Group #14569571 — subgroups

Subgroups — #14569571

Order 2432.

500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597321	C₂	1	1	yes	maximal, characteristic
3	#11926471	C₂	1	4	yes	maximal, complemented
4	#11926457	C₂	1	4	yes	maximal, complemented
5	#11926450	C₂	1	2	yes	maximal, complemented
6	#11926446	C₂	1	2	yes	maximal
7	C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₈	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	#10597321	—	2	4	no	—
19	#10597315	—	2	4	no	—
20	C₁₉×#95	C₂²	1	2	yes	—
21	C₁₉×#95	C₂²	1	2	yes	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₂³×D₁₉	C₂³	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	C₂³	1	2	yes	—
29	C₂²×Dic₁₉	C₂³	1	4	yes	—
30	C₂×D₇₆	—	2	2	no	—
31	C₂×D₇₆	—	2	4	no	—
32	C₂×Dic₃₈	—	2	4	no	—
33	C₂×Dic₃₈	—	2	2	no	—
34	C₂×Dic₃₈	—	2	4	no	—
35	C₂×Dic₃₈	—	4	4	no	—
36	C₄²×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	D₄	1	4	yes	—
38	(C₂×D₁₉)⋊C₄	—	2	4	no	—
39	(C₂×D₁₉)⋊C₄	—	2	4	no	—
40	(C₂×D₁₉)⋊C₄	—	4	8	no	—
41	C₄⋊Dic₁₉	—	2	4	no	—
42	C₄⋊Dic₁₉	—	2	4	no	—
43	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂²×D₁₉	—	2	2	no	—
45	C₂²×D₁₉	—	2	4	no	—
46	C₂²×D₁₉	—	2	4	no	—
47	C₂²×D₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	2	4	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	#41	1	4	yes	—
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	—	2	2	no	—
59	C₂×Dic₁₉	—	2	4	no	—
60	C₂×Dic₁₉	—	2	8	no	—
61	D₇₆	—	4	4	no	—
62	Dic₃₈	—	4	8	no	—
63	Dic₃₈	—	4	4	no	—
64	#2640	—	19	1	no	maximal, Sylow
65	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
66	C₂²×C₁₉	C₂×#41	1	2	yes	—
67	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
68	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
69	C₂×D₁₉	—	4	2	no	—
70	C₂×D₁₉	—	4	2	no	—
71	C₂×D₁₉	—	4	2	no	—
72	C₂×D₁₉	—	4	8	no	—
73	C₄×C₁₉	—	2	2	no	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	4	4	no	—
76	C₄×C₁₉	#124	1	4	yes	—
77	Dic₁₉	—	4	2	no	—
78	Dic₁₉	—	4	4	no	—
79	C₂×C₄⋊Q₈	—	19	1	no	—
80	C₂×#124	—	19	1	no	—
81	#397	—	19	4	no	—
82	#393	—	19	4	no	—
83	#391	—	19	2	no	—
84	#390	—	19	2	no	—
85	#376	D₁₉	1	1	yes	characteristic, complemented
86	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
87	C₂×C₁₉	#535	1	1	yes	characteristic
88	C₂×C₁₉	#536	1	1	yes	characteristic
89	C₂×C₁₉	#542	1	4	yes	—
90	D₁₉	—	8	2	no	—
91	C₂²×Q₈	—	19	1	no	—
92	C₂²×Q₈	—	19	2	no	—
93	C₂²×D₄	—	19	1	no	—
94	C₄⋊Q₈	—	38	4	no	—
95	#124	—	38	4	no	—
96	C₂×C₄⋊C₄	—	19	2	no	—
97	C₂×C₄⋊C₄	—	19	2	no	—
98	C₂×C₂²⋊C₄	—	19	2	no	—
99	C₂×C₂²⋊C₄	—	19	2	no	—
100	C₂×C₂²⋊C₄	—	19	8	no	—
101	C₂×C₄²	C₂×D₁₉	1	2	yes	—
102	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
103	#95	—	19	8	no	—
104	#95	C₂×D₁₉	1	2	yes	—
105	#95	C₂×D₁₉	1	2	yes	—
106	C₁₉	#2640	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	—	19	2	no	—
108	C₂×Q₈	—	38	2	no	—
109	C₂×Q₈	—	38	4	no	—
110	C₂×Q₈	—	38	4	no	—
111	C₂×Q₈	—	76	4	no	—
112	C₂×D₄	—	38	2	no	—
113	C₂×D₄	—	38	4	no	—
114	C₂²×C₄	—	19	2	no	—
115	C₂²×C₄	—	19	4	no	—
116	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
119	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₄⋊C₄	—	38	4	no	—
121	C₄⋊C₄	—	38	4	no	—
122	C₂²⋊C₄	—	38	4	no	—
123	C₂²⋊C₄	—	38	4	no	—
124	C₂²⋊C₄	—	76	8	no	—
125	C₄²	—	2	4	no	—
126	C₄²	D₇₆	1	4	yes	—
127	C₂³	—	38	2	no	—
128	C₂³	—	38	4	no	—
129	C₂³	—	38	4	no	—
130	C₂³	—	38	4	no	—
131	C₂³	C₂³×D₁₉	1	1	yes	characteristic
132	Q₈	—	76	8	no	—
133	Q₈	—	76	4	no	—
134	D₄	—	76	4	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	38	2	no	—
141	C₂×C₄	—	38	4	no	—
142	C₂×C₄	—	38	4	no	—
143	C₂×C₄	—	38	8	no	—
144	C₂×C₄	C₂×D₇₆	1	2	yes	—
145	C₂×C₄	C₂×D₇₆	1	2	yes	—
146	C₂×C₄	C₂×D₇₆	1	2	yes	—
147	C₂×C₄	#64541	1	4	yes	—
148	C₂²	—	76	2	no	—
149	C₂²	—	76	2	no	—
150	C₂²	—	76	2	no	—
151	C₂²	—	76	8	no	—
152	C₂²	C₂²×D₇₆	1	1	yes	characteristic
153	C₂²	C₂×#64541	1	2	yes	—
154	C₂²	#10597435	1	2	yes	—
155	C₂²	#10597436	1	2	yes	—
156	C₄	—	2	2	no	—
157	C₄	—	2	2	no	—
158	C₄	—	4	4	no	—
159	C₄	—	76	2	no	—
160	C₄	—	76	4	no	—
161	C₄	#10597321	1	4	yes	—
162	C₂	—	152	2	no	—
163	C₂	C₂×#10597321	1	1	yes	characteristic
164	C₂	#11927113	1	1	yes	characteristic
165	C₂	#11927120	1	1	yes	characteristic
166	C₂	#11927165	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

