Group #18083862 — subgroups

Subgroups — #18083862

Order 4864.

600 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11926906	C₂	1	2	yes	maximal, complemented
2	#14571681	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926283	C₂	1	2	yes	maximal, complemented
4	#14561516	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597321	C₂²	1	2	yes	—
7	#11926906	—	2	4	no	—
8	#11926906	—	2	4	no	—
9	C₂×#10597267	—	2	2	no	—
10	C₂×#10597266	—	2	2	no	—
11	C₂×#10597260	C₂²	1	2	yes	—
12	#11926461	—	2	2	no	—
13	#11926457	—	2	2	no	—
14	#11926454	—	2	2	no	—
15	#11926283	—	2	4	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#103	—	2	2	no	—
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₁₉×#382	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×D₇₆	—	2	2	no	—
22	C₂²×D₇₆	D₄	1	2	yes	—
23	C₂²×Dic₃₈	D₄	1	2	yes	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	1	no	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	complemented
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
32	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
33	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
34	C₂²×C₁₉⋊C₈	—	2	2	no	—
35	#10597321	—	2	2	no	—
36	#10597321	—	2	2	no	—
37	#10597321	—	2	2	no	—
38	#10597321	—	2	2	no	—
39	C₁₉×#103	—	4	4	no	—
40	C₁₉×#97	—	2	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	#10597267	—	2	8	no	—
44	#10597266	—	2	8	no	—
45	#10597260	—	2	2	no	—
46	#10597260	D₄	1	4	yes	complemented
47	C₂³×D₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	4	2	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	—	2	2	no	—
57	C₂×D₇₆	—	2	2	no	—
58	C₂×D₇₆	—	2	2	no	—
59	C₂×D₇₆	—	4	4	no	—
60	C₂×D₇₆	—	8	2	no	—
61	C₂×D₇₆	—	8	4	no	—
62	C₂×Dic₃₈	—	2	2	no	—
63	C₂×Dic₃₈	—	2	2	no	—
64	C₂×Dic₃₈	—	4	4	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	1	no	—
68	C₄⋊C₄×C₁₉	—	2	4	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	2	yes	—
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	(C₂×D₁₉)⋊C₄	—	4	2	no	—
75	(C₂×D₁₉)⋊C₄	—	4	2	no	—
76	(C₂×D₁₉)⋊C₄	—	4	2	no	—
77	(C₂×D₁₉)⋊C₄	—	4	2	no	—
78	(C₂×D₁₉)⋊C₄	—	8	4	no	—
79	C₂×C₁₉⋊C₈	—	2	4	no	—
80	C₂×C₁₉⋊C₈	—	4	4	no	—
81	#10085	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	#120	1	1	yes	characteristic
83	C₂²×D₁₉	—	4	2	no	—
84	C₂²×D₁₉	—	4	2	no	—
85	C₂²×D₁₉	—	4	2	no	—
86	C₂²×D₁₉	—	4	4	no	—
87	C₂²×D₁₉	—	4	4	no	—
88	Q₈×C₁₉	—	4	4	no	—
89	Q₈×C₁₉	—	8	2	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	#120	1	2	yes	—
99	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#121	1	2	yes	—
101	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	4	no	—
104	D₇₆	—	4	4	no	—
105	D₇₆	—	8	2	no	—
106	D₇₆	—	8	8	no	—
107	Dic₃₈	—	4	4	no	—
108	Dic₃₈	—	8	2	no	—
109	C₈×C₁₉	—	4	2	no	—
110	C₁₉⋊C₈	—	4	4	no	—
111	C₂×#489	—	19	2	no	—
112	#2819	—	19	1	no	—
113	#1960	D₁₉	1	1	yes	characteristic, complemented
114	C₂×#329	—	19	2	no	—
115	#1295	—	19	1	no	—
116	C₂²×C₁₉	#392	1	1	yes	characteristic
117	C₂²×C₁₉	#453	1	1	yes	characteristic
118	C₂²×C₁₉	#454	1	1	yes	characteristic
119	C₂²×C₁₉	#455	1	4	yes	—
120	C₂×D₁₉	—	8	4	no	—
121	C₂×D₁₉	—	8	4	no	—
122	C₂×D₁₉	—	8	2	no	—
123	C₂×D₁₉	—	8	2	no	—
124	C₂×D₁₉	—	8	2	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	—	8	2	no	—
