Group #18085316 — subgroups

Subgroups — #18085316

Order 4864.

670 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11926892	C₂	1	2	yes	maximal
2	#14564597	C₂	1	2	yes	maximal, complemented
3	#14564441	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	#11926892	—	2	4	no	—
8	#11926892	—	2	4	no	—
9	C₂×#10597278	—	2	2	no	—
10	C₂×#10597266	—	2	4	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926414	C₂²	1	1	yes	characteristic
13	#11926306	—	2	4	no	—
14	C₂²×Q₁₆×C₁₉	—	2	2	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₁₉×#494	—	2	4	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	—	2	2	no	—
19	C₂²×D₇₆	—	2	2	no	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂×Q₁₆×C₁₉	—	2	8	no	—
22	C₂×Q₁₆×C₁₉	—	4	4	no	—
23	C₂×Q₁₆×C₁₉	—	4	4	no	—
24	C₂²×C₈×C₁₉	D₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	2	no	—
27	C₁₉×C₄⋊Q₈	—	2	2	no	—
28	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	2	no	—
34	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
35	#10597320	—	2	2	no	—
36	#10597320	—	2	1	no	—
37	#10597320	D₄	1	2	yes	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	#10597278	—	4	4	no	—
40	#10597266	—	2	16	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₂³×D₁₉	—	4	1	no	—
44	C₂×Q₈×C₁₉	—	2	4	no	—
45	C₂×Q₈×C₁₉	—	4	2	no	—
46	C₂×Q₈×C₁₉	—	4	4	no	—
47	C₂×Q₈×C₁₉	—	4	4	no	—
48	C₂²×C₄×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	4	1	no	—
52	C₂×D₇₆	—	2	4	no	—
53	C₂×D₇₆	—	2	2	no	—
54	C₂×D₇₆	—	4	2	no	—
55	C₂×D₇₆	—	4	4	no	—
56	C₂×D₇₆	—	4	2	no	—
57	C₂×D₇₆	—	4	4	no	—
58	C₂×D₇₆	—	4	1	no	—
59	C₂×D₇₆	—	4	2	no	—
60	Q₁₆×C₁₉	—	4	16	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	D₈	1	4	yes	—
64	C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄⋊Dic₁₉	—	4	4	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	2	4	no	—
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	#10306	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	#127	1	1	yes	characteristic
78	C₂²×D₁₉	—	4	2	no	—
79	C₂²×D₁₉	—	8	1	no	—
80	C₂²×D₁₉	—	8	2	no	—
81	C₂²×D₁₉	—	8	1	no	—
82	C₂²×D₁₉	—	8	2	no	—
83	Q₈×C₁₉	—	4	8	no	—
84	Q₈×C₁₉	—	8	4	no	—
85	C₂×C₄×C₁₉	—	4	4	no	—
86	C₂×C₄×C₁₉	—	8	2	no	—
87	C₂×C₄×C₁₉	—	8	2	no	—
88	C₂×C₄×C₁₉	#120	1	2	yes	—
89	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	2	yes	—
92	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₁₉	#135	1	4	yes	—
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×C₄×C₁₉	#137	1	4	yes	—
96	C₂×Dic₁₉	—	8	1	no	—
97	C₂×Dic₁₉	—	8	2	no	—
98	D₇₆	—	4	8	no	—
99	D₇₆	—	4	4	no	—
100	D₇₆	—	8	2	no	—
101	D₇₆	—	8	4	no	—
102	C₈×C₁₉	—	2	4	no	—
103	C₁₉⋊C₈	—	4	4	no	—
104	C₂×#494	D₁₉	1	1	yes	characteristic, complemented
105	C₂×#486	—	19	2	no	—
106	#1990	—	19	2	no	—
107	#1957	—	19	1	no	—
108	#1273	—	19	1	no	—
109	C₂²×C₁₉	#392	1	1	yes	characteristic
110	C₂²×C₁₉	#493	1	1	yes	characteristic
111	C₂²×C₁₉	#495	1	2	yes	—
112	C₂²×C₁₉	#496	1	1	yes	characteristic
113	C₂²×C₁₉	#497	1	2	yes	—
114	C₂×D₁₉	—	8	2	no	—
115	C₂×D₁₉	—	8	4	no	—
116	C₂×D₁₉	—	16	1	no	—
117	C₂×D₁₉	—	16	2	no	—
118	C₂×D₁₉	—	16	1	no	—
119	C₄×C₁₉	—	8	4	no	—
120	C₄×C₁₉	#447	1	2	yes	—
121	C₄×C₁₉	#452	1	4	yes	—
122	C₄×C₁₉	#459	1	2	yes	—
123	C₄×C₁₉	#464	1	4	yes	—
124	Dic₁₉	—	16	1	no	—
125	C₂²×Q₁₆	—	2	2	no	—
126	C₂×C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
