Group #18085565 — subgroups

Subgroups — #18085565

Order 4864.

500 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 121 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	#14568877	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564561	C₂	1	2	yes	maximal
3	#14564440	C₂	1	1	yes	maximal, characteristic
4	#14561474	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	C₂×#10597278	—	2	2	no	—
8	C₂×#10597278	—	2	2	no	—
9	C₂×#10597266	—	2	2	no	—
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#11926483	—	2	2	no	—
12	#11926443	—	2	2	no	—
13	#11926409	—	2	2	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₁₉×#384	C₂²	1	1	yes	characteristic
17	C₂²×D₇₆	—	2	1	no	—
18	C₂²×D₇₆	—	2	2	no	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	1	no	—
28	#10597320	—	2	2	no	—
29	#10597320	—	2	1	no	—
30	#10597320	Q₈	1	2	yes	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉⋊#95	—	2	2	no	—
34	C₁₉⋊#95	—	2	4	no	—
35	C₁₉⋊#95	—	2	2	no	—
36	#10597278	—	4	4	no	—
37	#10597278	—	4	4	no	—
38	#10597266	—	4	4	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₂³×D₁₉	—	4	1	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂²×Dic₁₉	—	2	2	no	—
45	C₂²×Dic₁₉	—	2	2	no	—
46	C₂×D₇₆	—	2	4	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×D₇₆	—	4	2	no	—
49	C₂×D₇₆	—	4	2	no	—
50	C₂×D₇₆	—	4	2	no	—
51	C₂×D₇₆	—	4	2	no	—
52	C₂×D₇₆	—	4	2	no	—
53	C₂×D₇₆	—	4	2	no	—
54	C₂×D₇₆	—	4	1	no	—
55	C₂×D₇₆	—	4	2	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₄²×C₁₉	#41	1	1	yes	characteristic
65	C₄⋊Dic₁₉	—	2	2	no	—
66	C₄⋊Dic₁₉	—	2	2	no	—
67	C₄⋊Dic₁₉	—	2	2	no	—
68	C₄⋊Dic₁₉	—	2	2	no	—
69	C₄⋊Dic₁₉	—	8	2	no	—
70	C₄×Dic₁₉	—	4	2	no	—
71	C₄×Dic₁₉	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	#10351	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	#120	1	1	yes	characteristic
77	C₂²×D₁₉	—	4	2	no	—
78	C₂²×D₁₉	—	8	2	no	—
79	C₂²×D₁₉	—	8	2	no	—
80	C₂²×D₁₉	—	8	1	no	—
81	C₂²×D₁₉	—	8	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	4	4	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#124	1	2	yes	—
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₂×C₄×C₁₉	#135	1	2	yes	—
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	D₇₆	—	4	4	no	—
101	D₇₆	—	4	4	no	—
102	D₇₆	—	4	4	no	—
103	D₇₆	—	8	2	no	—
104	D₇₆	—	8	2	no	—
105	D₇₆	—	8	2	no	—
106	C₈×C₁₉	—	8	2	no	—
107	C₁₉⋊C₈	—	4	2	no	—
108	#2571	—	19	1	no	—
109	#1982	—	19	2	no	—
110	#1957	—	19	1	no	—
111	#1296	D₁₉	1	1	yes	characteristic, complemented
112	#1279	—	19	2	no	—
113	C₂²×C₁₉	#393	1	1	yes	characteristic
114	C₂²×C₁₉	#449	1	2	yes	—
115	C₂²×C₁₉	#449	1	2	yes	—
116	C₂²×C₁₉	#453	1	1	yes	characteristic
117	C₂²×C₁₉	#454	1	1	yes	characteristic
118	C₂×D₁₉	—	8	4	no	—
119	C₂×D₁₉	—	8	2	no	—
120	C₂×D₁₉	—	16	1	no	—
121	C₂×D₁₉	—	16	1	no	—
122	C₂×D₁₉	—	16	2	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	8	2	no	—
126	C₄×C₁₉	#478	1	2	yes	—
127	C₄×C₁₉	#478	1	2	yes	—
128	C₄×C₁₉	#488	1	2	yes	—
129	C₄×C₁₉	#490	1	2	yes	—
130	Dic₁₉	—	8	2	no	—
131	Dic₁₉	—	8	2	no	—
132	C₂×#127	—	19	1	no	—
133	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
134	C₂×#102	—	38	2	no	—
135	C₂×#102	—	38	2	no	—
136	C₂×#102	—	38	2	no	—
