Group #18080148 — subgroups

Subgroups — #18080148

Order 4864.

556 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14574088	C₂	1	1	yes	maximal, characteristic
2	#14562370	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562302	C₂	1	2	yes	maximal, complemented
4	#14561526	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597395	—	2	2	no	—
7	C₂×#10597320	C₂²	1	1	yes	characteristic
8	#11926934	C₄	1	4	yes	—
9	#11926920	—	2	1	no	—
10	#11926918	—	2	1	no	—
11	#11926568	C₂²	1	2	yes	—
12	C₄×#64520	C₂²	1	1	yes	characteristic
13	#11926293	—	2	1	no	—
14	#11926288	—	2	1	no	—
15	#11926287	—	2	2	no	—
16	#11926287	—	2	2	no	—
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#436	—	2	2	no	—
19	C₈×D₄×C₁₉	—	2	2	no	—
20	C₁₉×#431	C₂²	1	2	yes	—
21	C₁₉×#408	—	2	2	no	—
22	C₂×#41×C₁₉	D₄	1	2	yes	—
23	C₂²×D₇₆	—	2	1	no	—
24	C₂²×D₇₆	—	2	2	no	—
25	C₂×M₁₆×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
28	C₁₉×#127	D₄	1	1	yes	characteristic
29	C₁₉×#124	C₂×C₄	1	2	yes	—
30	C₁₉×#121	—	2	2	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	#10597395	—	4	4	no	—
34	#10597395	—	4	4	no	—
35	C₂×#64527	—	2	4	no	—
36	C₂×#64525	—	2	4	no	—
37	C₂×#64520	—	2	1	no	—
38	C₂×#64520	—	2	2	no	—
39	#10597320	—	2	2	no	—
40	#10597320	—	2	1	no	—
41	#10597320	C₂×C₄	1	2	yes	—
42	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
43	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
44	C₁₉×C₂²⋊C₈	—	2	4	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₄×C₈×C₁₉	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	#10597260	C₂×C₄	1	2	yes	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₂³×D₁₉	—	4	1	no	—
52	#41×C₁₉	—	4	2	no	—
53	#41×C₁₉	—	4	2	no	—
54	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	2	yes	—
61	C₂×D₇₆	—	2	2	no	—
62	C₂×D₇₆	—	2	4	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	—	4	2	no	—
65	C₂×D₇₆	—	4	1	no	—
66	C₂×D₇₆	—	4	2	no	—
67	C₂×D₇₆	—	8	2	no	—
68	C₂×D₇₆	—	8	2	no	—
69	M₁₆×C₁₉	—	8	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	8	2	no	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂²⋊C₄×C₁₉	—	2	4	no	—
75	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	#64527	—	4	8	no	—
79	#64525	—	4	8	no	—
80	#64520	—	2	2	no	—
81	#64520	—	2	2	no	—
82	#64520	—	8	2	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	4	2	no	—
85	#9437	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	—	2	2	no	—
87	C₂³×C₁₉	#123	1	1	yes	characteristic
88	C₂²×D₁₉	—	4	2	no	—
89	C₂²×D₁₉	—	8	2	no	—
90	C₂²×D₁₉	—	8	4	no	—
91	Q₈×C₁₉	—	4	2	no	—
92	D₄×C₁₉	—	4	2	no	—
93	D₄×C₁₉	—	4	2	no	—
94	D₄×C₁₉	—	4	2	no	—
95	D₄×C₁₉	—	8	2	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#121	1	2	yes	—
107	D₇₆	—	4	4	no	—
108	D₇₆	—	8	4	no	—
109	D₇₆	—	8	1	no	—
110	D₇₆	—	8	1	no	—
111	D₇₆	—	8	2	no	—
112	D₇₆	—	8	2	no	—
113	C₈×C₁₉	—	4	2	no	—
114	C₈×C₁₉	—	4	2	no	—
115	C₁₉⋊C₈	—	2	4	no	—
116	C₁₉⋊C₈	—	8	2	no	—
117	#3151	—	19	1	no	—
118	#2979	D₁₉	1	1	yes	characteristic, complemented
119	#1560	—	19	1	no	—
120	#1545	—	19	2	no	—
121	#1299	—	19	2	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	2	2	no	—
124	C₂²×C₁₉	—	4	2	no	—
125	C₂²×C₁₉	—	4	4	no	—
126	C₂²×C₁₉	#386	1	1	yes	characteristic
127	C₂×D₁₉	—	8	2	no	—
128	C₂×D₁₉	—	8	4	no	—
129	C₂×D₁₉	—	16	4	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	#453	1	1	yes	characteristic
134	C₄×C₁₉	#453	1	1	yes	characteristic
135	C₄×C₁₉	#471	1	2	yes	—
136	C₄×C₁₉	#472	1	2	yes	—
137	C₂×AGL(1,ℤ/8)	—	38	2	no	—
138	#532	C₂×D₁₉	1	1	yes	characteristic
