Group #18075459 — subgroups

Subgroups — #18075459

Order 4864.

486 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14563627	C₂	1	2	yes	maximal
2	#14562391	C₂	1	2	yes	maximal, complemented
3	#14561510	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926568	C₂²	1	4	yes	—
6	C₂×#10597290	—	2	2	no	—
7	#11926313	—	2	2	no	—
8	#11926295	—	2	2	no	—
9	#11926295	—	2	2	no	—
10	C₂³×C₈×C₁₉	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₈×D₄×C₁₉	—	2	2	no	—
13	C₈×D₄×C₁₉	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	4	4	no	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×#64520	—	2	4	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₂²⋊C₈	—	2	4	no	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	C₄×C₈×C₁₉	D₄	1	2	yes	—
35	#10597290	—	4	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
38	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
39	C₂×D₄×C₁₉	—	2	2	no	—
40	C₂×D₄×C₁₉	—	2	2	no	—
41	C₂×D₄×C₁₉	SD₁₆	1	4	yes	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	4	2	no	—
45	C₂²×C₄×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	4	4	no	—
54	C₂×C₈×C₁₉	—	4	4	no	—
55	C₂×C₈×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₄²×C₁₉	C₂×D₄	1	2	yes	—
62	C₄²×C₁₉	#41	1	2	yes	—
63	#64520	—	4	4	no	—
64	#64520	—	4	4	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	#8614	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	—	2	2	no	—
68	C₂³×C₁₉	—	2	2	no	—
69	C₂³×C₁₉	—	4	2	no	—
70	C₂³×C₁₉	—	4	2	no	—
71	C₂³×C₁₉	#106	1	4	yes	—
72	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	D₄×C₁₉	—	2	8	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	2	yes	—
85	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
87	C₂×C₄×C₁₉	#135	1	2	yes	—
88	C₈×C₁₉	—	2	1	no	—
89	C₈×C₁₉	—	2	2	no	—
90	C₈×C₁₉	—	4	2	no	—
91	C₈×C₁₉	#100	1	2	yes	complemented
92	C₁₉⋊C₈	—	8	4	no	—
93	C₂×C₈×D₄	D₁₉	1	1	yes	characteristic
94	#1800	—	19	2	no	—
95	#1566	—	19	2	no	—
96	#1292	—	19	2	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	—	2	4	no	—
100	C₂²×C₁₉	—	4	4	no	—
101	C₂²×C₁₉	—	4	4	no	—
102	C₂²×C₁₉	—	4	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	#380	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
106	C₂²×C₁₉	#427	1	1	yes	characteristic
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	4	2	no	—
110	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
111	C₄×C₁₉	#413	1	1	yes	characteristic
112	C₄×C₁₉	#465	1	4	yes	—
113	C₂³×C₈	Dic₁₉	1	2	yes	—
114	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
115	C₈×D₄	—	2	2	no	—
116	C₈×D₄	—	2	2	no	—
117	#423	—	19	4	no	—
118	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
119	C₂×#100	—	38	2	no	—
120	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
121	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
122	#343	—	38	2	no	—
123	#334	—	38	2	no	—
124	#334	—	38	2	no	—
125	C₂×C₁₉	—	2	1	no	—
126	C₂×C₁₉	—	2	1	no	—
127	C₂×C₁₉	—	4	4	no	—
128	C₂×C₁₉	#1800	1	1	yes	characteristic
129	C₂×C₁₉	#1807	1	1	yes	characteristic
130	C₂×C₁₉	#1813	1	1	yes	characteristic
131	C₂²×D₄	D₇₆	1	1	yes	characteristic
132	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
133	C₂×M₁₆	—	38	4	no	—
134	C₂²×C₈	—	2	2	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₂²×C₈	—	4	4	no	—
137	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
138	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
139	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
140	C₄×D₄	—	2	2	no	—
141	C₄×D₄	—	2	2	no	—
142	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
143	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
144	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	38	4	no	—
147	C₄⋊C₈	—	38	4	no	—
148	#100	—	76	4	no	—
149	C₂²⋊C₈	—	2	4	no	—
150	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
151	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
152	C₁₉	#8614	1	1	yes	characteristic, complemented, Sylow
153	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	2	no	—
156	C₂×D₄	#64516	1	4	yes	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
162	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
164	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
165	M₁₆	—	76	4	no	—
166	M₁₆	—	76	4	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	—	4	4	no	—
171	C₂×C₈	—	4	4	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	—	76	4	no	—
174	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
175	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
176	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
177	C₄⋊C₄	—	2	2	no	—
178	C₂²⋊C₄	—	2	4	no	—
179	C₄²	#64541	1	2	yes	—
180	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	2	no	—
183	C₂³	—	4	2	no	—
184	C₂³	—	4	2	no	—
185	C₂³	#10597274	1	4	yes	—
186	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
187	D₄	—	2	8	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	C₂×#64516	1	2	yes	—
197	C₂×C₄	#10597350	1	2	yes	—
198	C₂×C₄	#10597370	1	2	yes	—
199	C₂×C₄	#10597372	1	1	yes	characteristic
200	C₂×C₄	#10597376	1	2	yes	—
201	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	2	1	no	—
204	C₈	—	4	2	no	—
205	C₈	—	152	4	no	—
206	C₈	#10597290	1	2	yes	complemented
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	4	4	no	—
211	C₂²	—	4	4	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	#11926404	1	1	yes	characteristic
215	C₂²	C₂×#10597274	1	1	yes	characteristic
216	C₂²	#11926582	1	1	yes	characteristic
217	C₄	—	2	1	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	2	no	—
220	C₄	C₂×#10597290	1	1	yes	characteristic
221	C₄	#11926528	1	1	yes	characteristic
222	C₄	#11926773	1	4	yes	—
223	C₂	—	2	1	no	—
224	C₂	—	2	1	no	—
225	C₂	—	4	4	no	—
226	C₂	#14563627	1	1	yes	characteristic
227	C₂	#14563660	1	1	yes	characteristic
228	C₂	#14563685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563627