131	Dic₁₉	—	8	2	no	—
132	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
133	C₂×#124	—	19	2	no	—
134	#489	—	38	4	no	—
135	#489	—	38	4	no	—
136	C₂×#103	—	2	2	no	—
137	C₂×#103	—	38	2	no	—
138	C₂×#102	—	38	2	no	—
139	C₂×#97	—	19	2	no	—
140	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
141	#394	—	38	2	no	—
142	#393	—	38	2	no	—
143	#392	—	38	2	no	—
144	#382	C₂×D₁₉	1	1	yes	characteristic
145	#329	—	38	4	no	—
146	C₂×C₁₉	#1659	1	2	yes	—
147	C₂×C₁₉	#1662	1	2	yes	—
148	C₂×C₁₉	#2004	1	2	yes	—
149	C₂×C₁₉	#2006	1	1	yes	characteristic
150	D₁₉	—	16	2	no	—
151	C₂²×Q₈	—	2	1	no	—
152	C₂²×Q₈	—	19	2	no	—
153	C₂²×D₄	—	19	2	no	—
154	C₂²×D₄	—	38	2	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	38	2	no	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	D₇₆	1	2	yes	complemented
160	#124	—	38	2	no	—
161	#124	—	38	2	no	—
162	#124	—	38	2	no	—
163	#124	—	38	2	no	—
164	C₂×C₄⋊C₄	—	2	2	no	—
165	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
166	C₂×C₂²⋊C₄	—	38	2	no	—
167	C₂×C₂²⋊C₄	—	38	2	no	—
168	C₂×C₂²⋊C₄	—	38	4	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	#103	—	4	4	no	—
171	#103	—	38	8	no	—
172	#102	—	38	8	no	—
173	#97	—	2	2	no	—
174	#97	—	19	4	no	—
175	#97	—	38	2	no	—
176	#95	—	2	2	no	—
177	#95	—	38	2	no	—
178	C₁₉	#10085	1	1	yes	characteristic, complemented, Sylow
179	C₂⁴	—	38	2	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	—	38	2	no	—
185	C₂×Q₈	—	38	2	no	—
186	C₂×Q₈	—	76	4	no	—
187	C₂×D₄	—	38	2	no	—
188	C₂×D₄	—	38	2	no	—
189	C₂×D₄	—	76	4	no	—
190	C₂×D₄	—	152	2	no	—
191	C₂×D₄	—	152	4	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	—	38	2	no	—
195	C₂²×C₄	D₄×D₁₉	1	2	yes	—
196	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	38	4	no	—
201	C₂×C₈	—	76	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₂²⋊C₄	—	76	2	no	—
206	C₂²⋊C₄	—	76	2	no	—
207	C₂²⋊C₄	—	76	2	no	—
208	C₂²⋊C₄	—	76	2	no	—
209	C₂²⋊C₄	—	152	4	no	—
210	C₄²	C₂×D₇₆	1	1	yes	characteristic
211	C₄²	#64541	1	1	yes	characteristic
212	C₄²	D₄×D₁₉	1	2	yes	—
213	C₂³	—	76	2	no	—
214	C₂³	—	76	2	no	—
215	C₂³	—	76	2	no	—
216	C₂³	—	76	4	no	—
217	C₂³	—	76	4	no	—
218	C₂³	#10597383	1	1	yes	characteristic
219	Q₈	—	4	4	no	—
220	Q₈	—	8	2	no	—
221	Q₈	—	76	4	no	—
222	Q₈	—	152	2	no	—
223	D₄	—	76	4	no	—
224	D₄	—	152	2	no	—
225	D₄	—	152	8	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	4	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	8	1	no	—
234	C₂×C₄	—	76	2	no	—
235	C₂×C₄	—	76	4	no	—
236	C₂×C₄	#10597328	1	2	yes	—
237	C₂×C₄	#10597330	1	2	yes	—
238	C₂×C₄	#10597376	1	1	yes	characteristic
239	C₂×C₄	#10597386	1	1	yes	characteristic
240	C₈	—	4	2	no	—
241	C₈	—	76	4	no	—
242	C₂²	—	152	2	no	—
243	C₂²	—	152	2	no	—
244	C₂²	—	152	2	no	—
245	C₂²	—	152	4	no	—
246	C₂²	—	152	4	no	—
247	C₂²	#11926453	1	1	yes	characteristic
248	C₂²	#11926711	1	1	yes	characteristic
249	C₂²	#11926716	1	1	yes	characteristic
250	C₂²	#11926720	1	4	yes	—
251	C₄	—	2	2	no	—
252	C₄	—	2	2	no	—
253	C₄	—	2	1	no	—
254	C₄	—	2	1	no	—
255	C₄	—	8	2	no	—
256	C₄	—	8	2	no	—
257	C₄	—	152	2	no	—
258	C₂	—	304	2	no	—
259	C₂	#14562939	1	2	yes	—
260	C₂	#14562956	1	2	yes	—
261	C₂	#14564665	1	2	yes	—
262	C₂	#14564676	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926906

