Group #14562200 — subgroups

Subgroups — #14562200

Order 2432.

220 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 85 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	#11926410	C₂	1	1	yes	maximal, characteristic
3	#11926282	C₂	1	4	yes	maximal
4	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	#10597372	—	2	1	no	—
7	C₂×C₄⋊Dic₁₉	—	2	1	no	—
8	#10597370	—	2	1	no	—
9	#10597370	C₂²	1	2	yes	—
10	#10597316	—	2	1	no	—
11	#10597315	C₄	1	1	yes	characteristic, complemented
12	#10597315	C₄	1	1	yes	characteristic, complemented
13	C₄×Dic₃₈	—	2	1	no	—
14	C₄×Dic₃₈	C₄	1	2	yes	complemented
15	C₁₉×C₄⋊C₈	—	2	1	no	—
16	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	C₂²	1	2	yes	—
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂²⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	—	4	2	no	—
36	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	Dic₁₉⋊C₄	—	2	2	no	—
38	Dic₁₉⋊C₄	—	2	2	no	—
39	C₄×Dic₁₉	—	2	2	no	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
48	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	C₂×Dic₁₉	—	4	2	no	—
55	C₂×Dic₁₉	—	4	2	no	—
56	Dic₃₈	—	4	2	no	—
57	Dic₃₈	—	4	2	no	—
58	C₈×C₁₉	—	4	2	no	—
59	#1518	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
64	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	#103	1	2	yes	—
70	C₄×C₁₉	#103	1	2	yes	—
71	Dic₁₉	—	4	2	no	—
72	Dic₁₉	—	4	2	no	—
73	Dic₁₉	—	8	2	no	—
74	#533	—	19	1	no	—
75	#431	D₁₉	1	1	yes	characteristic
76	#382	—	19	1	no	—
77	#328	—	19	4	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	#410	1	1	yes	characteristic
81	C₂×C₁₉	C₂×#103	1	1	yes	characteristic
82	C₂×C₁₉	#421	1	1	yes	characteristic
83	C₄⋊Q₈	—	19	1	no	—
84	C₄⋊Q₈	—	19	1	no	—
85	#125	—	38	1	no	—
86	C₂²⋊Q₈	—	19	2	no	—
87	C₂²⋊Q₈	—	38	1	no	—
88	C₄×Q₈	—	19	2	no	—
89	C₄×Q₈	—	38	1	no	—
90	#117	—	38	1	no	—
91	C₂×C₄⋊C₄	—	38	1	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	C₄⋊C₈	—	2	1	no	—
94	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
95	C₄×C₈	—	2	1	no	—
96	#95	—	19	2	no	—
97	#95	—	38	1	no	—
98	C₁₉	#1518	1	1	yes	characteristic, complemented, Sylow
99	C₂×Q₈	—	19	2	no	—
100	C₂×Q₈	—	38	1	no	—
101	C₂²×C₄	—	38	2	no	—
102	C₂²×C₄	D₇₆	1	1	yes	characteristic
103	C₂²×C₄	D₇₆	1	1	yes	characteristic
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	C₂×C₈	—	2	2	no	—
106	C₄⋊C₄	—	19	2	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₄⋊C₄	—	38	1	no	—
109	C₄⋊C₄	—	38	1	no	—
110	C₄⋊C₄	—	38	1	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄⋊C₄	—	76	2	no	—
113	C₂²⋊C₄	—	38	2	no	—
114	C₄²	—	38	2	no	—
115	C₄²	C₄×D₁₉	1	1	yes	characteristic
116	C₄²	C₄×D₁₉	1	1	yes	characteristic
117	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
118	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
119	C₂³	C₂×D₇₆	1	1	yes	characteristic
120	Q₈	—	76	2	no	—
121	Q₈	—	76	2	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	38	2	no	—
125	C₂×C₄	—	38	2	no	—
126	C₂×C₄	—	76	2	no	—
127	C₂×C₄	—	76	2	no	—
128	C₂×C₄	—	76	2	no	—
129	C₂×C₄	#64516	1	2	yes	—
130	C₂×C₄	Dic₇₆	1	2	yes	—
131	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
132	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
133	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
134	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
135	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
136	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
137	C₈	—	4	2	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₂×#64516	1	1	yes	characteristic
141	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
142	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	76	2	no	—
148	C₄	—	76	2	no	—
149	C₄	—	152	2	no	—
150	C₄	#10597273	1	2	yes	—
151	C₄	#10597273	1	2	yes	—
152	C₂	—	2	1	no	—
153	C₂	—	2	1	no	—
154	C₂	#11926517	1	1	yes	characteristic
155	C₂	C₂×#10597273	1	1	yes	characteristic
156	C₂	#11926560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

#11926410

C₂

yes

maximal, characteristic

#11926282

C₂

yes

maximal

C₁₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597370

C₂²

yes

—

#10597316

—

#10597315

C₄

yes

characteristic, complemented

#10597315

C₄

yes

characteristic, complemented

C₄×Dic₃₈

—

C₄×Dic₃₈

C₄

yes

complemented

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#1518

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#103

yes

—

C₄×C₁₉

#103

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#533

—

#431

D₁₉

yes

characteristic

#382

—

#328

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

C₂×D₁₉

yes

—

C₄×C₈

—

#95

—

#95

—

C₁₉

#1518

yes

characteristic, complemented, Sylow

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂²×C₄

—

102

C₂²×C₄

D₇₆

yes

characteristic

103

C₂²×C₄

D₇₆

yes

characteristic

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₂²⋊C₄

—

114

C₄²

—

115

C₄²

C₄×D₁₉

yes

characteristic

116

C₄²

C₄×D₁₉

yes

characteristic

117

C₄²

C₂²⋊D₁₉

yes

characteristic

118

C₄²

C₂²⋊D₁₉

yes

characteristic

119

C₂³

C₂×D₇₆

yes

characteristic

120

Q₈

—

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

#64516

yes

—

130

C₂×C₄

Dic₇₆

yes

—

131

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

132

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

133

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

134

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

135

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

136

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

137

C₈

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×#64516

yes

characteristic

141

C₂²

C₂×Dic₇₆

yes

characteristic

142

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

152

—

150

C₄

#10597273

yes

—

151

C₄

#10597273

yes

—

152

C₂

—

153

C₂

—

154

C₂

#11926517

yes

characteristic

155

C₂

C₂×#10597273

yes

characteristic

156

C₂

#11926560

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#431	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#431	D₁₉
hypocenter	C₁₉	#1518
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#431

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
11. #10597315	C₄	semidirect
12. #10597315	C₄	semidirect
14. C₄×Dic₃₈	C₄	semidirect
98. C₁₉	#1518	semidirect

H ≅ G/N

type

11. #10597315

C₄

semidirect

12. #10597315

C₄

semidirect

14. C₄×Dic₃₈

C₄

semidirect

98. C₁₉

#1518

semidirect

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

subgroup	index
#11927101	2
#11926410	2
#11926282	2
C₁₉×#431	2
#1518	19

subgroup

index

C₁₉×#431

Subgroups — #14562200

Conjugacy classes of subgroups

Complements

Maximal subgroups