Group #18083529 — subgroups

Subgroups — #18083529

Order 4864.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14574159	C₂	1	1	yes	maximal, characteristic, complemented
2	#14573643	C₂	1	2	yes	maximal
3	#14562037	C₂	1	2	yes	maximal, complemented
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1955	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926953	—	2	2	no	—
8	#11926953	—	2	2	no	—
9	#11926874	—	2	2	no	—
10	#11926834	—	2	2	no	—
11	#11926749	—	2	2	no	—
12	#11926695	—	2	2	no	—
13	C₄×#64526	—	2	4	no	—
14	#11926597	C₂²	1	2	yes	—
15	#11926582	—	2	2	no	—
16	#11926274	—	2	4	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	D₄	1	2	yes	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×#64526	—	2	4	no	—
31	#10597372	—	2	2	no	—
32	#10597370	—	2	2	no	—
33	#10597370	—	2	2	no	—
34	#10597316	—	2	2	no	—
35	#10597315	D₄	1	2	yes	—
36	#10597315	D₄	1	2	yes	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	4	4	no	—
41	C₁₉×#97	—	2	2	no	—
42	#10597289	—	2	4	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
44	#10597275	—	2	2	no	—
45	#10597275	—	2	2	no	—
46	#10597274	—	2	4	no	—
47	#10597267	—	2	4	no	—
48	#10597265	—	2	4	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×Dic₃₈	—	2	2	no	—
63	C₂×Dic₃₈	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	C₄²×C₁₉	C₂×D₄	1	2	yes	—
73	C₂²⋊Dic₁₉	—	4	2	no	—
74	#64526	—	4	8	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	Dic₁₉⋊C₄	—	4	2	no	—
80	Dic₁₉⋊C₄	—	4	2	no	—
81	C₄×Dic₁₉	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	2	4	no	—
83	#10036	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	2	2	no	—
85	C₂³×C₁₉	—	4	1	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	—	4	1	no	—
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	#121	1	1	yes	characteristic
90	D₄×C₁₉	—	2	4	no	—
91	D₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	8	2	no	—
97	C₂×C₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	—	8	1	no	—
99	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#120	1	2	yes	—
101	C₂×C₄×C₁₉	#121	1	2	yes	—
102	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₁₉	#137	1	2	yes	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	Dic₃₈	—	4	4	no	—
108	Dic₃₈	—	4	4	no	—
109	C₈×C₁₉	—	2	4	no	—
110	C₈×C₁₉	—	8	1	no	—
111	C₁₉⋊C₈	—	4	4	no	—
112	#3162	—	19	1	no	—
113	#3101	—	19	2	no	—
114	#1955	D₁₉	1	1	yes	characteristic
115	#1481	—	19	2	no	—
116	#1275	—	19	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	4	4	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	8	2	no	—
122	C₂²×C₁₉	—	8	1	no	—
123	C₂²×C₁₉	—	8	1	no	—
124	C₂²×C₁₉	#392	1	1	yes	characteristic
125	C₂²×C₁₉	#461	1	2	yes	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	2	2	no	—
128	C₄×C₁₉	—	8	1	no	—
129	C₄×C₁₉	#448	1	2	yes	—
130	C₄×C₁₉	#492	1	1	yes	characteristic
131	C₄×C₁₉	#497	1	1	yes	characteristic
132	Dic₁₉	—	8	2	no	—
133	Dic₁₉	—	8	2	no	—
134	#533	—	19	2	no	—
135	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
136	#501	—	38	2	no	—
137	#501	—	38	2	no	—
138	#483	—	38	2	no	—
139	#476	—	38	2	no	—
140	#461	—	38	2	no	—
141	#450	—	38	2	no	—
142	C₄×SD₁₆	—	38	4	no	—
143	#431	—	19	2	no	—
