Group #18013152 — subgroups

Subgroups — C₁₉×#7193 #18013152

Order 4864.

342 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 110 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×C₁₉×#349	C₂	1	2	yes	maximal
2	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
3	C₂²×M₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
6	C₂×C₁₉×M₃₂	—	2	2	no	—
7	C₁₉×#349	—	2	2	no	—
8	C₁₉×#349	C₄	1	4	yes	complemented
9	C₁₉×#336	—	2	2	no	—
10	C₂³×C₄×C₁₉	—	2	1	no	—
11	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	—	2	1	no	—
13	C₂×M₁₆×C₁₉	—	4	1	no	—
14	C₂×M₁₆×C₁₉	—	4	1	no	—
15	C₂×M₁₆×C₁₉	—	4	1	no	—
16	C₂×M₁₆×C₁₉	—	4	1	no	—
17	C₂×M₁₆×C₁₉	C₈	1	2	yes	—
18	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
20	C₂×M₁₆×C₁₉	Q₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	—	2	1	no	—
24	C₂×C₄²×C₁₉	—	4	1	no	—
25	C₂×C₄²×C₁₉	—	4	1	no	—
26	C₂×C₄²×C₁₉	C₈	1	2	yes	—
27	C₁₉×M₃₂	—	2	4	no	—
28	C₁₉×M₃₂	—	4	2	no	—
29	C₂×C₁₆×C₁₉	—	4	2	no	—
30	C₂⁴×C₁₉	M₁₆	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	—	2	1	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	4	4	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
44	M₁₆×C₁₉	—	4	2	no	—
45	M₁₆×C₁₉	—	4	1	no	—
46	M₁₆×C₁₉	—	4	1	no	—
47	M₁₆×C₁₉	—	4	2	no	—
48	M₁₆×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	—	2	2	no	—
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	1	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
56	C₄²×C₁₉	—	4	2	no	—
57	C₄²×C₁₉	—	4	1	no	—
58	C₄²×C₁₉	—	4	1	no	—
59	C₁₆×C₁₉	—	4	4	no	—
60	#7193	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	2	1	no	—
63	C₂³×C₁₉	—	4	2	no	—
64	C₂³×C₁₉	#97	1	1	yes	characteristic
65	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
66	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	8	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
89	C₈×C₁₉	—	2	2	no	—
90	C₈×C₁₉	—	2	2	no	—
91	C₈×C₁₉	—	4	2	no	—
92	C₂×#349	C₂×C₁₉	1	2	yes	—
93	#1728	C₂×C₁₉	1	1	yes	characteristic
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	—	2	1	no	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	4	1	no	—
98	C₂²×C₁₉	—	4	1	no	—
99	C₂²×C₁₉	—	4	2	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	#323	1	1	yes	characteristic
102	C₂²×C₁₉	#324	1	1	yes	characteristic
103	C₂²×C₁₉	#336	1	1	yes	characteristic
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	4	4	no	—
107	C₄×C₁₉	#323	1	1	yes	characteristic
108	C₄×C₁₉	#324	1	1	yes	characteristic
109	C₄×C₁₉	#342	1	1	yes	characteristic
110	C₄×C₁₉	#343	1	1	yes	characteristic
111	C₂²×M₁₆	C₄×C₁₉	1	1	yes	characteristic
112	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
113	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic
114	C₂×M₃₂	—	2	2	no	—
115	#349	—	2	2	no	—
116	#349	C₄×C₁₉	1	4	yes	complemented
117	#336	—	2	2	no	—
118	C₂×C₁₉	—	2	1	no	—
119	C₂×C₁₉	—	2	1	no	—
120	C₂×C₁₉	—	4	1	no	—
121	C₂×C₁₉	—	4	1	no	—