139	C₂×#127	—	19	1	no	—
140	#496	—	19	4	no	—
141	#493	—	38	1	no	—
142	#492	—	38	1	no	—
143	#436	—	2	2	no	—
144	C₈×D₄	—	2	2	no	—
145	#431	C₂×D₁₉	1	2	yes	—
146	#423	—	19	2	no	—
147	#408	—	2	2	no	—
148	C₄×M₁₆	—	19	1	no	—
149	#333	—	38	1	no	—
150	#331	—	38	1	no	—
151	#331	—	38	2	no	—
152	#331	—	38	2	no	—
153	C₂×C₁₉	—	4	1	no	—
154	C₂×C₁₉	—	8	2	no	—
155	C₂×C₁₉	#1887	1	1	yes	characteristic
156	C₂×C₁₉	#1907	1	2	yes	—
157	D₁₉	—	16	2	no	—
158	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
159	C₂²×D₄	—	38	2	no	—
160	C₂²×D₄	—	38	1	no	—
161	AGL(1,ℤ/8)	—	76	4	no	—
162	AGL(1,ℤ/8)	—	76	4	no	—
163	C₂×SD₁₆	—	38	4	no	—
164	C₂×D₈	—	38	4	no	—
165	C₂×M₁₆	—	2	2	no	—
166	C₂×M₁₆	—	38	1	no	—
167	C₂×M₁₆	—	38	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
170	#127	—	19	2	no	—
171	#127	—	38	1	no	—
172	#127	—	38	2	no	—
173	#127	D₇₆	1	1	yes	characteristic
174	#124	C₄×D₁₉	1	2	yes	—
175	#121	—	2	2	no	—
176	C₄×D₄	—	2	2	no	—
177	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
178	C₄⋊C₈	—	38	2	no	—
179	C₄⋊C₈	—	38	2	no	—
180	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
181	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
182	C₂²⋊C₈	—	2	4	no	—
183	C₂²⋊C₈	—	2	2	no	—
184	#97	—	19	2	no	—
185	C₄×C₈	—	2	2	no	—
186	C₄×C₈	—	38	1	no	—
187	C₁₉	#9437	1	1	yes	characteristic, complemented, Sylow
188	C₂⁴	—	76	1	no	—
189	#41	—	4	2	no	—
190	#41	—	4	2	no	—
191	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
192	C₂×D₄	—	2	2	no	—
193	C₂×D₄	—	2	2	no	—
194	C₂×D₄	—	38	2	no	—
195	C₂×D₄	—	38	4	no	—
196	C₂×D₄	—	76	2	no	—
197	C₂×D₄	—	76	2	no	—
198	C₂×D₄	—	76	2	no	—
199	C₂×D₄	—	76	1	no	—
200	C₂×D₄	—	152	2	no	—
201	C₂×D₄	—	152	2	no	—
202	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	#64541	1	2	yes	—
205	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
206	SD₁₆	—	76	8	no	—
207	D₈	—	76	8	no	—
208	M₁₆	—	8	2	no	—
209	M₁₆	—	38	2	no	—
210	M₁₆	—	38	2	no	—
211	M₁₆	—	152	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	8	2	no	—
215	C₂×C₈	—	38	2	no	—
216	C₂×C₈	—	76	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₂²⋊C₄	—	2	4	no	—
219	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
220	C₄²	C₂×D₇₆	1	1	yes	characteristic
221	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
222	C₂³	—	2	2	no	—
223	C₂³	—	76	2	no	—
224	C₂³	—	152	2	no	—
225	C₂³	—	152	4	no	—
226	C₂³	#10597375	1	1	yes	characteristic
227	Q₈	—	4	2	no	—
228	D₄	—	4	2	no	—
229	D₄	—	4	2	no	—
230	D₄	—	4	2	no	—
231	D₄	—	8	2	no	—
232	D₄	—	76	4	no	—
233	D₄	—	152	4	no	—
234	D₄	—	152	2	no	—
235	D₄	—	152	2	no	—
236	D₄	—	152	1	no	—
237	D₄	—	152	1	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	2	no	—
245	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
246	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
247	C₂×C₄	#10597376	1	2	yes	—
248	C₂×C₄	#10597399	1	1	yes	characteristic
249	C₈	—	4	2	no	—
250	C₈	—	4	2	no	—
251	C₈	—	38	4	no	—
252	C₈	—	152	2	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	4	4	no	—
256	C₂²	—	4	2	no	—
257	C₂²	—	304	4	no	—
258	C₂²	—	152	4	no	—
259	C₂²	—	152	2	no	—
260	C₂²	#11926423	1	1	yes	characteristic
261	C₄	—	2	2	no	—
262	C₄	—	2	1	no	—
263	C₄	—	4	2	no	—
264	C₄	#11926712	1	1	yes	characteristic
265	C₄	#11926712	1	1	yes	characteristic
266	C₄	#11926807	1	2	yes	—
267	C₄	#11926814	1	2	yes	—
268	C₂	—	4	1	no	—
269	C₂	—	8	2	no	—
270	C₂	—	304	2	no	—
271	C₂	#14564033	1	1	yes	characteristic
272	C₂	#14564143	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574088