144	#427	—	38	2	no	—
145	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
146	C₂×C₂²⋊C₈	—	2	2	no	—
147	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
148	Q₈⋊C₈	—	38	4	no	—
149	C₂×C₁₉	—	2	2	no	—
150	C₂×C₁₉	—	8	2	no	—
151	C₂×C₁₉	#2010	1	1	yes	characteristic
152	C₂×C₁₉	#2013	1	1	yes	characteristic
153	C₂×C₁₉	#2017	1	1	yes	characteristic
154	C₂²×D₄	D₇₆	1	1	yes	characteristic
155	C₂³×C₄	—	2	1	no	—
156	C₂×SD₁₆	—	38	4	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
159	C₄⋊Q₈	—	19	2	no	—
160	C₄⋊Q₈	—	19	2	no	—
161	#125	—	38	2	no	—
162	C₂²⋊Q₈	—	38	2	no	—
163	C₂²⋊Q₈	—	38	2	no	—
164	C₄×Q₈	—	38	2	no	—
165	C₄×Q₈	—	38	2	no	—
166	C₄×D₄	—	2	2	no	—
167	C₄×D₄	—	2	2	no	—
168	#117	—	38	2	no	—
169	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	#107	—	38	2	no	—
173	#107	—	38	2	no	—
174	#106	—	38	4	no	—
175	#106	—	38	4	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	38	2	no	—
178	#103	—	38	4	no	—
179	#102	—	38	4	no	—
180	C₂²⋊C₈	—	4	4	no	—
181	C₂²⋊C₈	—	38	2	no	—
182	#97	—	2	2	no	—
183	C₄×C₈	—	19	4	no	—
184	C₁₉	#10036	1	1	yes	characteristic, complemented, Sylow
185	C₂⁴	—	2	1	no	—
186	C₂×Q₈	—	38	2	no	—
187	C₂×Q₈	—	38	2	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	4	2	no	—
192	C₂²×C₄	—	4	1	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	—	4	2	no	—
195	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
196	C₂²×C₄	#64541	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	SD₁₆	—	76	8	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	—	4	1	no	—
203	C₂×C₈	—	38	4	no	—
204	C₂×C₈	#64526	1	4	yes	complemented
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	38	2	no	—
207	C₄⋊C₄	—	38	2	no	—
208	C₄⋊C₄	—	38	2	no	—
209	C₄⋊C₄	—	38	2	no	—
210	C₄⋊C₄	—	76	2	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₂²⋊C₄	—	4	2	no	—
213	C₂²⋊C₄	—	76	2	no	—
214	C₄²	—	76	2	no	—
215	C₄²	D₄×D₁₉	1	2	yes	—
216	C₄²	D₄×D₁₉	1	2	yes	—
217	C₂³	—	2	2	no	—
218	C₂³	—	4	1	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	1	no	—
221	C₂³	—	4	2	no	—
222	C₂³	#10597376	1	1	yes	characteristic
223	Q₈	—	76	4	no	—
224	Q₈	—	76	4	no	—
225	D₄	—	2	4	no	—
226	D₄	—	4	2	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	8	1	no	—
232	C₂×C₄	—	8	2	no	—
233	C₂×C₄	—	8	1	no	—
234	C₂×C₄	—	76	2	no	—
235	C₂×C₄	—	76	2	no	—
236	C₂×C₄	#10597328	1	2	yes	—
237	C₂×C₄	#10597330	1	2	yes	—
238	C₂×C₄	C₂×#64526	1	2	yes	—
239	C₂×C₄	#10597383	1	1	yes	characteristic
240	C₂×C₄	#10597386	1	1	yes	characteristic
241	C₂×C₄	#10597397	1	2	yes	—
242	C₈	—	2	4	no	—
243	C₈	—	8	1	no	—
244	C₈	—	76	4	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	8	2	no	—
250	C₂²	—	8	1	no	—
251	C₂²	—	8	1	no	—
252	C₂²	#11926453	1	1	yes	characteristic
253	C₂²	#11926749	1	2	yes	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	8	1	no	—
257	C₄	—	152	2	no	—
258	C₄	—	152	2	no	—
259	C₄	#11926682	1	2	yes	—
260	C₄	#11926916	1	1	yes	characteristic
261	C₄	#11926939	1	1	yes	characteristic
262	C₂	—	2	2	no	—
263	C₂	—	8	2	no	—
264	C₂	#14564702	1	1	yes	characteristic
265	C₂	#14564717	1	1	yes	characteristic
266	C₂	#14564739	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574159