C₂×#10597321

C₂

yes

maximal, characteristic

#11926471

C₂

yes

maximal, complemented

#11926457

C₂

yes

maximal, complemented

#11926450

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal

C₁₉×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597321

—

#10597315

—

C₁₉×#95

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

#2640

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×D₄

—

C₄⋊Q₈

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

100

C₂×C₂²⋊C₄

—

101

C₂×C₄²

C₂×D₁₉

yes

—

102

C₂×C₄²

C₂×D₁₉

yes

characteristic

103

#95

—

104

#95

C₂×D₁₉

yes

—

105

#95

C₂×D₁₉

yes

—

106

C₁₉

#2640

yes

characteristic, complemented, Sylow

107

C₂⁴

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

C₂²×D₁₉

yes

—

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

C₂²×C₄

C₂²×D₁₉

yes

characteristic

119

C₂²×C₄

C₂²×D₁₉

yes

characteristic

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

D₇₆

yes

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

C₂³×D₁₉

yes

characteristic

132

Q₈

—

133

Q₈

—

134

D₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂×D₇₆

yes

—

145

C₂×C₄

C₂×D₇₆

yes

—

146

C₂×C₄

C₂×D₇₆

yes

—

147

C₂×C₄

#64541

yes

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

C₂²×D₇₆

yes

characteristic

153

C₂²

C₂×#64541

yes

—

154

C₂²

#10597435

yes

—

155

C₂²

#10597436

yes

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

#10597321

yes

—

162

C₂

—

152

—

163

C₂

C₂×#10597321

yes

characteristic

164

C₂

#11927113

yes

characteristic

165

C₂

#11927120

yes

characteristic

166

C₂

#11927165

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#376	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	#376	D₁₉
hypocenter	C₁₉	#2640
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#376

C₂

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. C₂×#10597315	C₂	semidirect
3. #11926471	C₂	semidirect
4. #11926457	C₂	semidirect
5. #11926450	C₂	semidirect
7. C₁₉×#376	C₂	semidirect
85. #376	D₁₉	semidirect
106. C₁₉	#2640	semidirect

H ≅ G/N

type

1. C₂×#10597315

C₂

semidirect

3. #11926471

C₂

semidirect

4. #11926457

C₂

semidirect

5. #11926450

C₂

semidirect

7. C₁₉×#376

C₂

semidirect

85. #376

D₁₉

semidirect

106. C₁₉

#2640

semidirect

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

subgroup	index
C₂×#10597315	2
C₂×#10597321	2
#11926471	2
#11926457	2
#11926450	2
#11926446	2
C₁₉×#376	2
#2640	19

subgroup

index

C₁₉×#376

Subgroups — #14569571

Conjugacy classes of subgroups

Complements

Maximal subgroups