Group #18016396 — subgroups

Subgroups — C₁₉×#10437 #18016396

Order 4864.

478 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 146 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	C₁₉×#2582	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1803	C₂	1	2	yes	maximal
4	C₂×C₁₉×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂×C₁₉×#106	—	2	2	no	—
8	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₉×#103	—	2	2	no	—
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#398	—	2	2	no	—
12	C₁₉×#391	—	2	2	no	—
13	C₁₉×#389	—	2	2	no	—
14	C₁₉×#384	C₂²	1	1	yes	characteristic
15	C₁₉×#384	C₂²	1	1	yes	characteristic
16	C₁₉×#340	—	2	2	no	—
17	C₁₉×Q₈⋊C₈	—	2	4	no	—
18	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
19	C₂²×C₈×C₁₉	—	2	1	no	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₁₉×#106	—	4	4	no	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×#103	—	4	4	no	—
38	C₄×C₈×C₁₉	—	2	1	no	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	C₁₉×#95	—	2	4	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₂×Q₈×C₁₉	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	SD₁₆	1	4	yes	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	8	2	no	—
71	C₄²×C₁₉	—	4	2	no	—
72	C₄²×C₁₉	—	4	2	no	—
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₄²×C₁₉	#41	1	2	yes	—
76	#10437	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₁₉	#120	1	1	yes	characteristic
78	Q₈×C₁₉	—	2	4	no	—
79	Q₈×C₁₉	—	2	4	no	—
80	Q₈×C₁₉	—	4	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	4	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	8	2	no	—
93	C₂×C₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	2	yes	—
96	C₂×C₄×C₁₉	#123	1	2	yes	—
97	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
99	C₂×C₄×C₁₉	#135	1	2	yes	—
100	C₂×C₄×C₁₉	#137	1	2	yes	—
101	C₂×C₄×C₁₉	#137	1	2	yes	—
102	C₈×C₁₉	—	2	4	no	—
103	C₈×C₁₉	—	8	2	no	—
104	#2582	C₂×C₁₉	1	1	yes	characteristic
105	#1844	C₂×C₁₉	1	1	yes	characteristic
106	#1803	C₂×C₁₉	1	2	yes	—
107	C₂×Q₈⋊C₈	C₂×C₁₉	1	2	yes	—
108	#1296	C₂×C₁₉	1	1	yes	characteristic
109	C₂²×C₁₉	#394	1	1	yes	characteristic
110	C₂²×C₁₉	#448	1	2	yes	—
111	C₂²×C₁₉	#452	1	2	yes	—
112	C₂²×C₁₉	#453	1	1	yes	characteristic
113	C₂²×C₁₉	#456	1	1	yes	characteristic
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	4	4	no	—
117	C₄×C₁₉	—	8	2	no	—
118	C₄×C₁₉	—	8	2	no	—
119	C₄×C₁₉	—	16	1	no	—
120	C₄×C₁₉	#465	1	2	yes	—
121	C₄×C₁₉	#470	1	2	yes	—
122	C₄×C₁₉	#483	1	2	yes	—
123	C₄×C₁₉	#485	1	2	yes	—
124	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
125	C₂×#106	—	2	2	no	—
126	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
127	C₂×#103	—	2	2	no	—
128	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
129	#398	—	2	2	no	—
130	#391	—	2	2	no	—
131	#389	—	2	2	no	—
132	#384	C₂²×C₁₉	1	1	yes	characteristic
133	#384	C₂²×C₁₉	1	1	yes	characteristic
134	#340	—	2	2	no	—
135	Q₈⋊C₈	—	2	4	no	—
136	C₂×C₁₉	#1623	1	1	yes	characteristic
137	C₂×C₁₉	#1630	1	1	yes	characteristic
138	C₂×C₁₉	#1653	1	2	yes	—
139	C₂×C₁₉	#2035	1	2	yes	—
140	C₂×C₁₉	#2039	1	1	yes	characteristic
141	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
154	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
155	C₂×C₄²	—	2	2	no	—
156	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
157	#106	—	4	4	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	#103	—	4	4	no	—
161	C₄×C₈	—	2	1	no	—
162	C₄×C₈	D₄×C₁₉	1	2	yes	—
163	#95	—	2	4	no	—
164	#95	—	2	2	no	—
165	C₁₉	#10437	1	1	yes	characteristic, direct product factor, Sylow
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	SD₁₆×C₁₉	1	4	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	4	1	no	—
176	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	8	2	no	—
195	C₄²	—	4	2	no	—
196	C₄²	—	4	2	no	—
197	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
198	C₄²	#41×C₁₉	1	1	yes	characteristic
199	C₄²	#41×C₁₉	1	2	yes	—
200	C₂³	C₁₉×#120	1	1	yes	characteristic
201	Q₈	—	2	4	no	—
202	Q₈	—	2	4	no	—
203	Q₈	—	4	2	no	—
204	Q₈	—	4	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	8	2	no	—
216	C₂×C₄	—	8	1	no	—
217	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
218	C₂×C₄	C₁₉×#121	1	2	yes	—
219	C₂×C₄	C₁₉×#123	1	2	yes	—
220	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
221	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
222	C₂×C₄	C₁₉×#135	1	2	yes	—
223	C₂×C₄	C₁₉×#137	1	2	yes	—
224	C₂×C₄	C₁₉×#137	1	2	yes	—
225	C₈	—	2	4	no	—
226	C₈	—	8	2	no	—
227	C₂²	C₁₉×#394	1	1	yes	characteristic
228	C₂²	C₁₉×#448	1	2	yes	—
229	C₂²	C₁₉×#452	1	2	yes	—
230	C₂²	C₁₉×#453	1	1	yes	characteristic
231	C₂²	C₁₉×#456	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	4	no	—
235	C₄	—	8	2	no	—
236	C₄	—	8	2	no	—
237	C₄	—	16	1	no	—
238	C₄	C₁₉×#465	1	2	yes	—
239	C₄	C₁₉×#470	1	2	yes	—
240	C₄	C₁₉×#483	1	2	yes	—
241	C₄	C₁₉×#485	1	2	yes	—
242	C₂	C₁₉×#1623	1	1	yes	characteristic
243	C₂	C₁₉×#1630	1	1	yes	characteristic
244	C₂	C₁₉×#1653	1	2	yes	—
245	C₂	C₁₉×#2035	1	2	yes	—
246	C₂	C₁₉×#2039	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2582

