Group #18081609 — subgroups

Subgroups — #18081609

Order 4864.

478 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 151 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	#14572013	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926291	C₂	1	2	yes	maximal
4	C₂×#11926289	C₂	1	2	yes	maximal
5	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
10	#11926450	—	2	1	no	—
11	#11926450	—	2	1	no	—
12	#11926450	—	2	2	no	—
13	#11926410	C₄	1	4	yes	—
14	#11926299	—	2	1	no	—
15	#11926291	—	2	4	no	—
16	#11926289	—	2	4	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	2	no	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉⋊#95	—	2	4	no	—
40	C₁₉⋊#95	—	2	4	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
43	C₄×C₁₉⋊C₈	—	4	2	no	—
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₁₉	—	2	2	no	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂×Dic₃₈	—	4	2	no	—
52	C₂×Dic₃₈	—	4	1	no	—
53	C₂×Dic₃₈	—	4	1	no	—
54	C₂×Dic₃₈	—	4	4	no	—
55	C₂×Dic₃₈	—	4	2	no	—
56	C₂×Dic₃₈	—	4	1	no	—
57	C₂×Dic₃₈	—	4	1	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	4	no	—
60	C₄²×C₁₉	—	2	4	no	—
61	C₄²×C₁₉	—	2	4	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	C₄²×C₁₉	—	2	1	no	—
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	C₄²×C₁₉	#41	1	2	yes	—
67	C₄⋊Dic₁₉	—	2	4	no	—
68	C₄⋊Dic₁₉	—	2	4	no	—
69	C₄⋊Dic₁₉	—	4	2	no	—
70	C₄⋊Dic₁₉	—	4	1	no	—
71	C₄⋊Dic₁₉	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	2	4	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	#9700	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	#101	1	4	yes	—
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	#121	1	2	yes	—
86	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#135	1	4	yes	—
89	C₂×C₄×C₁₉	#135	1	2	yes	—
90	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	4	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	Dic₃₈	—	8	2	no	—
98	Dic₃₈	—	8	2	no	—
99	Dic₃₈	—	8	2	no	—
100	Dic₃₈	—	8	2	no	—
101	C₈×C₁₉	—	8	2	no	—
102	C₁₉⋊C₈	—	4	4	no	—
103	#2862	—	19	1	no	—
104	#1831	D₁₉	1	1	yes	characteristic
105	C₄×C₄⋊C₈	—	19	1	no	—
106	C₂×#332	—	19	2	no	—
107	C₂×#332	—	19	2	no	—
108	C₂²×C₁₉	#390	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#101	1	2	yes	—
110	C₂²×C₁₉	#416	1	2	yes	—
111	C₂²×C₁₉	#416	1	1	yes	characteristic
112	C₂²×C₁₉	#417	1	1	yes	characteristic
113	C₄×C₁₉	—	2	4	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	4	2	no	—
116	C₄×C₁₉	#463	1	2	yes	—
117	C₄×C₁₉	#464	1	2	yes	—
118	C₄×C₁₉	#488	1	2	yes	—
119	C₄×C₁₉	#495	1	2	yes	—
120	Dic₁₉	—	8	2	no	—
121	Dic₁₉	—	8	2	no	—
122	C₂×C₄⋊Q₈	—	19	1	no	—
123	C₂×C₄⋊Q₈	—	19	1	no	—
124	C₂×C₄⋊C₈	—	19	2	no	—
125	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
126	C₂×C₄×C₈	—	38	1	no	—
127	#391	—	38	1	no	—
128	#391	—	38	1	no	—
129	#391	—	38	2	no	—
130	#382	—	19	4	no	—
131	C₄³	C₂×D₁₉	1	1	yes	characteristic
132	#336	—	2	2	no	—
133	#336	—	38	1	no	—