137	C₂×C₄×C₈	—	19	1	no	—
138	#400	—	38	2	no	—
139	#389	—	38	2	no	—
140	#384	C₂×D₁₉	1	1	yes	characteristic
141	#382	—	38	2	no	—
142	C₄×C₄⋊C₄	—	19	2	no	—
143	C₂×C₁₉	#1620	1	1	yes	characteristic
144	C₂×C₁₉	#1624	1	1	yes	characteristic
145	C₂×C₁₉	#1628	1	2	yes	—
146	C₂×C₁₉	#2025	1	2	yes	—
147	C₂×C₁₉	#2027	1	1	yes	characteristic
148	D₁₉	—	16	2	no	—
149	C₂²×D₄	—	38	1	no	—
150	C₂²×D₄	—	38	2	no	—
151	C₂²×C₈	—	2	2	no	—
152	C₂²×C₈	—	38	1	no	—
153	#127	—	19	2	no	—
154	#127	—	38	2	no	—
155	#127	—	38	1	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄⋊C₄	—	19	2	no	—
158	C₂×C₄⋊C₄	—	19	2	no	—
159	C₂×C₄⋊C₄	—	38	2	no	—
160	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
161	C₂×C₄²	—	38	2	no	—
162	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	#102	—	76	4	no	—
166	#102	—	76	4	no	—
167	#102	—	76	4	no	—
168	C₄×C₈	—	38	2	no	—
169	#95	—	38	2	no	—
170	#95	—	38	4	no	—
171	#95	—	38	2	no	—
172	C₁₉	#10351	1	1	yes	characteristic, complemented, Sylow
173	C₂⁴	—	76	1	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	1	no	—
179	C₂×D₄	—	76	2	no	—
180	C₂×D₄	—	76	2	no	—
181	C₂×D₄	—	76	2	no	—
182	C₂×D₄	—	76	2	no	—
183	C₂×D₄	—	76	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	38	2	no	—
186	C₂²×C₄	—	38	2	no	—
187	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
188	C₂²×C₄	D₄×D₁₉	1	2	yes	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	2	no	—
192	C₂×C₈	—	38	2	no	—
193	C₂×C₈	—	76	1	no	—
194	C₂×C₈	—	76	1	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	—	38	2	no	—
199	C₄⋊C₄	—	38	2	no	—
200	C₄⋊C₄	—	38	2	no	—
201	C₄⋊C₄	—	38	2	no	—
202	C₄⋊C₄	—	152	2	no	—
203	C₄²	—	76	2	no	—
204	C₄²	—	76	2	no	—
205	C₄²	#64541	1	2	yes	—
206	C₄²	#64543	1	1	yes	characteristic
207	C₄²	Q₈×D₁₉	1	1	yes	characteristic
208	C₂³	—	76	2	no	—
209	C₂³	—	152	2	no	—
210	C₂³	—	152	2	no	—
211	C₂³	—	152	1	no	—
212	C₂³	—	152	1	no	—
213	C₂³	#10597328	1	1	yes	characteristic
214	D₄	—	76	4	no	—
215	D₄	—	76	4	no	—
216	D₄	—	76	4	no	—
217	D₄	—	152	2	no	—
218	D₄	—	152	2	no	—
219	D₄	—	152	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	76	2	no	—
225	C₂×C₄	—	76	2	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	#10597321	1	1	yes	characteristic
231	C₂×C₄	#10597331	1	2	yes	—
232	C₂×C₄	#10597342	1	2	yes	—
233	C₂×C₄	#10597343	1	1	yes	characteristic
234	C₂×C₄	#10597357	1	2	yes	—
235	C₂×C₄	#10597360	1	2	yes	—
236	C₂×C₄	#10597362	1	2	yes	—
237	C₂×C₄	#10597365	1	2	yes	—
238	C₈	—	8	2	no	—
239	C₈	—	76	2	no	—
240	C₂²	—	304	1	no	—
241	C₂²	—	304	1	no	—
242	C₂²	—	304	2	no	—
243	C₂²	—	152	4	no	—
244	C₂²	—	152	2	no	—
245	C₂²	#11926457	1	1	yes	characteristic
246	C₂²	#11926690	1	2	yes	—
247	C₂²	#11926692	1	2	yes	—
248	C₂²	#11926714	1	1	yes	characteristic
249	C₂²	#11926719	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	8	2	no	—
253	C₄	—	152	2	no	—
254	C₄	—	152	2	no	—
255	C₄	#11926843	1	2	yes	—
256	C₄	#11926847	1	2	yes	—
257	C₄	#11926900	1	2	yes	—
258	C₄	#11926907	1	2	yes	—
259	C₂	—	304	2	no	—
260	C₂	#14562695	1	1	yes	characteristic
261	C₂	#14562719	1	1	yes	characteristic
262	C₂	#14562746	1	2	yes	—
263	C₂	#14564780	1	2	yes	—
264	C₂	#14564792	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14568877