122	C₂×C₁₉	#1280	1	1	yes	characteristic
123	C₂×C₁₉	#1327	1	2	yes	—
124	C₂³×C₄	—	2	1	no	—
125	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
126	C₂×M₁₆	—	2	1	no	—
127	C₂×M₁₆	—	4	1	no	—
128	C₂×M₁₆	—	4	1	no	—
129	C₂×M₁₆	—	4	1	no	—
130	C₂×M₁₆	—	4	1	no	—
131	C₂×M₁₆	C₈×C₁₉	1	2	yes	—
132	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
133	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
134	C₂×M₁₆	Q₈×C₁₉	1	1	yes	characteristic
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	D₄×C₁₉	1	2	yes	—
137	C₂×C₄²	—	2	1	no	—
138	C₂×C₄²	—	4	1	no	—
139	C₂×C₄²	—	4	1	no	—
140	C₂×C₄²	C₈×C₁₉	1	2	yes	—
141	M₃₂	—	2	4	no	—
142	M₃₂	—	4	2	no	—
143	C₂×C₁₆	—	4	2	no	—
144	C₁₉	#7193	1	1	yes	characteristic, direct product factor, Sylow
145	C₂⁴	M₁₆×C₁₉	1	1	yes	characteristic
146	C₂²×C₄	—	2	1	no	—
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	—	2	1	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	4	4	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	C₄²×C₁₉	1	1	yes	characteristic
154	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
156	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	M₁₆×C₁₉	1	1	yes	characteristic
159	M₁₆	—	4	2	no	—
160	M₁₆	—	4	1	no	—
161	M₁₆	—	4	1	no	—
162	M₁₆	—	4	2	no	—
163	M₁₆	—	4	2	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	4	1	no	—
168	C₂×C₈	—	4	1	no	—
169	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
170	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
171	C₄²	—	4	2	no	—
172	C₄²	—	4	1	no	—
173	C₄²	—	4	1	no	—
174	C₁₆	—	4	4	no	—
175	C₂³	—	2	1	no	—
176	C₂³	—	2	1	no	—
177	C₂³	—	4	2	no	—
178	C₂³	C₁₉×#97	1	1	yes	characteristic
179	C₂³	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
180	C₂³	C₁₉×C₄⋊C₈	1	1	yes	characteristic
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	8	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
196	C₂×C₄	C₄×C₈×C₁₉	1	1	yes	characteristic
197	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
198	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
199	C₂×C₄	C₁₉×#99	1	1	yes	characteristic
200	C₂×C₄	C₁₉×#100	1	1	yes	characteristic
201	C₂×C₄	C₁₉×#101	1	1	yes	characteristic
202	C₂×C₄	C₁₉×C₄⋊C₈	1	1	yes	characteristic
203	C₈	—	2	2	no	—
204	C₈	—	2	2	no	—
205	C₈	—	4	2	no	—
206	C₂²	—	2	2	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	4	1	no	—
210	C₂²	—	4	1	no	—
211	C₂²	—	4	2	no	—
212	C₂²	—	4	2	no	—
213	C₂²	C₁₉×#323	1	1	yes	characteristic
214	C₂²	C₁₉×#324	1	1	yes	characteristic
215	C₂²	C₁₉×#336	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	4	no	—
219	C₄	C₁₉×#323	1	1	yes	characteristic
220	C₄	C₁₉×#324	1	1	yes	characteristic
221	C₄	C₁₉×#342	1	1	yes	characteristic
222	C₄	C₁₉×#343	1	1	yes	characteristic
223	C₂	—	2	1	no	—
224	C₂	—	2	1	no	—
225	C₂	—	4	1	no	—
226	C₂	—	4	1	no	—
227	C₂	C₁₉×#1280	1	1	yes	characteristic
228	C₂	C₁₉×#1327	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#349

