Group #18079949 — subgroups

Subgroups — #18079949

Order 4864.

486 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14568620	C₂	1	1	yes	maximal, characteristic
2	#14563631	C₂	1	1	yes	maximal, characteristic
3	#14562306	C₂	1	2	yes	maximal
4	#14561537	C₂	1	2	yes	maximal
5	C₁₉×#2983	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597390	—	2	1	no	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×#10597293	—	2	1	no	—
10	#11926474	C₄	1	4	yes	—
11	#11926449	—	2	1	no	—
12	#11926442	—	2	2	no	—
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926313	—	2	1	no	—
15	#11926289	—	2	4	no	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#446	—	2	4	no	—
18	C₁₉×#432	—	2	2	no	—
19	C₁₉×#431	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×Dic₃₈	—	2	1	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597390	—	4	4	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂×Dic₁₉⋊C₄	—	2	4	no	—
33	C₂×C₄×Dic₁₉	—	2	1	no	—
34	C₂×#64520	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	4	no	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₁₉×#97	—	2	4	no	—
41	C₄×C₈×C₁₉	—	2	2	no	—
42	#10597293	—	4	2	no	—
43	C₁₉⋊#95	—	2	4	no	—
44	C₁₉⋊#95	C₂×C₄	1	2	yes	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	1	no	—
50	C₂×Q₈×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	—	2	2	no	—
57	C₂²×Dic₁₉	—	2	2	no	—
58	C₂×Dic₃₈	—	4	2	no	—
59	C₂×Dic₃₈	—	4	2	no	—
60	C₂×Dic₃₈	—	4	1	no	—
61	C₂×Dic₃₈	—	4	1	no	—
62	C₂×C₈×C₁₉	—	2	4	no	—
63	C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	C₂×D₄	1	2	yes	—
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₄⋊Dic₁₉	—	2	4	no	—
70	C₄⋊Dic₁₉	—	2	4	no	—
71	C₄⋊Dic₁₉	—	4	1	no	—
72	C₄⋊Dic₁₉	—	4	1	no	—
73	Dic₁₉⋊C₄	—	4	8	no	—
74	C₄×Dic₁₉	—	4	2	no	—
75	#64520	—	4	2	no	—
76	#64520	—	4	2	no	—
77	C₂×C₁₉⋊C₈	—	4	2	no	—
78	#9402	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	Q₈×C₁₉	—	4	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
90	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	2	yes	—
92	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
93	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
96	C₂×Dic₁₉	—	2	4	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	Dic₃₈	—	8	2	no	—
103	Dic₃₈	—	8	2	no	—
104	C₈×C₁₉	—	4	4	no	—
105	C₁₉⋊C₈	—	8	2	no	—
106	#2983	D₁₉	1	1	yes	characteristic
107	#2546	—	19	1	no	—
108	#1801	—	19	1	no	—
109	#1546	—	19	2	no	—
110	#1303	—	19	2	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	#386	1	1	yes	characteristic
114	C₂²×C₁₉	#417	1	1	yes	characteristic
115	C₂²×C₁₉	#418	1	1	yes	characteristic
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	—	4	2	no	—
120	C₄×C₁₉	#456	1	2	yes	—
121	C₄×C₁₉	#468	1	2	yes	—
122	C₄×C₁₉	#469	1	2	yes	—
123	Dic₁₉	—	4	4	no	—
124	Dic₁₉	—	8	2	no	—
125	C₂×C₄⋊Q₈	—	19	1	no	—
126	C₂×C₄⋊Q₈	—	38	1	no	—
127	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
128	#446	—	2	4	no	—
129	#432	—	2	2	no	—
130	#431	C₂×D₁₉	1	2	yes	—
131	#423	—	19	2	no	—
132	C₂×#101	—	38	1	no	—
133	#398	—	19	4	no	—
134	#391	—	38	1	no	—
135	#389	—	38	2	no	—
136	C₄×C₄⋊C₄	—	19	1	no	—