C₂

yes

maximal, characteristic

#14562370

C₂

yes

maximal, characteristic, complemented

#14562302

C₂

yes

maximal, complemented

#14561526

C₂

yes

maximal, complemented

C₁₉×#2979

C₂

yes

maximal, characteristic, complemented

C₂×#10597395

—

C₂×#10597320

C₂²

yes

characteristic

#11926934

C₄

yes

—

#11926920

—

#11926918

—

#11926568

C₂²

yes

—

C₄×#64520

C₂²

yes

—

—

—

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#436

—

C₈×D₄×C₁₉

—

C₁₉×#431

C₂²

yes

—

C₁₉×#408

—

C₂×#41×C₁₉

D₄

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9437

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₁₉

C₄×D₄

yes

—

105

C₂×C₄×C₁₉

#120

yes

characteristic

106

C₂×C₄×C₁₉

#121

yes

—

107

D₇₆

—

108

D₇₆

—

109

D₇₆

—

110

D₇₆

—

111

D₇₆

—

112

D₇₆

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

#3151

—

118

#2979

D₁₉

yes

characteristic, complemented

119

#1560

—

120

#1545

—

121

#1299

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#386

yes

characteristic

127

C₂×D₁₉

—

128

C₂×D₁₉

—

129

C₂×D₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

#453

yes

characteristic

134

C₄×C₁₉

#453

yes

characteristic

135

C₄×C₁₉

#471

yes

—

136

C₄×C₁₉

#472

yes

—

137

C₂×AGL(1,ℤ/8)