C₂

yes

maximal

C₁₉×#1728

C₂

yes

maximal, characteristic

C₂²×M₁₆×C₁₉

C₄

yes

characteristic

C₂²×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₄²×C₁₉

C₄

yes

characteristic

C₂×C₁₉×M₃₂

—

C₁₉×#349

—

C₁₉×#349

C₄

yes

complemented

C₁₉×#336

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₈

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₈

yes

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂⁴×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#7193

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#97

yes

characteristic

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂³×C₁₉

C₄⋊C₈

yes

characteristic

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₂×#349

C₂×C₁₉

yes

—

#1728

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

#323

yes

characteristic

102

C₂²×C₁₉

#324

yes

characteristic

103

C₂²×C₁₉

#336

yes

characteristic

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

#323

yes

characteristic

108

C₄×C₁₉

#324

yes

characteristic

109

C₄×C₁₉

#342

yes

characteristic

110

C₄×C₁₉

#343

yes

characteristic

111

C₂²×M₁₆

C₄×C₁₉

yes

characteristic

112

C₂²×M₁₆

C₂²×C₁₉

yes

characteristic

113

C₂²×C₄²

C₄×C₁₉

yes

characteristic

114

C₂×M₃₂

—

115

#349

—

116

#349

C₄×C₁₉

yes

complemented

117

#336

—

118

C₂×C₁₉

—

119

C₂×C₁₉

—

120

C₂×C₁₉

—

121

C₂×C₁₉

—

122

C₂×C₁₉

#1280

yes

characteristic

123

C₂×C₁₉

#1327

yes

—

124

C₂³×C₄

—

125

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

126

C₂×M₁₆

—

127

C₂×M₁₆

—

128

C₂×M₁₆

—

129

C₂×M₁₆

—

130

C₂×M₁₆

—

131

C₂×M₁₆

C₈×C₁₉

yes

—

132

C₂×M₁₆

C₂×C₄×C₁₉

yes

—

133

C₂×M₁₆

D₄×C₁₉

yes

characteristic

134

C₂×M₁₆

Q₈×C₁₉

yes

characteristic

135

C₂²×C₈

—

136

C₂²×C₈

D₄×C₁₉

yes

—

137

C₂×C₄²

—

138

C₂×C₄²

—

139

C₂×C₄²

—

140

C₂×C₄²

C₈×C₁₉

yes

—

141

M₃₂

—

142

M₃₂

—

143

C₂×C₁₆

—

144

C₁₉

#7193

yes

characteristic, direct product factor, Sylow

145

C₂⁴

M₁₆×C₁₉

yes

characteristic

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

C₄²×C₁₉

yes

characteristic

154

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

155

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

156

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

157

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

158

C₂²×C₄

M₁₆×C₁₉

yes

characteristic

159

M₁₆

—

160

M₁₆

—

161

M₁₆

—

162

M₁₆

—

163

M₁₆

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

C₂²⋊C₄×C₁₉

yes

—

170

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

171

C₄²

—

172

C₄²

—

173

C₄²

—

174

C₁₆

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

C₁₉×#97

yes

characteristic

179

C₂³

C₁₉×C₂²⋊C₈

yes

characteristic

180

C₂³

C₁₉×C₄⋊C₈

yes

characteristic

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

C₁₉×#95

yes

characteristic

196

C₂×C₄

C₄×C₈×C₁₉

yes

characteristic

197

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

198

C₂×C₄

C₁₉×#99

yes

characteristic

199

C₂×C₄

C₁₉×#99

yes

characteristic

200

C₂×C₄

C₁₉×#100

yes

characteristic

201

C₂×C₄

C₁₉×#101

yes

characteristic

202

C₂×C₄

C₁₉×C₄⋊C₈

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

C₁₉×#323

yes

characteristic

214

C₂²

C₁₉×#324

yes

characteristic

215

C₂²

C₁₉×#336

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

C₁₉×#323

yes

characteristic

220

C₄

C₁₉×#324

yes

characteristic

221

C₄

C₁₉×#342

yes

characteristic

222

C₄

C₁₉×#343

yes

characteristic

223

C₂

—

224

C₂

—

225

C₂

—

226

C₂

—

227

C₂

C₁₉×#1280

yes

characteristic

228

C₂

C₁₉×#1327

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₉	#99
commutator	C₂×C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂²×M₁₆	C₂²×C₁₉
socle	C₂²×C₁₉	#324
prime radical	C₂⁴×C₁₉	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#99

commutator

C₂×C₄

C₄×C₈×C₁₉

Frattini, cosocle

C₂²×M₁₆

C₂²×C₁₉

socle

C₂²×C₁₉

#324

prime radical

C₂⁴×C₁₉

M₁₆

LCS

G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
8. C₁₉×#349	C₄	semidirect
60. #7193	C₁₉	direct (N × H)
116. #349	C₄×C₁₉	semidirect
144. C₁₉	#7193	direct (N × H)

H ≅ G/N

type

8. C₁₉×#349

C₄

semidirect

60. #7193

C₁₉

direct (N × H)

116. #349

C₄×C₁₉

semidirect

144. C₁₉

#7193

direct (N × H)

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

subgroup	index
C₂×C₁₉×#349	2
C₁₉×#1728	2
#7193	19

subgroup

index

C₂×C₁₉×#349

C₁₉×#1728

#7193

Subgroups — C₁₉×#7193 #18013152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7193 #18013152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7193 #18013152