134	#332	—	38	4	no	—
135	#332	—	38	4	no	—
136	C₂×C₁₉	#1544	1	2	yes	—
137	C₂×C₁₉	#1552	1	2	yes	—
138	C₂×C₁₉	#1958	1	1	yes	characteristic
139	C₂×C₁₉	#1966	1	1	yes	characteristic
140	C₂×C₁₉	#1983	1	1	yes	characteristic
141	C₂²×Q₈	—	38	1	no	—
142	C₂²×Q₈	—	38	1	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	38	2	no	—
145	C₄⋊Q₈	—	38	2	no	—
146	C₄⋊Q₈	—	38	2	no	—
147	C₄⋊Q₈	—	38	2	no	—
148	C₄⋊Q₈	—	38	2	no	—
149	C₂×C₄⋊C₄	—	19	2	no	—
150	C₂×C₄⋊C₄	—	19	2	no	—
151	C₂×C₄⋊C₄	—	38	1	no	—
152	C₂×C₄⋊C₄	—	38	1	no	—
153	C₂×C₄²	C₄×D₁₉	1	2	yes	—
154	C₂×C₄²	D₇₆	1	1	yes	characteristic
155	C₂×C₄²	D₇₆	1	1	yes	characteristic
156	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
157	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	19	4	no	—
161	C₄⋊C₈	—	38	2	no	—
162	C₄×C₈	—	76	2	no	—
163	#95	—	38	4	no	—
164	#95	—	38	4	no	—
165	C₁₉	#9700	1	1	yes	characteristic, complemented, Sylow
166	C₂×Q₈	—	76	1	no	—
167	C₂×Q₈	—	76	1	no	—
168	C₂×Q₈	—	76	4	no	—
169	C₂×Q₈	—	76	2	no	—
170	C₂×Q₈	—	76	2	no	—
171	C₂×Q₈	—	76	1	no	—
172	C₂×Q₈	—	76	1	no	—
173	C₂²×C₄	—	38	2	no	—
174	C₂²×C₄	—	38	2	no	—
175	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
176	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
177	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	4	no	—
182	C₂×C₈	—	38	4	no	—
183	C₂×C₈	—	76	2	no	—
184	C₂×C₈	—	76	2	no	—
185	C₄⋊C₄	—	38	4	no	—
186	C₄⋊C₄	—	38	4	no	—
187	C₄⋊C₄	—	76	1	no	—
188	C₄⋊C₄	—	76	1	no	—
189	C₄⋊C₄	—	76	2	no	—
190	C₄²	—	2	4	no	—
191	C₄²	—	2	4	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	2	1	no	—
194	C₄²	—	2	1	no	—
195	C₄²	D₄×D₁₉	1	2	yes	—
196	C₄²	#64545	1	2	yes	—
197	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
198	Q₈	—	152	2	no	—
199	Q₈	—	152	2	no	—
200	Q₈	—	152	2	no	—
201	Q₈	—	152	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	76	4	no	—
209	C₂×C₄	—	76	2	no	—
210	C₂×C₄	—	76	2	no	—
211	C₂×C₄	—	76	2	no	—
212	C₂×C₄	—	76	2	no	—
213	C₂×C₄	#10597281	1	4	yes	—
214	C₂×C₄	#10597339	1	2	yes	—
215	C₂×C₄	#10597341	1	2	yes	—
216	C₂×C₄	#10597350	1	2	yes	—
217	C₂×C₄	#10597354	1	1	yes	characteristic
218	C₂×C₄	#10597355	1	1	yes	characteristic
219	C₂×C₄	#10597386	1	1	yes	characteristic
220	C₂×C₄	#10597393	1	1	yes	characteristic
221	C₂×C₄	#10597396	1	4	yes	—
222	C₈	—	8	2	no	—
223	C₈	—	76	4	no	—
224	C₂²	#11926445	1	1	yes	characteristic
225	C₂²	C₂×#10597281	1	2	yes	—
226	C₂²	#11926538	1	2	yes	—
227	C₂²	#11926541	1	1	yes	characteristic
228	C₂²	#11926546	1	1	yes	characteristic
229	C₄	—	2	4	no	—
230	C₄	—	2	2	no	—
231	C₄	—	4	2	no	—
232	C₄	—	152	2	no	—
233	C₄	—	152	2	no	—
234	C₄	#11926760	1	2	yes	—
235	C₄	#11926767	1	2	yes	—
236	C₄	#11926901	1	2	yes	—
237	C₄	#11926926	1	2	yes	—
238	C₂	#14562299	1	2	yes	—
239	C₂	#14562336	1	2	yes	—
240	C₂	#14564444	1	1	yes	characteristic
241	C₂	#14564478	1	1	yes	characteristic
242	C₂	#14564565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572013