C₂

yes

maximal

#14562391

C₂

yes

maximal, complemented

#14561510

C₂

yes

maximal, complemented

C₂×C₈×D₄×C₁₉

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

—

—

—

—

C₂³×C₈×C₁₉

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₈×D₄×C₁₉

—

C₈×D₄×C₁₉

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597290

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#8614

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#106

yes

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

D₄×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

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#100

yes

complemented

C₁₉⋊C₈

—

C₂×C₈×D₄

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

#380

yes

characteristic

105

C₂²×C₁₉

C₂×#106

yes

characteristic

106

C₂²×C₁₉

#427

yes

characteristic

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

C₂×#100

yes

characteristic

111

C₄×C₁₉

#413

yes

characteristic

112

C₄×C₁₉

#465

yes

—

113

C₂³×C₈

Dic₁₉

yes

—

114

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

115

C₈×D₄

—

116

C₈×D₄

—

117

#423

—

118

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

119

C₂×#100

—

120

C₂×C₂²⋊C₈

Dic₁₉

yes

—

121

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

122

#343

—

123

#334

—

124

#334

—

125

C₂×C₁₉

—

126

C₂×C₁₉

—

127

C₂×C₁₉

—

128

C₂×C₁₉

#1800

yes

characteristic

129

C₂×C₁₉

#1807

yes

characteristic

130

C₂×C₁₉

#1813

yes

characteristic

131

C₂²×D₄

D₇₆

yes

characteristic

132

C₂³×C₄

C₂×Dic₁₉

yes

—

133

C₂×M₁₆

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

138

C₂²×C₈

C₂×Dic₁₉

yes

—

139

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

140

C₄×D₄

—

141

C₄×D₄

—

142

C₂×C₄⋊C₄

D₇₆

yes

characteristic

143

C₂×C₂²⋊C₄

Dic₃₈

yes

—

144

C₂×C₄²

C₂²×D₁₉

yes

characteristic

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

#100

—

149

C₂²⋊C₈

—

150

C₄×C₈

C₂²⋊D₁₉

yes

—

151

C₄×C₈

C₂²⋊D₁₉

yes

—

152

C₁₉

#8614

yes

characteristic, complemented, Sylow

153

C₂⁴

C₄⋊Dic₁₉

yes

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

#64516

yes

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

C₄⋊Dic₁₉

yes

—

162

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

163

C₂²×C₄

C₂×D₇₆

yes

characteristic

164

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

165

M₁₆

—

166

M₁₆

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

C₂²⋊Dic₁₉

yes

—

175

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

176

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

#64541

yes

—

180

C₄²

C₂×C₂²⋊D₁₉

yes

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

#10597274

yes

—

186

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

C₂×#64516

yes

—

197

C₂×C₄

#10597350

yes

—

198

C₂×C₄

#10597370

yes

—

199

C₂×C₄

#10597372

yes

characteristic

200

C₂×C₄

#10597376

yes

—

201

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

152

—

206

C₈

#10597290

yes

complemented

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

#11926404

yes

characteristic

215

C₂²

C₂×#10597274

yes

characteristic

216

C₂²

#11926582

yes

characteristic

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₂×#10597290

yes

characteristic

221

C₄

#11926528

yes

characteristic

222

C₄

#11926773

yes

—

223

C₂

—

224

C₂

—

225

C₂

—

226

C₂

#14563627

yes

characteristic

227

C₂

#14563660

yes

characteristic

228

C₂

#14563685

yes

characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈×D₄×C₁₉	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈×D₄	D₁₉
hypocenter	C₁₉	#8614
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

subgroup

G/H

center

C₂²

#11926404

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₈×D₄×C₁₉

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₂×C₈×D₄

D₁₉

hypocenter

C₁₉

#8614

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

N	H ≅ G/N	type
2. #14562391	C₂	semidirect
3. #14561510	C₂	semidirect
91. C₈×C₁₉	#100	semidirect
152. C₁₉	#8614	semidirect
206. C₈	#10597290	semidirect

H ≅ G/N

type

2. #14562391

C₂

semidirect

3. #14561510

C₂

semidirect

91. C₈×C₁₉

#100

semidirect

152. C₁₉

#8614

semidirect

206. C₈

#10597290

semidirect

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

subgroup	index
#14563627	2
#14562391	2
#14561510	2
C₂×C₈×D₄×C₁₉	2
#8614	19

subgroup

index

C₂×C₈×D₄×C₁₉

Subgroups — #18075459

Conjugacy classes of subgroups

Complements

Maximal subgroups