137	#343	—	38	1	no	—
138	#332	—	38	4	no	—
139	C₂×C₁₉	—	2	1	no	—
140	C₂×C₁₉	—	2	1	no	—
141	C₂×C₁₉	#1886	1	1	yes	characteristic
142	C₂×C₁₉	#1895	1	1	yes	characteristic
143	C₂×C₁₉	#1915	1	1	yes	characteristic
144	C₂²×Q₈	—	38	1	no	—
145	C₂²×Q₈	D₇₆	1	1	yes	characteristic
146	C₂×M₁₆	—	38	2	no	—
147	C₄⋊Q₈	—	38	2	no	—
148	C₄⋊Q₈	—	38	2	no	—
149	C₄⋊Q₈	—	76	4	no	—
150	C₄×Q₈	—	2	2	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₂×C₄⋊C₄	—	19	2	no	—
153	C₂×C₄⋊C₄	—	38	1	no	—
154	C₂×C₄⋊C₄	—	38	4	no	—
155	C₂×C₄⋊C₄	—	38	1	no	—
156	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
157	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
158	C₂×C₄²	—	38	1	no	—
159	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
160	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
161	C₄⋊C₈	—	2	4	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₄⋊C₈	—	38	2	no	—
164	C₄⋊C₈	C₂²⋊D₁₉	1	4	yes	—
165	#101	—	76	2	no	—
166	C₂²⋊C₈	—	2	2	no	—
167	#97	—	2	4	no	—
168	C₄×C₈	—	2	2	no	—
169	#95	—	19	2	no	—
170	#95	—	38	4	no	—
171	C₁₉	#9402	1	1	yes	characteristic, complemented, Sylow
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	76	2	no	—
177	C₂×Q₈	—	76	2	no	—
178	C₂×Q₈	—	76	1	no	—
179	C₂×Q₈	—	76	1	no	—
180	C₂²×C₄	—	38	2	no	—
181	C₂²×C₄	—	38	2	no	—
182	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
183	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
184	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
187	M₁₆	—	76	2	no	—
188	M₁₆	—	76	2	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	76	2	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	2	4	no	—
193	C₄⋊C₄	—	38	4	no	—
194	C₄⋊C₄	—	38	4	no	—
195	C₄⋊C₄	—	76	8	no	—
196	C₄⋊C₄	—	76	1	no	—
197	C₄⋊C₄	—	76	1	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	76	2	no	—
201	C₄²	#64541	1	2	yes	—
202	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
203	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
204	Q₈	—	4	2	no	—
205	Q₈	—	4	2	no	—
206	Q₈	—	152	2	no	—
207	Q₈	—	152	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	38	4	no	—
216	C₂×C₄	—	76	2	no	—
217	C₂×C₄	—	76	2	no	—
218	C₂×C₄	—	76	2	no	—
219	C₂×C₄	—	76	2	no	—
220	C₂×C₄	—	76	2	no	—
221	C₂×C₄	#10597354	1	2	yes	—
222	C₂×C₄	#10597354	1	1	yes	characteristic
223	C₂×C₄	#10597355	1	1	yes	characteristic
224	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
225	C₂×C₄	#10597375	1	1	yes	characteristic
226	C₂×C₄	#10597376	1	2	yes	—
227	C₂×C₄	#10597399	1	1	yes	characteristic
228	C₈	—	4	4	no	—
229	C₈	—	152	2	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	#11926423	1	1	yes	characteristic
233	C₂²	#11926546	1	1	yes	characteristic
234	C₂²	#11926550	1	1	yes	characteristic
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	4	2	no	—
238	C₄	—	4	2	no	—
239	C₄	—	76	4	no	—
240	C₄	—	152	2	no	—
241	C₄	#11926727	1	2	yes	—
242	C₄	#11926790	1	2	yes	—
243	C₄	#11926797	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	#14564028	1	1	yes	characteristic
247	C₂	#14564073	1	1	yes	characteristic
248	C₂	#14564187	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14568620