C₂

yes

maximal, characteristic, complemented

#14573643

C₂

yes

maximal

#14562037

C₂

yes

maximal, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#1955

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

—

—

—

—

—

—

C₂²

yes

—

#11926582

—

#11926274

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

D₄

yes

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

complemented

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₂²⋊Dic₁₉

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#10036

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

D₄×C₁₉

—

D₄×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

characteristic

100

C₂×C₄×C₁₉

#120

yes

—

101

C₂×C₄×C₁₉

#121

yes

—

102

C₂×C₄×C₁₉

#127

yes

characteristic

103

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

104

C₂×C₄×C₁₉

#137

yes

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

Dic₃₈

—

108

Dic₃₈

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₁₉⋊C₈

—

112

#3162

—

113

#3101

—

114

#1955

D₁₉

yes

characteristic

115

#1481

—

116

#1275

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

#392

yes

characteristic

125

C₂²×C₁₉

#461

yes

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

#448

yes

—

130

C₄×C₁₉

#492

yes

characteristic

131

C₄×C₁₉

#497

yes

characteristic

132

Dic₁₉

—

133

Dic₁₉

—

134

#533

—

135

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

136

#501

—

137

#501

—

138

#483

—

139

#476

—

140

#461

—

141

#450

—

142

C₄×SD₁₆

—

143

#431

—

144

#427

—

145

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

146

C₂×C₂²⋊C₈

—

147

C₂×#97

C₂×D₁₉

yes

characteristic

148

Q₈⋊C₈

—

149

C₂×C₁₉

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#2010

yes

characteristic

152

C₂×C₁₉

#2013

yes

characteristic

153

C₂×C₁₉

#2017

yes

characteristic

154

C₂²×D₄

D₇₆

yes

characteristic

155

C₂³×C₄

—

156

C₂×SD₁₆

—

157

C₂²×C₈

—

158

C₂²×C₈

C₂²⋊D₁₉

yes

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

#125

—

162

C₂²⋊Q₈

—

163

C₂²⋊Q₈

—

164

C₄×Q₈

—

165

C₄×Q₈

—

166

C₄×D₄

—

167

C₄×D₄

—

168

#117

—

169

C₂×C₄⋊C₄

D₇₆

yes

characteristic

170

C₂×C₂²⋊C₄

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

#107

—

173

#107

—

174

#106

—

175

#106

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

#103

—

179

#102

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

#97

—

183

C₄×C₈

—

184

C₁₉

#10036

yes

characteristic, complemented, Sylow

185

C₂⁴

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂×D₇₆

yes

characteristic

196

C₂²×C₄

#64541

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

198

SD₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

#64526

yes

complemented

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

—

215

C₄²

D₄×D₁₉

yes

—

216

C₄²

D₄×D₁₉

yes

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

#10597376

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

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

C₂×#64526

yes

—

239

C₂×C₄

#10597383

yes

characteristic

240

C₂×C₄

#10597386

yes

characteristic

241

C₂×C₄

#10597397

yes

—

242

C₈

—

243

C₈

—

244

C₈

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#11926453

yes

characteristic

253

C₂²

#11926749

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

152

—

258

C₄

—

152

—

259

C₄

#11926682

yes

—

260

C₄

#11926916

yes

characteristic

261

C₄

#11926939

yes

characteristic

262

C₂

—

263

C₂

—

264

C₂

#14564702

yes

characteristic

265

C₂

#14564717

yes

characteristic

266

C₂

#14564739

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1955	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂²×D₄×C₁₉	D₄
hypercenter	#1955	D₁₉
hypocenter	C₁₉	#10036
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1955

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1955

C₂

socle

C₂²×C₁₉

#392

prime radical

C₂²×D₄×C₁₉

D₄

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1955

N	H ≅ G/N	type
1. #14574159	C₂	semidirect
3. #14562037	C₂	semidirect
4. #14561466	C₂	semidirect
68. C₂×C₈×C₁₉	SD₁₆	semidirect
184. C₁₉	#10036	semidirect
204. C₂×C₈	#64526	semidirect

H ≅ G/N

type

1. #14574159

C₂

semidirect

3. #14562037

C₂

semidirect

4. #14561466

C₂

semidirect

68. C₂×C₈×C₁₉

SD₁₆

semidirect

184. C₁₉

#10036

semidirect

204. C₂×C₈

#64526

semidirect

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

subgroup	index
#14574159	2
#14573643	2
#14562037	2
#14561466	2
C₁₉×#1955	2
#10036	19

subgroup

index

C₁₉×#1955

Subgroups — #18083529

Conjugacy classes of subgroups

Complements

Maximal subgroups