C₂

yes

maximal, characteristic, complemented

#14564561

C₂

yes

maximal

#14564440

C₂

yes

maximal, characteristic

#14561474

C₂

yes

maximal, complemented

C₁₉×#1296

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597320

—

#10597320

—

#10597320

Q₈

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597278

—

#10597278

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

D₇₆

—

101

D₇₆

—

102

D₇₆

—

103

D₇₆

—

104

D₇₆

—

105

D₇₆

—

106

C₈×C₁₉

—

107

C₁₉⋊C₈

—

108

#2571

—

109

#1982

—

110

#1957

—

111

#1296

D₁₉

yes

characteristic, complemented

112

#1279

—

113

C₂²×C₁₉

#393

yes

characteristic

114

C₂²×C₁₉

#449

yes

—

115

C₂²×C₁₉

#449

yes

—

116

C₂²×C₁₉

#453

yes

characteristic

117

C₂²×C₁₉

#454

yes

characteristic

118

C₂×D₁₉

—

119

C₂×D₁₉

—

120

C₂×D₁₉

—

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

#478

yes

—

127

C₄×C₁₉

#478

yes

—

128

C₄×C₁₉

#488

yes

—

129

C₄×C₁₉

#490

yes

—

130

Dic₁₉

—

131

Dic₁₉

—

132

C₂×#127

—

133

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

134

C₂×#102

—

135

C₂×#102

—

136

C₂×#102

—

137

C₂×C₄×C₈

—

138

#400

—

139

#389

—

140

#384

C₂×D₁₉

yes

characteristic

141

#382

—

142

C₄×C₄⋊C₄

—

143

C₂×C₁₉

#1620

yes

characteristic

144

C₂×C₁₉

#1624

yes

characteristic

145

C₂×C₁₉

#1628

yes

—

146

C₂×C₁₉

#2025

yes

—

147

C₂×C₁₉

#2027

yes

characteristic

148

D₁₉

—

149

C₂²×D₄

—

150

C₂²×D₄

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

#127

—

154

#127

—

155

#127

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

D₇₆

yes

—

161

C₂×C₄²

—

162

C₂×C₄²

C₂²×D₁₉

yes

characteristic

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#102

—

166

#102

—

167

#102

—

168

C₄×C₈

—

169

#95

—

170

#95

—

171

#95

—

172

C₁₉

#10351

yes

characteristic, complemented, Sylow

173

C₂⁴

—

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

C₂×D₄

—

183

C₂×D₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

C₂×D₇₆

yes

characteristic

188

C₂²×C₄

D₄×D₁₉

yes

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

152

—

203

C₄²

—

204

C₄²

—

205

C₄²

#64541

yes

—

206

C₄²

#64543

yes

characteristic

207

C₄²

Q₈×D₁₉

yes

characteristic

208

C₂³

—

209

C₂³

—

152

—

210

C₂³

—

152

—

211

C₂³

—

152

—

212

C₂³

—

152

—

213

C₂³

#10597328

yes

characteristic

214

D₄

—

215

D₄

—

216

D₄

—

217

D₄

—

152

—

218

D₄

—

152

—

219

D₄

—

152

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

#10597321

yes

characteristic

231

C₂×C₄

#10597331

yes

—

232

C₂×C₄

#10597342

yes

—

233

C₂×C₄

#10597343

yes

characteristic

234

C₂×C₄

#10597357

yes

—

235

C₂×C₄

#10597360

yes

—

236

C₂×C₄

#10597362

yes

—

237

C₂×C₄

#10597365

yes

—

238

C₈

—

239

C₈

—

240

C₂²

—

304

—

241

C₂²

—

304

—

242

C₂²

—

304

—

243

C₂²

—

152

—

244

C₂²

—

152

—

245

C₂²

#11926457

yes

characteristic

246

C₂²

#11926690

yes

—

247

C₂²

#11926692

yes

—

248

C₂²

#11926714

yes

characteristic

249

C₂²

#11926719

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

152

—

254

C₄

—

152

—

255

C₄

#11926843

yes

—

256

C₄

#11926847

yes

—

257

C₄

#11926900

yes

—

258

C₄

#11926907

yes

—

259

C₂

—

304

—

260

C₂

#14562695

yes

characteristic

261

C₂

#14562719

yes

characteristic

262

C₂

#14562746

yes

—

263

C₂

#14564780

yes

—

264

C₂

#14564792

yes

characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#10351
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#10597328

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1296

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
1. #14568877	C₂	semidirect
4. #14561474	C₂	semidirect
5. C₁₉×#1296	C₂	semidirect
111. #1296	D₁₉	semidirect
172. C₁₉	#10351	semidirect

H ≅ G/N

type

1. #14568877

C₂

semidirect

4. #14561474

C₂

semidirect

5. C₁₉×#1296

C₂

semidirect

111. #1296

D₁₉

semidirect

172. C₁₉

#10351

semidirect

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

subgroup	index
#14568877	2
#14564561	2
#14564440	2
#14561474	2
C₁₉×#1296	2
#10351	19

subgroup

index

C₁₉×#1296

Subgroups — #18085565

Conjugacy classes of subgroups

Complements

Maximal subgroups