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

#14562306

C₂

yes

maximal

#14561537

C₂

yes

maximal

C₁₉×#2983

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597390

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926474

C₄

yes

—

#11926449

—

#11926442

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926313

—

#11926289

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#446

—

C₁₉×#432

—

C₁₉×#431

C₂²

yes

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×Dic₃₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597390

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

#10597315

—

#10597315

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

#10597293

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

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×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#9402

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

Dic₃₈

—

103

Dic₃₈

—

104

C₈×C₁₉

—

105

C₁₉⋊C₈

—

106

#2983

D₁₉

yes

characteristic

107

#2546

—

108

#1801

—

109

#1546

—

110

#1303

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#386

yes

characteristic

114

C₂²×C₁₉

#417

yes

characteristic

115

C₂²×C₁₉

#418

yes

characteristic

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

#456

yes

—

121

C₄×C₁₉

#468

yes

—

122

C₄×C₁₉

#469

yes

—

123

Dic₁₉

—

124

Dic₁₉

—

125

C₂×C₄⋊Q₈

—

126

C₂×C₄⋊Q₈

—

127

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

128

#446

—

129

#432

—

130

#431

C₂×D₁₉

yes

—

131

#423

—

132

C₂×#101

—

133

#398

—

134

#391

—

135

#389

—

136

C₄×C₄⋊C₄

—

137

#343

—

138

#332

—

139

C₂×C₁₉

—

140

C₂×C₁₉

—

141

C₂×C₁₉

#1886

yes

characteristic

142

C₂×C₁₉

#1895

yes

characteristic

143

C₂×C₁₉

#1915

yes

characteristic

144

C₂²×Q₈

—

145

C₂²×Q₈

D₇₆

yes

characteristic

146

C₂×M₁₆

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

157

C₂×C₄⋊C₄

D₇₆

yes

characteristic

158

C₂×C₄²

—

159

C₂×C₄²

C₂²⋊D₁₉

yes

—

160

C₂×C₄²

C₂²×D₁₉

yes

characteristic

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

C₂²⋊D₁₉

yes

—

165

#101

—

166

C₂²⋊C₈

—

167

#97

—

168

C₄×C₈

—

169

#95

—

170

#95

—

171

C₁₉

#9402

yes

characteristic, complemented, Sylow

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

183

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

184

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

185

C₂²×C₄

C₂×D₇₆

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

187

M₁₆

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

#64541

yes

—

202

C₄²

C₂×C₂²⋊D₁₉

yes

—

203

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

204

Q₈

—

205

Q₈

—

206

Q₈

—

152

—

207

Q₈

—

152

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

#10597354

yes

—

222

C₂×C₄

#10597354

yes

characteristic

223

C₂×C₄

#10597355

yes

characteristic

224

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

225

C₂×C₄

#10597375

yes

characteristic

226

C₂×C₄

#10597376

yes

—

227

C₂×C₄

#10597399

yes

characteristic

228

C₈

—

229

C₈

—

152

—

230

C₂²

—

231

C₂²

—

232

C₂²

#11926423

yes

characteristic

233

C₂²

#11926546

yes

characteristic

234

C₂²

#11926550

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

152

—

241

C₄

#11926727

yes

—

242

C₄

#11926790

yes

—

243

C₄

#11926797

yes

—

244

C₂

—

245

C₂

—

246

C₂

#14564028

yes

characteristic

247

C₂

#14564073

yes

characteristic

248

C₂

#14564187

yes

characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2983	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2983	D₁₉
hypocenter	C₁₉	#9402
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2983

subgroup

G/H

center

C₂²

#11926423

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2983

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2983

N	H ≅ G/N	type
171. C₁₉	#9402	semidirect

H ≅ G/N

type

171. C₁₉

#9402

semidirect

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

subgroup	index
#14568620	2
#14563631	2
#14562306	2
#14561537	2
C₁₉×#2983	2
#9402	19

subgroup

index

C₁₉×#2983

Subgroups — #18079949

Conjugacy classes of subgroups

Complements

Maximal subgroups