Group #18017156 — subgroups

Subgroups — C₁₉×#11197 #18017156

Order 4864.

1134 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 238 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×#381	C₂	1	2	yes	maximal
2	C₂×C₁₉×#381	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#342	C₂	1	4	yes	maximal
4	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
6	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
7	C₁₉×#381	—	2	4	no	—
8	C₁₉×#381	—	2	8	no	—
9	C₂×C₁₉×#95	—	2	4	no	—
10	C₂×C₁₉×#95	C₄	1	4	yes	complemented
11	C₁₉×#342	—	2	8	no	—
12	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
13	C₂³×C₄×C₁₉	—	2	4	no	—
14	C₂³×C₄×C₁₉	—	2	4	no	—
15	C₂³×C₄×C₁₉	—	2	4	no	—
16	C₂³×C₄×C₁₉	—	2	4	no	—
17	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
19	C₂³×C₄×C₁₉	D₄	1	4	yes	—
20	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
21	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
30	C₁₉×#95	—	2	16	no	—
31	C₁₉×#95	—	2	8	no	—
32	C₂⁴×C₁₉	—	4	4	no	—
33	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
35	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
36	C₂⁴×C₁₉	#41	1	4	yes	—
37	C₂⁴×C₁₉	#41	1	4	yes	—
38	C₂²×C₄×C₁₉	—	2	4	no	—
39	C₂²×C₄×C₁₉	—	2	8	no	—
40	C₂²×C₄×C₁₉	—	2	4	no	—
41	C₂²×C₄×C₁₉	—	2	8	no	—
42	C₂²×C₄×C₁₉	—	2	8	no	—
43	C₂²×C₄×C₁₉	—	2	4	no	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	—	2	8	no	—
46	C₂²×C₄×C₁₉	—	2	8	no	—
47	C₂²×C₄×C₁₉	—	4	4	no	—
48	C₂²×C₄×C₁₉	—	4	4	no	—
49	C₂²×C₄×C₁₉	—	4	4	no	—
50	C₂²×C₄×C₁₉	—	4	4	no	—
51	C₂²×C₄×C₁₉	—	4	16	no	—
52	C₂²×C₄×C₁₉	—	4	4	no	—
53	C₂²×C₄×C₁₉	—	4	4	no	—
54	C₂²×C₄×C₁₉	—	4	8	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂²⋊C₄×C₁₉	—	2	8	no	—
57	C₂²⋊C₄×C₁₉	—	2	8	no	—
58	C₂²⋊C₄×C₁₉	—	4	2	no	—
59	C₂²⋊C₄×C₁₉	—	4	4	no	—
60	C₂²⋊C₄×C₁₉	—	4	4	no	—
61	C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₂²⋊C₄×C₁₉	—	4	4	no	—
63	#11197	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂³×C₁₉	—	2	4	no	—
65	C₂³×C₁₉	—	2	8	no	—
66	C₂³×C₁₉	—	4	8	no	—
67	C₂³×C₁₉	—	4	8	no	—
68	C₂³×C₁₉	—	4	8	no	—
69	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂³×C₁₉	#117	1	2	yes	—
71	C₂³×C₁₉	C₄×D₄	1	4	yes	—
72	C₂³×C₁₉	#120	1	2	yes	—
73	C₂³×C₁₉	#121	1	4	yes	—
74	C₂³×C₁₉	#121	1	4	yes	—
75	C₂³×C₁₉	#123	1	4	yes	—