—

138

#532

C₂×D₁₉

yes

characteristic

139

C₂×#127

—

140

#496

—

141

#493

—

142

#492

—

143

#436

—

144

C₈×D₄

—

145

#431

C₂×D₁₉

yes

—

146

#423

—

147

#408

—

148

C₄×M₁₆

—

149

#333

—

150

#331

—

151

#331

—

152

#331

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#1887

yes

characteristic

156

C₂×C₁₉

#1907

yes

—

157

D₁₉

—

158

C₂×#41

C₂²⋊D₁₉

yes

—

159

C₂²×D₄

—

160

C₂²×D₄

—

161

AGL(1,ℤ/8)

—

162

AGL(1,ℤ/8)

—

163

C₂×SD₁₆

—

164

C₂×D₈

—

165

C₂×M₁₆

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₄⋊Q₈

D₇₆

yes

characteristic

170

#127

—

171

#127

—

172

#127

—

173

#127

D₇₆

yes

characteristic

174

#124

C₄×D₁₉

yes

—

175

#121

—

176

C₄×D₄

—

177

C₂×C₄²

C₂²×D₁₉

yes

characteristic

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

C₂²⋊D₁₉

yes

—

181

C₄⋊C₈

C₂²⋊D₁₉

yes

—

182

C₂²⋊C₈

—

183

C₂²⋊C₈

—

184

#97

—

185

C₄×C₈

—

186

C₄×C₈

—

187

C₁₉

#9437

yes

characteristic, complemented, Sylow

188

C₂⁴

—

189

#41

—

190

#41

—

191

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

152

—

201

C₂×D₄

—

152

—

202

C₂×D₄

(C₂×D₁₉)⋊C₄

yes

—

203

C₂²×C₄

—

204

C₂²×C₄

#64541

yes

—

205

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

206

SD₁₆

—

207

D₈

—

208

M₁₆

—

209

M₁₆

—

210

M₁₆

—

211

M₁₆

—

152

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₄⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

C₂×C₄×D₁₉

yes

characteristic

220

C₄²

C₂×D₇₆

yes

characteristic

221

C₄²

C₂×C₂²⋊D₁₉

yes

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

152

—

225

C₂³

—

152

—

226

C₂³

#10597375

yes

characteristic

227

Q₈

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

232

D₄

—

233

D₄

—

152

—

234

D₄

—

152

—

235

D₄

—

152

—

236

D₄

—

152

—

237

D₄

—

152

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

246

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

247

C₂×C₄

#10597376

yes

—

248

C₂×C₄

#10597399

yes

characteristic

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

152

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

304

—

258

C₂²

—

152

—

259

C₂²

—

152

—

260

C₂²

#11926423

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

#11926712

yes

characteristic

265

C₄

#11926712

yes

characteristic

266

C₄

#11926807

yes

—

267

C₄

#11926814

yes

—

268

C₂

—

269

C₂

—

270

C₂

—

304

—

271

C₂

#14564033

yes

characteristic

272

C₂

#14564143

yes

—

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2979	C₂
socle	C₂²×C₁₉	#386
prime radical	#14574088	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2979	D₁₉
hypocenter	C₁₉	#9437
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2979

subgroup

G/H

center

C₂²

#11926423

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2979

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2979

N	H ≅ G/N	type
2. #14562370	C₂	semidirect
3. #14562302	C₂	semidirect
4. #14561526	C₂	semidirect
5. C₁₉×#2979	C₂	semidirect
118. #2979	D₁₉	semidirect
187. C₁₉	#9437	semidirect

H ≅ G/N

type

2. #14562370

C₂

semidirect

3. #14562302

C₂

semidirect

4. #14561526

C₂

semidirect

5. C₁₉×#2979

C₂

semidirect

118. #2979

D₁₉

semidirect

187. C₁₉

#9437

semidirect

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

subgroup	index
#14574088	2
#14562370	2
#14562302	2
#14561526	2
C₁₉×#2979	2
#9437	19

subgroup

index

C₁₉×#2979

Subgroups — #18080148

Conjugacy classes of subgroups

Complements

Maximal subgroups