C₂

yes

maximal, complemented

#14571681

C₂

yes

maximal, characteristic

C₂×#11926283

C₂

yes

maximal, complemented

#14561516

C₂

yes

maximal, characteristic, complemented

C₁₉×#1960

C₂

yes

maximal, characteristic, complemented

C₂×#10597321

C₂²

yes

—

—

—

—

—

C₂²

yes

—

—

—

—

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₇₆

—

C₂²×D₇₆

D₄

yes

—

C₂²×Dic₃₈

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×#103

—

C₁₉×#97

—

C₁₉×#95

—

C₁₉⋊#95

—

—

—

—

D₄

yes

complemented

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

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

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

100

C₂×C₄×C₁₉

#121

yes

—

101

C₂×C₄×C₁₉

#127

yes

characteristic

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

D₇₆

—

105

D₇₆

—

106

D₇₆

—

107

Dic₃₈

—

108

Dic₃₈

—

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₂×#489

—

112

#2819

—

113

#1960

D₁₉

yes

characteristic, complemented

114

C₂×#329

—

115

#1295

—

116

C₂²×C₁₉

#392

yes

characteristic

117

C₂²×C₁₉

#453

yes

characteristic

118

C₂²×C₁₉

#454

yes

characteristic

119

C₂²×C₁₉

#455

yes

—

120

C₂×D₁₉

—

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

Dic₁₉

—

132

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

133

C₂×#124

—

134

#489

—

135

#489

—

136

C₂×#103

—

137

C₂×#103

—

138

C₂×#102

—

139

C₂×#97

—

140

C₂×#97

C₂×D₁₉

yes

characteristic

141

#394

—

142

#393

—

143

#392

—

144

#382

C₂×D₁₉

yes

characteristic

145

#329

—

146

C₂×C₁₉

#1659

yes

—

147

C₂×C₁₉

#1662

yes

—

148

C₂×C₁₉

#2004

yes

—

149

C₂×C₁₉

#2006

yes

characteristic

150

D₁₉

—

151

C₂²×Q₈

—

152

C₂²×Q₈

—

153

C₂²×D₄

—

154

C₂²×D₄

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

D₇₆

yes

complemented

160

#124

—

161

#124

—

162

#124

—

163

#124

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

#103

—

171

#103

—

172

#102

—

173

#97

—

174

#97

—

175

#97

—

176

#95

—

177

#95

—

178

C₁₉

#10085

yes

characteristic, complemented, Sylow

179

C₂⁴

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

152

—

191

C₂×D₄

—

152

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

D₄×D₁₉

yes

—

196

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

152

—

210

C₄²

C₂×D₇₆

yes

characteristic

211

C₄²

#64541

yes

characteristic

212

C₄²

D₄×D₁₉

yes

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

#10597383

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

Q₈

—

152

—

223

D₄

—

224

D₄

—

152

—

225

D₄

—

152

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

#10597328

yes

—

237

C₂×C₄

#10597330

yes

—

238

C₂×C₄

#10597376

yes

characteristic

239

C₂×C₄

#10597386

yes

characteristic

240

C₈

—

241

C₈

—

242

C₂²

—

152

—

243

C₂²

—

152

—

244

C₂²

—

152

—

245

C₂²

—

152

—

246

C₂²

—

152

—

247

C₂²

#11926453

yes

characteristic

248

C₂²

#11926711

yes

characteristic

249

C₂²

#11926716

yes

characteristic

250

C₂²

#11926720

yes

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

152

—

258

C₂

—

304

—

259

C₂

#14562939

yes

—

260

C₂

#14562956

yes

—

261

C₂

#14564665

yes

—

262

C₂

#14564676

yes

characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1960	C₂
socle	C₂³×C₁₉	#120
prime radical	#14571681	C₂
hypercenter	#1960	D₁₉
hypocenter	C₁₉	#10085
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1960

subgroup

G/H

center

C₂³

#10597383

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1960

C₂

C₂³×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1960

N	H ≅ G/N	type
1. C₂×#11926906	C₂	semidirect
3. C₂×#11926283	C₂	semidirect
4. #14561516	C₂	semidirect
5. C₁₉×#1960	C₂	semidirect
27. C₁₉×C₄⋊Q₈	D₄	semidirect
46. #10597260	D₄	semidirect
113. #1960	D₁₉	semidirect
159. C₄⋊Q₈	D₇₆	semidirect
178. C₁₉	#10085	semidirect

H ≅ G/N

type

1. C₂×#11926906

C₂

semidirect

3. C₂×#11926283

C₂

semidirect

4. #14561516

C₂

semidirect

5. C₁₉×#1960

C₂

semidirect

27. C₁₉×C₄⋊Q₈

D₄

semidirect

46. #10597260

D₄

semidirect

113. #1960

D₁₉

semidirect

159. C₄⋊Q₈

D₇₆

semidirect

178. C₁₉

#10085

semidirect

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

subgroup	index
C₂×#11926906	2
#14571681	2
C₂×#11926283	2
#14561516	2
C₁₉×#1960	2
#10085	19

subgroup

index

C₁₉×#1960

Subgroups — #18083862

Conjugacy classes of subgroups

Complements

Maximal subgroups