127	C₂×#127	—	19	1	no	—
128	#494	—	2	4	no	—
129	#486	—	38	4	no	—
130	#486	—	38	4	no	—
131	C₂×#102	—	38	4	no	—
132	C₂×#102	—	38	2	no	—
133	C₂×C₄×C₈	—	19	2	no	—
134	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
135	#384	—	19	1	no	—
136	#340	—	38	4	no	—
137	C₂×C₁₉	#1709	1	1	yes	characteristic
138	C₂×C₁₉	#1720	1	2	yes	—
139	C₂×C₁₉	#1722	1	1	yes	characteristic
140	C₂×C₁₉	#2011	1	1	yes	characteristic
141	C₂×C₁₉	#2015	1	2	yes	—
142	D₁₉	—	16	2	no	—
143	C₂²×Q₈	—	2	2	no	—
144	C₂²×D₄	—	38	2	no	—
145	C₂²×D₄	—	38	1	no	—
146	C₂×Q₁₆	—	2	8	no	—
147	C₂×Q₁₆	—	4	4	no	—
148	C₂×Q₁₆	—	4	4	no	—
149	C₂²×C₈	—	19	4	no	—
150	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
155	#127	—	19	2	no	—
156	#127	—	38	1	no	—
157	#127	—	38	2	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	38	2	no	—
161	C₂×C₄⋊C₄	—	38	1	no	—
162	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
163	#102	—	38	16	no	—
164	#102	—	76	4	no	—
165	C₄×C₈	—	2	2	no	—
166	C₄×C₈	—	38	2	no	—
167	C₄×C₈	—	38	2	no	—
168	C₁₉	#10306	1	1	yes	characteristic, complemented, Sylow
169	C₂⁴	—	76	1	no	—
170	C₂×Q₈	—	2	4	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	4	no	—
173	C₂×Q₈	—	4	4	no	—
174	C₂×D₄	—	38	4	no	—
175	C₂×D₄	—	38	2	no	—
176	C₂×D₄	—	76	2	no	—
177	C₂×D₄	—	76	2	no	—
178	C₂×D₄	—	76	2	no	—
179	C₂×D₄	—	76	1	no	—
180	C₂×D₄	—	76	4	no	—
181	C₂×D₄	—	76	4	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	76	1	no	—
184	C₂²×C₄	D₄×D₁₉	1	2	yes	—
185	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	Q₁₆	—	4	16	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	38	4	no	—
190	C₂×C₈	—	38	4	no	—
191	C₂×C₈	—	38	4	no	—
192	C₂×C₈	#64525	1	4	yes	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	76	2	no	—
198	C₄⋊C₄	—	76	4	no	—
199	C₄²	D₄×D₁₉	1	1	yes	characteristic
200	C₄²	#64543	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
202	C₂³	—	76	2	no	—
203	C₂³	—	152	1	no	—
204	C₂³	—	152	2	no	—
205	C₂³	—	152	1	no	—
206	C₂³	—	152	2	no	—
207	C₂³	#10597386	1	1	yes	characteristic
208	Q₈	—	4	8	no	—
209	Q₈	—	8	4	no	—
210	D₄	—	76	8	no	—
211	D₄	—	76	4	no	—
212	D₄	—	152	2	no	—
213	D₄	—	152	4	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	—	8	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	152	1	no	—
218	C₂×C₄	—	152	2	no	—
219	C₂×C₄	#10597364	1	4	yes	—
220	C₂×C₄	#10597365	1	4	yes	—
221	C₂×C₄	C₂×#64525	1	2	yes	—
222	C₂×C₄	#10597378	1	2	yes	—
223	C₂×C₄	#10597383	1	2	yes	—
224	C₂×C₄	#10597384	1	1	yes	characteristic
225	C₂×C₄	#10597385	1	2	yes	—
226	C₂×C₄	#10597399	1	1	yes	characteristic
227	C₈	—	2	4	no	—
228	C₈	—	76	4	no	—
229	C₂²	—	304	1	no	—
230	C₂²	—	304	2	no	—
231	C₂²	—	304	1	no	—
232	C₂²	—	152	2	no	—
233	C₂²	—	152	4	no	—
234	C₂²	#11926452	1	1	yes	characteristic
235	C₂²	#11926920	1	1	yes	characteristic
236	C₂²	#11926929	1	2	yes	—
237	C₂²	#11926931	1	1	yes	characteristic
238	C₂²	#11926937	1	2	yes	—
239	C₄	—	8	4	no	—
240	C₄	—	304	1	no	—
241	C₄	#11926678	1	2	yes	—
242	C₄	#11926705	1	4	yes	—
243	C₄	#11926736	1	2	yes	—
244	C₄	#11926768	1	4	yes	—
245	C₂	—	304	2	no	—
246	C₂	#14563242	1	1	yes	characteristic
247	C₂	#14563298	1	2	yes	—
248	C₂	#14563307	1	1	yes	characteristic
249	C₂	#14564706	1	1	yes	characteristic
250	C₂	#14564726	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926892