C₂

yes

maximal, characteristic

C₄×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₂×#11926291

C₂

yes

maximal

C₂×#11926289

C₂

yes

maximal

C₁₉×#1831

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

—

—

—

—

C₄

yes

—

#11926299

—

#11926291

—

#11926289

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9700

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

100

Dic₃₈

—

101

C₈×C₁₉

—

102

C₁₉⋊C₈

—

103

#2862

—

104

#1831

D₁₉

yes

characteristic

105

C₄×C₄⋊C₈

—

106

C₂×#332

—

107

C₂×#332

—

108

C₂²×C₁₉

#390

yes

characteristic

109

C₂²×C₁₉

C₂×#101

yes

—

110

C₂²×C₁₉

#416

yes

—

111

C₂²×C₁₉

#416

yes

characteristic

112

C₂²×C₁₉

#417

yes

characteristic

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

#463

yes

—

117

C₄×C₁₉

#464

yes

—

118

C₄×C₁₉

#488

yes

—

119

C₄×C₁₉

#495

yes

—

120

Dic₁₉

—

121

Dic₁₉

—

122

C₂×C₄⋊Q₈

—

123

C₂×C₄⋊Q₈

—

124

C₂×C₄⋊C₈

—

125

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

126

C₂×C₄×C₈

—

127

#391

—

128

#391

—

129

#391

—

130

#382

—

131

C₄³

C₂×D₁₉

yes

characteristic

132

#336

—

133

#336

—

134

#332

—

135

#332

—

136

C₂×C₁₉

#1544

yes

—

137

C₂×C₁₉

#1552

yes

—

138

C₂×C₁₉

#1958

yes

characteristic

139

C₂×C₁₉

#1966

yes

characteristic

140

C₂×C₁₉

#1983

yes

characteristic

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

C₄×D₁₉

yes

—

154

C₂×C₄²

D₇₆

yes

characteristic

155

C₂×C₄²

D₇₆

yes

characteristic

156

C₂×C₄²

C₂²⋊D₁₉

yes

—

157

C₂×C₄²

C₂²×D₁₉

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄×C₈

—

163

#95

—

164

#95

—

165

C₁₉

#9700

yes

characteristic, complemented, Sylow

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

176

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

177

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

178

C₂²×C₄

C₂×D₇₆

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

D₄×D₁₉

yes

—

196

C₄²

#64545

yes

—

197

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

198

Q₈

—

152

—

199

Q₈

—

152

—

200

Q₈

—

152

—

201

Q₈

—

152

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#10597281

yes

—

214

C₂×C₄

#10597339

yes

—

215

C₂×C₄

#10597341

yes

—

216

C₂×C₄

#10597350

yes

—

217

C₂×C₄

#10597354

yes

characteristic

218

C₂×C₄

#10597355

yes

characteristic

219

C₂×C₄

#10597386

yes

characteristic

220

C₂×C₄

#10597393

yes

characteristic

221

C₂×C₄

#10597396

yes

—

222

C₈

—

223

C₈

—

224

C₂²

#11926445

yes

characteristic

225

C₂²

C₂×#10597281

yes

—

226

C₂²

#11926538

yes

—

227

C₂²

#11926541

yes

characteristic

228

C₂²

#11926546

yes

characteristic

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

152

—

233

C₄

—

152

—

234

C₄

#11926760

yes

—

235

C₄

#11926767

yes

—

236

C₄

#11926901

yes

—

237

C₄

#11926926

yes

—

238

C₂

#14562299

yes

—

239

C₂

#14562336

yes

—

240

C₂

#14564444

yes

characteristic

241

C₂

#14564478

yes

characteristic

242

C₂

#14564565

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#9700
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1831

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
165. C₁₉	#9700	semidirect

H ≅ G/N

type

165. C₁₉

#9700

semidirect

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

subgroup	index
#14572013	2
C₄×C₄⋊(C₁₉⋊C₈)	2
C₂×#11926291	2
C₂×#11926289	2
C₁₉×#1831	2
#9700	19

subgroup

index

C₄×C₄⋊(C₁₉⋊C₈)

C₁₉×#1831

Subgroups — #18081609

Conjugacy classes of subgroups

Complements

Maximal subgroups