₃×C₇²	C₂×D₁₉⋊C₃	semidirect
101. C₇×C₁₉	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
102. C₇×C₁₉	C₂×C₃⋊AGL(1,𝔽₇)	semidirect
110. C₃×D₁₉	#64425	semidirect
127. C₃×C₁₉	C₂×#64425	semidirect
130. C₇²	D₃×D₁₉⋊C₃	semidirect
150. D₁₉	C₃⋊#64425	semidirect
156. C₃×C₇	#11716321⋊C₂	semidirect
157. C₃×C₇	#11716322⋊C₂	semidirect
162. C₁₉	C₂×C₃⋊#64425	semidirect
179. C₇	#11716321⋊D₃	semidirect
180. C₇	#11716322⋊D₃	semidirect
191. C₃	D₁₉⋊#64425	semidirect

H ≅ G/N

type

1. C₃⋊#19150291

C₂

semidirect

2. C₃⋊#19150290

C₂

semidirect

3. C₃×D₁₉⋊#3862

C₂

semidirect

4. D₁₉×C₃⋊(C₇⋊D₇)

C₃

semidirect

6. C₃×C₁₉⋊#3862

C₂²

semidirect

7. C₃⋊(C₇⋊D₁₃₃)

C₂×C₃

semidirect

8. C₁₉×C₃⋊(C₇⋊D₇)

C₂×C₃

semidirect

9. C₃×C₇²×D₁₉

C₂×C₃

semidirect

11. D₁₉⋊#3862

D₃

semidirect

18. C₁₉⋊#3862

C₂×D₃

semidirect

19. C₃×C₇²×C₁₉

C₂²×C₃

semidirect

28. C₇²×D₁₉

C₃×D₃

semidirect

37. C₇²×C₁₉

C₂×C₃×D₃

semidirect

48. C₃×C₇×D₁₉

semidirect

49. C₃×C₇×D₁₉

semidirect

66. C₃×C₇×C₁₉

semidirect

67. C₃×C₇×C₁₉

semidirect

77. C₃⋊(C₇⋊D₇)

D₁₉⋊C₃

semidirect

86. C₇×D₁₉

semidirect

87. C₇×D₁₉

semidirect

97. C₃×C₇²

C₂×D₁₉⋊C₃

semidirect

101. C₇×C₁₉

semidirect

102. C₇×C₁₉

semidirect

110. C₃×D₁₉

#64425

semidirect

127. C₃×C₁₉

C₂×#64425

semidirect

130. C₇²

D₃×D₁₉⋊C₃

semidirect

150. D₁₉

semidirect

156. C₃×C₇

#11716321⋊C₂

semidirect

157. C₃×C₇

#11716322⋊C₂

semidirect

162. C₁₉

semidirect

179. C₇

#11716321⋊D₃

semidirect

180. C₇

#11716322⋊D₃

semidirect

191. C₃

semidirect

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

subgroup	index
C₃⋊#19150291	2
C₃⋊#19150290	2
C₃×D₁₉⋊#3862	2
D₁₉×C₃⋊(C₇⋊D₇)	3
D₁₉⋊#64425	3
#11716322⋊D₃	7
#11716321⋊D₃	7
C₂×C₃⋊#64425	19

subgroup

index

C₃⋊#19150291

C₃⋊#19150290

C₃×D₁₉⋊#3862

D₁₉×C₃⋊(C₇⋊D₇)

#11716322⋊D₃

#11716321⋊D₃