C₂

yes

maximal

#14564597

C₂

yes

maximal, complemented

#14564441

C₂

yes

maximal, characteristic

C₁₉⋊#1273

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#494

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

—

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926306

—

C₂²×Q₁₆×C₁₉

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#494

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

#10597320

—

#10597320

—

#10597320

D₄

yes

—

C₄×C₈×C₁₉

—

#10597278

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄⋊C₄×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

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

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

#120

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

100

D₇₆

—

101

D₇₆

—

102

C₈×C₁₉

—

103

C₁₉⋊C₈

—

104

C₂×#494

D₁₉

yes

characteristic, complemented

105

C₂×#486

—

106

#1990

—

107

#1957

—

108

#1273

—

109

C₂²×C₁₉

#392

yes

characteristic

110

C₂²×C₁₉

#493

yes

characteristic

111

C₂²×C₁₉

#495

yes

—

112

C₂²×C₁₉

#496

yes

characteristic

113

C₂²×C₁₉

#497

yes

—

114

C₂×D₁₉

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

—

118

C₂×D₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

#447

yes

—

121

C₄×C₁₉

#452

yes

—

122

C₄×C₁₉

#459

yes

—

123

C₄×C₁₉

#464

yes

—

124

Dic₁₉

—

125

C₂²×Q₁₆

—

126

C₂×C₄⋊Q₈

C₂×D₁₉

yes

—

127

C₂×#127

—

128

#494

—

129

#486

—

130

#486

—

131

C₂×#102

—

132

C₂×#102

—

133

C₂×C₄×C₈

—

134

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

135

#384

—

136

#340

—

137

C₂×C₁₉

#1709

yes

characteristic

138

C₂×C₁₉

#1720

yes

—

139

C₂×C₁₉

#1722

yes

characteristic

140

C₂×C₁₉

#2011

yes

characteristic

141

C₂×C₁₉

#2015

yes

—

142

D₁₉

—

143

C₂²×Q₈

—

144

C₂²×D₄

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂²×C₈

—

150

C₂²×C₈

C₂²⋊D₁₉

yes

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

155

#127

—

156

#127

—

157

#127

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄²

C₂²×D₁₉

yes

characteristic

163

#102

—

164

#102

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₁₉

#10306

yes

characteristic, complemented, Sylow

169

C₂⁴

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

D₄×D₁₉

yes

—

185

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

186

Q₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

#64525

yes

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄²

D₄×D₁₉

yes

characteristic

200

C₄²

#64543

yes

characteristic

201

C₄²

C₂×C₂²⋊D₁₉

yes

—

202

C₂³

—

203

C₂³

—

152

—

204

C₂³

—

152

—

205

C₂³

—

152

—

206

C₂³

—

152

—

207

C₂³

#10597386

yes

characteristic

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

D₄

—

152

—

213

D₄

—

152

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

152

—

218

C₂×C₄

—

152

—

219

C₂×C₄

#10597364

yes

—

220

C₂×C₄

#10597365

yes

—

221

C₂×C₄

C₂×#64525

yes

—

222

C₂×C₄

#10597378

yes

—

223

C₂×C₄

#10597383

yes

—

224

C₂×C₄

#10597384

yes

characteristic

225

C₂×C₄

#10597385

yes

—

226

C₂×C₄

#10597399

yes

characteristic

227

C₈

—

228

C₈

—

229

C₂²

—

304

—

230

C₂²

—

304

—

231

C₂²

—

304

—

232

C₂²

—

152

—

233

C₂²

—

152

—

234

C₂²

#11926452

yes

characteristic

235

C₂²

#11926920

yes

characteristic

236

C₂²

#11926929

yes

—

237

C₂²

#11926931

yes

characteristic

238

C₂²

#11926937

yes

—

239

C₄

—

240

C₄

—

304

—

241

C₄

#11926678

yes

—

242

C₄

#11926705

yes

—

243

C₄

#11926736

yes

—

244

C₄

#11926768

yes

—

245

C₂

—

304

—

246

C₂

#14563242

yes

characteristic

247

C₂

#14563298

yes

—

248

C₂

#14563307

yes

characteristic

249

C₂

#14564706

yes

characteristic

250

C₂

#14564726

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#494	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
hypercenter	C₂×#494	D₁₉
hypocenter	C₁₉	#10306
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#494

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
2. #14564597	C₂	semidirect
4. C₁₉⋊#1273	C₂	semidirect
5. C₂×C₁₉×#494	C₂	semidirect
104. C₂×#494	D₁₉	semidirect
168. C₁₉	#10306	semidirect

H ≅ G/N

type

2. #14564597

C₂

semidirect

4. C₁₉⋊#1273

C₂

semidirect

5. C₂×C₁₉×#494

C₂

semidirect

104. C₂×#494

D₁₉

semidirect

168. C₁₉

#10306

semidirect

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

subgroup	index
C₂×#11926892	2
#14564597	2
#14564441	2
C₁₉⋊#1273	2
C₂×C₁₉×#494	2
#10306	19

subgroup

index

C₂×#11926892

#14564597

#14564441

C₁₉⋊#1273

C₂×C₁₉×#494

#10306

Subgroups — #18085316

Conjugacy classes of subgroups

Complements

Maximal subgroups