76	C₂³×C₁₉	#123	1	2	yes	—
77	C₂³×C₁₉	#123	1	4	yes	—
78	C₂³×C₁₉	#124	1	4	yes	—
79	C₂³×C₁₉	#126	1	4	yes	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	2	8	no	—
82	C₂×C₄×C₁₉	—	4	8	no	—
83	C₂×C₄×C₁₉	—	4	8	no	—
84	C₂×C₄×C₁₉	—	4	8	no	—
85	C₂×C₄×C₁₉	—	4	16	no	—
86	C₂×C₄×C₁₉	—	4	4	no	—
87	C₂×C₄×C₁₉	—	4	8	no	—
88	C₂×C₄×C₁₉	—	4	8	no	—
89	C₂×C₄×C₁₉	—	8	8	no	—
90	C₂×C₄×C₁₉	—	8	8	no	—
91	C₂×C₄×C₁₉	—	8	8	no	—
92	C₂×#381	C₂×C₁₉	1	2	yes	—
93	C₂×#381	C₂×C₁₉	1	1	yes	characteristic
94	C₂×#342	C₂×C₁₉	1	4	yes	—
95	C₂²×C₁₉	—	2	8	no	—
96	C₂²×C₁₉	—	2	4	no	—
97	C₂²×C₁₉	—	2	4	no	—
98	C₂²×C₁₉	—	2	8	no	—
99	C₂²×C₁₉	—	2	8	no	—
100	C₂²×C₁₉	—	2	4	no	—
101	C₂²×C₁₉	—	4	4	no	—
102	C₂²×C₁₉	—	4	4	no	—
103	C₂²×C₁₉	—	4	4	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	#381	1	1	yes	characteristic
106	C₂²×C₁₉	#386	1	2	yes	—
107	C₂²×C₁₉	#388	1	4	yes	—
108	C₂²×C₁₉	#394	1	4	yes	—
109	C₂²×C₁₉	#397	1	4	yes	—
110	C₂²×C₁₉	#410	1	4	yes	—
111	C₄×C₁₉	—	4	4	no	—
112	C₄×C₁₉	—	8	8	no	—
113	C₄×C₁₉	—	8	4	no	—
114	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
115	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
116	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
117	#381	—	2	4	no	—
118	#381	—	2	8	no	—
119	C₂×#95	—	2	4	no	—
120	C₂×#95	C₄×C₁₉	1	4	yes	complemented
121	#342	—	2	8	no	—
122	C₂×C₁₉	—	2	4	no	—
123	C₂×C₁₉	—	2	4	no	—
124	C₂×C₁₉	—	2	4	no	—
125	C₂×C₁₉	#1440	1	1	yes	characteristic
126	C₂×C₁₉	#1820	1	2	yes	—
127	C₂×C₁₉	#1899	1	4	yes	—
128	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
129	C₂³×C₄	—	2	4	no	—
130	C₂³×C₄	—	2	4	no	—
131	C₂³×C₄	—	2	4	no	—
132	C₂³×C₄	—	2	4	no	—
133	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
134	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
135	C₂³×C₄	D₄×C₁₉	1	4	yes	—
136	C₂×C₂²⋊C₄	—	2	4	no	—
137	C₂×C₂²⋊C₄	—	2	4	no	—
138	C₂×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₂²⋊C₄	—	2	4	no	—
140	C₂×C₂²⋊C₄	—	2	4	no	—
141	C₂×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₂²⋊C₄	—	2	2	no	—
143	C₂×C₂²⋊C₄	—	2	4	no	—
144	C₂×C₂²⋊C₄	—	2	4	no	—
145	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
146	#95	—	2	16	no	—
147	#95	—	2	8	no	—
148	C₁₉	#11197	1	1	yes	characteristic, direct product factor, Sylow