C₂

yes

maximal, characteristic

C₁₉×#1844

C₂

yes

maximal, characteristic

C₁₉×#1803

C₂

yes

maximal

C₂×C₁₉×Q₈⋊C₈

C₂

yes

maximal

C₁₉×#1296

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

—

C₂×C₁₉×#106

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#398

—

C₁₉×#391

—

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#340

—

C₁₉×Q₈⋊C₈

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

#10437

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#120

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

#121

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

100

C₂×C₄×C₁₉

#137

yes

—

101

C₂×C₄×C₁₉

#137

yes

—

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

#2582

C₂×C₁₉

yes

characteristic

105

#1844

C₂×C₁₉

yes

characteristic

106

#1803

C₂×C₁₉

yes

—

107

C₂×Q₈⋊C₈

C₂×C₁₉

yes

—

108

#1296

C₂×C₁₉

yes

characteristic

109

C₂²×C₁₉

#394

yes

characteristic

110

C₂²×C₁₉

#448

yes

—

111

C₂²×C₁₉

#452

yes

—

112

C₂²×C₁₉

#453

yes

characteristic

113

C₂²×C₁₉

#456

yes

characteristic

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

#465

yes

—

121

C₄×C₁₉

#470

yes

—

122

C₄×C₁₉

#483

yes

—

123

C₄×C₁₉

#485

yes

—

124

C₂×C₄×Q₈

C₂²×C₁₉

yes

—

125

C₂×#106

—

126

C₂×C₄⋊C₈

C₂²×C₁₉

yes

—

127

C₂×#103

—

128

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

129

#398

—

130

#391

—

131

#389

—

132

#384

C₂²×C₁₉

yes

characteristic

133

#384

C₂²×C₁₉

yes

characteristic

134

#340

—

135

Q₈⋊C₈

—

136

C₂×C₁₉

#1623

yes

characteristic

137

C₂×C₁₉

#1630

yes

characteristic

138

C₂×C₁₉

#1653

yes

—

139

C₂×C₁₉

#2035

yes

—

140

C₂×C₁₉

#2039

yes

characteristic

141

C₂²×Q₈

D₄×C₁₉

yes

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

154

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂³×C₁₉

yes

characteristic

157

#106

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

161

C₄×C₈

—

162

C₄×C₈

D₄×C₁₉

yes

—

163

#95

—

164

#95

—

165

C₁₉

#10437

yes

characteristic, direct product factor, Sylow

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

SD₁₆×C₁₉

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

177

C₂²×C₄

C₂×D₄×C₁₉

yes

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄²

—

196

C₄²

—

197

C₄²

C₂×D₄×C₁₉

yes

characteristic

198

C₄²

#41×C₁₉

yes

characteristic

199

C₄²

#41×C₁₉

yes

—

200

C₂³

C₁₉×#120

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

C₁₉×#121

yes

characteristic

218

C₂×C₄

C₁₉×#121

yes

—

219

C₂×C₄

C₁₉×#123

yes

—

220

C₂×C₄

C₁₉×#124

yes

characteristic

221

C₂×C₄

C₂×SD₁₆×C₁₉

yes

—

222

C₂×C₄

C₁₉×#135

yes

—

223

C₂×C₄

C₁₉×#137

yes

—

224

C₂×C₄

C₁₉×#137

yes

—

225

C₈

—

226

C₈

—

227

C₂²

C₁₉×#394

yes

characteristic

228

C₂²

C₁₉×#448

yes

—

229

C₂²

C₁₉×#452

yes

—

230

C₂²

C₁₉×#453

yes

characteristic

231

C₂²

C₁₉×#456

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

C₁₉×#465

yes

—

239

C₄

C₁₉×#470

yes

—

240

C₄

C₁₉×#483

yes

—

241

C₄

C₁₉×#485

yes

—

242

C₂

C₁₉×#1623

yes

characteristic

243

C₂

C₁₉×#1630

yes

characteristic

244

C₂

C₁₉×#1653

yes

—

245

C₂

C₁₉×#2035

yes

—

246

C₂

C₁₉×#2039

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₉

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
76. #10437	C₁₉	direct (N × H)
165. C₁₉	#10437	direct (N × H)

H ≅ G/N

type

76. #10437

C₁₉

direct (N × H)

165. C₁₉

#10437

direct (N × H)

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

subgroup	index
C₁₉×#2582	2
C₁₉×#1844	2
C₁₉×#1803	2
C₂×C₁₉×Q₈⋊C₈	2
C₁₉×#1296	2
#10437	19

subgroup

index

C₁₉×#2582

C₁₉×#1844

C₁₉×#1803

C₂×C₁₉×Q₈⋊C₈

C₁₉×#1296

#10437

Subgroups — C₁₉×#10437 #18016396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10437 #18016396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10437 #18016396