149	C₂⁴	—	4	4	no	—
150	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
151	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
152	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
153	C₂⁴	#41×C₁₉	1	4	yes	—
154	C₂⁴	#41×C₁₉	1	4	yes	—
155	C₂²×C₄	—	2	4	no	—
156	C₂²×C₄	—	2	8	no	—
157	C₂²×C₄	—	2	4	no	—
158	C₂²×C₄	—	2	8	no	—
159	C₂²×C₄	—	2	8	no	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	4	no	—
162	C₂²×C₄	—	2	8	no	—
163	C₂²×C₄	—	2	8	no	—
164	C₂²×C₄	—	4	4	no	—
165	C₂²×C₄	—	4	4	no	—
166	C₂²×C₄	—	4	4	no	—
167	C₂²×C₄	—	4	4	no	—
168	C₂²×C₄	—	4	16	no	—
169	C₂²×C₄	—	4	4	no	—
170	C₂²×C₄	—	4	4	no	—
171	C₂²×C₄	—	4	8	no	—
172	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
173	C₂²⋊C₄	—	2	8	no	—
174	C₂²⋊C₄	—	2	8	no	—
175	C₂²⋊C₄	—	4	2	no	—
176	C₂²⋊C₄	—	4	4	no	—
177	C₂²⋊C₄	—	4	4	no	—
178	C₂²⋊C₄	—	4	2	no	—
179	C₂²⋊C₄	—	4	4	no	—
180	C₂³	—	2	4	no	—
181	C₂³	—	2	8	no	—
182	C₂³	—	4	8	no	—
183	C₂³	—	4	8	no	—
184	C₂³	—	4	8	no	—
185	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
186	C₂³	C₁₉×#117	1	2	yes	—
187	C₂³	C₄×D₄×C₁₉	1	4	yes	—
188	C₂³	C₁₉×#120	1	2	yes	—
189	C₂³	C₁₉×#121	1	4	yes	—
190	C₂³	C₁₉×#121	1	4	yes	—
191	C₂³	C₁₉×#123	1	4	yes	—
192	C₂³	C₁₉×#123	1	2	yes	—
193	C₂³	C₁₉×#123	1	4	yes	—
194	C₂³	C₁₉×#124	1	4	yes	—
195	C₂³	C₁₉×#126	1	4	yes	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	8	no	—
198	C₂×C₄	—	4	8	no	—
199	C₂×C₄	—	4	8	no	—
200	C₂×C₄	—	4	8	no	—
201	C₂×C₄	—	4	16	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	4	8	no	—
204	C₂×C₄	—	4	8	no	—
205	C₂×C₄	—	8	8	no	—
206	C₂×C₄	—	8	8	no	—
207	C₂×C₄	—	8	8	no	—
208	C₂²	—	2	4	no	—
209	C₂²	—	2	8	no	—
210	C₂²	—	2	8	no	—
211	C₂²	—	2	4	no	—
212	C₂²	—	2	8	no	—
213	C₂²	—	2	4	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	4	4	no	—
216	C₂²	—	4	4	no	—
217	C₂²	—	4	4	no	—
218	C₂²	C₁₉×#381	1	1	yes	characteristic
219	C₂²	C₁₉×#386	1	2	yes	—
220	C₂²	C₁₉×#388	1	4	yes	—
221	C₂²	C₁₉×#394	1	4	yes	—
222	C₂²	C₁₉×#397	1	4	yes	—
223	C₂²	C₁₉×#410	1	4	yes	—
224	C₄	—	4	4	no	—
225	C₄	—	8	8	no	—
226	C₄	—	8	4	no	—
227	C₂	—	2	4	no	—
228	C₂	—	2	4	no	—
229	C₂	—	2	4	no	—
230	C₂	C₁₉×#1440	1	1	yes	characteristic
231	C₂	C₁₉×#1820	1	2	yes	—
232	C₂	C₁₉×#1899	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#381

C₂

yes

maximal

C₂×C₁₉×#381

C₂

yes

maximal, characteristic

C₂×C₁₉×#342

C₂

yes

maximal

C₂⁴×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#381

—

C₁₉×#381

—

C₂×C₁₉×#95

—

C₂×C₁₉×#95

C₄

yes

complemented

C₁₉×#342

—

C₂⁵×C₁₉

C₂³

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

#41

yes

—

C₂⁴×C₁₉

#41

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#11197

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

C₄×D₄

yes

—

C₂³×C₁₉

#120

yes

—

C₂³×C₁₉

#121

yes

—

C₂³×C₁₉

#121

yes

—

C₂³×C₁₉

#123

yes

—

C₂³×C₁₉

#123

yes

—

C₂³×C₁₉

#123

yes

—

C₂³×C₁₉

#124

yes

—

C₂³×C₁₉

#126

yes

—

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×#381

C₂×C₁₉

yes

—

C₂×#381

C₂×C₁₉

yes

characteristic

C₂×#342

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#381

yes

characteristic

106

C₂²×C₁₉

#386

yes

—

107

C₂²×C₁₉

#388

yes

—

108

C₂²×C₁₉

#394

yes

—

109

C₂²×C₁₉

#397

yes

—

110

C₂²×C₁₉

#410

yes

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₂⁴×C₄

C₂²×C₁₉

yes

characteristic

115

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

—

116

C₂²×C₂²⋊C₄

C₂²×C₁₉

yes

—

117

#381

—

118

#381

—

119

C₂×#95

—

120

C₂×#95

C₄×C₁₉

yes

complemented

121

#342

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

—

125

C₂×C₁₉

#1440

yes

characteristic

126

C₂×C₁₉

#1820

yes

—

127

C₂×C₁₉

#1899

yes

—

128

C₂⁵

C₂³×C₁₉

yes

characteristic

129

C₂³×C₄

—

130

C₂³×C₄

—

131

C₂³×C₄

—

132

C₂³×C₄

—

133

C₂³×C₄

C₂×C₄×C₁₉

yes

—

134

C₂³×C₄

C₂×C₄×C₁₉

yes

—

135

C₂³×C₄

D₄×C₁₉

yes

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₂²⋊C₄

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

—

141

C₂×C₂²⋊C₄

—

142

C₂×C₂²⋊C₄

—

143

C₂×C₂²⋊C₄

—

144

C₂×C₂²⋊C₄

—

145

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

146

#95

—

147

#95

—

148

C₁₉

#11197

yes

characteristic, direct product factor, Sylow

149

C₂⁴

—

150

C₂⁴

C₂²×C₄×C₁₉

yes

characteristic

151

C₂⁴

C₂×D₄×C₁₉

yes

—

152

C₂⁴

C₂×D₄×C₁₉

yes

—

153

C₂⁴

#41×C₁₉

yes

—

154

C₂⁴

#41×C₁₉

yes

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₂²⋊C₄

—

179

C₂²⋊C₄

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

186

C₂³

C₁₉×#117

yes

—

187

C₂³

C₄×D₄×C₁₉

yes

—

188

C₂³

C₁₉×#120

yes

—

189

C₂³

C₁₉×#121

yes

—

190

C₂³

C₁₉×#121

yes

—

191

C₂³

C₁₉×#123

yes

—

192

C₂³

C₁₉×#123

yes

—

193

C₂³

C₁₉×#123

yes

—

194

C₂³

C₁₉×#124

yes

—

195

C₂³

C₁₉×#126

yes

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

C₁₉×#381

yes

characteristic

219

C₂²

C₁₉×#386

yes

—

220

C₂²

C₁₉×#388

yes

—

221

C₂²

C₁₉×#394

yes

—

222

C₂²

C₁₉×#397

yes

—

223

C₂²

C₁₉×#410

yes

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₂

—

228

C₂

—

229

C₂

—

230

C₂

C₁₉×#1440

yes

characteristic

231

C₂

C₁₉×#1820

yes

—

232

C₂

C₁₉×#1899

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₁₉

Frattini, cosocle

C₂⁵

C₂³×C₁₉

prime radical

C₂⁵×C₁₉

C₂³

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
10. C₂×C₁₉×#95	C₄	semidirect
63. #11197	C₁₉	direct (N × H)
120. C₂×#95	C₄×C₁₉	semidirect
148. C₁₉	#11197	direct (N × H)

H ≅ G/N

type

10. C₂×C₁₉×#95

C₄

semidirect

63. #11197

C₁₉

direct (N × H)

120. C₂×#95

C₄×C₁₉

semidirect

148. C₁₉

#11197

direct (N × H)

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

subgroup	index
C₂×C₁₉×#381	2
C₂×C₁₉×#342	2
#11197	19

subgroup

index

C₂×C₁₉×#381

C₂×C₁₉×#342

#11197

Subgroups — C₁₉×#11197 #18017156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11197 #18017156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11197 #18017156