Subgroups — C₁₉×#22616 #18028575

Order 4864.

766 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2347	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2346	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1944	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1921	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1918	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1776	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1752	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₁₉×#427	C₄	1	8	yes	complemented
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#97	C₂²	1	2	yes	—
23	C₁₉×#389	C₂²	1	2	yes	—
24	C₁₉×#389	C₂²	1	2	yes	—
25	C₁₉×#388	—	2	2	no	—
26	C₁₉×#388	—	2	2	no	—
27	C₁₉×#383	—	2	1	no	—
28	C₁₉×#382	—	2	1	no	—
29	C₁₉×#380	C₂²	1	1	yes	characteristic
30	C₁₉×#380	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#376	—	2	1	no	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	—	2	4	no	—
44	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×#117	—	2	2	no	—
49	C₁₉×#117	—	2	2	no	—
50	C₁₉×#117	C₂×C₄	1	4	yes	—
51	C₁₉×#117	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	2	no	—
68	C₂×C₄²×C₁₉	—	2	2	no	—
69	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#107	—	2	4	no	—
71	C₁₉×#107	C₂×C₄	1	4	yes	—
72	C₁₉×#107	C₂×C₄	1	4	yes	—
73	C₁₉×#106	C₂×C₄	1	4	yes	—
74	C₁₉×#106	C₂×C₄	1	4	yes	—
75	C₁₉×C₂²⋊C₈	—	2	2	no	—
76	C₁₉×#97	—	2	4	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₁₉×#95	D₄	1	1	yes	characteristic
84	C₁₉×#95	D₄	1	1	yes	characteristic
85	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	8	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₉	#41	1	4	yes	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	8	2	no	—
118	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²⋊C₄×C₁₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	4	2	no	—
125	C₂²⋊C₄×C₁₉	—	8	1	no	—
126	C₂²⋊C₄×C₁₉	—	8	1	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	C₄²×C₁₉	—	2	4	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	—	4	4	no	—
132	C₄²×C₁₉	—	8	2	no	—
133	#22616	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	C₄×D₄	1	2	yes	—
139	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	—	4	2	no	—
173	C₈×C₁₉	#117	1	4	yes	—
174	C₂×#427	C₂×C₁₉	1	1	yes	characteristic
175	#2347	C₂×C₁₉	1	1	yes	characteristic
176	#2346	C₂×C₁₉	1	1	yes	characteristic
177	#1944	C₂×C₁₉	1	2	yes	complemented
178	#1921	C₂×C₁₉	1	2	yes	complemented
179	#1918	C₂×C₁₉	1	2	yes	complemented
180	#1825	C₂×C₁₉	1	1	yes	characteristic
181	#1825	C₂×C₁₉	1	1	yes	characteristic
182	#1808	C₂×C₁₉	1	1	yes	characteristic
183	#1776	C₂×C₁₉	1	2	yes	complemented
184	#1752	C₂×C₁₉	1	1	yes	characteristic
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	2	no	—
190	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₁₉	#547	1	2	yes	—
192	C₂²×C₁₉	#575	1	2	yes	—
193	C₂²×C₁₉	#576	1	1	yes	characteristic
194	C₂²×C₁₉	#578	1	1	yes	characteristic
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	4	2	no	—
197	C₄×C₁₉	—	4	2	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	2	no	—
204	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
205	C₄×C₁₉	#519	1	1	yes	characteristic
206	C₄×C₁₉	#552	1	2	yes	—
207	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
209	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
210	#427	C₄×C₁₉	1	8	yes	complemented
211	C₂×#107	C₂²×C₁₉	1	2	yes	—
212	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
214	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#97	C₂²×C₁₉	1	2	yes	—
218	#389	C₂²×C₁₉	1	2	yes	—
219	#389	C₂²×C₁₉	1	2	yes	—
220	#388	—	2	2	no	—
221	#388	—	2	2	no	—
222	#383	—	2	1	no	—
223	#382	—	2	1	no	—
224	#380	C₂²×C₁₉	1	1	yes	characteristic
225	#380	C₂²×C₁₉	1	1	yes	characteristic
226	C₄×C₄⋊C₄	—	2	1	no	—
227	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	#376	—	2	1	no	—
231	#340	C₂²×C₁₉	1	2	yes	—
232	#340	C₂²×C₁₉	1	2	yes	—
233	#340	C₂²×C₁₉	1	2	yes	—
234	#340	C₂²×C₁₉	1	2	yes	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#336	C₂²×C₁₉	1	2	yes	—
237	C₂×C₁₉	—	4	2	no	—
238	C₂×C₁₉	#2344	1	1	yes	characteristic
239	C₂×C₁₉	#2943	1	1	yes	characteristic
240	C₂×C₁₉	#2951	1	1	yes	characteristic
241	C₂×C₁₉	#3347	1	2	yes	—
242	C₂×C₁₉	#3349	1	2	yes	—
243	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	—
246	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	C₂×C₄×C₁₉	1	4	yes	—
252	#117	C₂×C₄×C₁₉	1	4	yes	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
271	#107	—	2	4	no	—
272	#107	C₂×C₄×C₁₉	1	4	yes	—
273	#107	C₂×C₄×C₁₉	1	4	yes	—
274	#106	C₂×C₄×C₁₉	1	4	yes	—
275	#106	C₂×C₄×C₁₉	1	4	yes	—
276	C₂²⋊C₈	—	2	2	no	—
277	#97	—	2	4	no	—
278	#95	—	2	1	no	—
279	#95	—	2	2	no	—
280	#95	—	2	1	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	D₄×C₁₉	1	1	yes	characteristic
285	#95	D₄×C₁₉	1	1	yes	characteristic
286	C₁₉	#22616	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	#41×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
308	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
309	C₂×C₈	#41×C₁₉	1	4	yes	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	8	2	no	—
320	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
321	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
322	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
323	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	8	1	no	—
328	C₂²⋊C₄	—	8	1	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	4	no	—
334	C₄²	—	8	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	C₄×D₄×C₁₉	1	2	yes	—
340	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
368	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
370	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
371	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	C₁₉×#117	1	4	yes	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
381	C₂²	C₁₉×#547	1	2	yes	—
382	C₂²	C₁₉×#575	1	2	yes	—
383	C₂²	C₁₉×#576	1	1	yes	characteristic
384	C₂²	C₁₉×#578	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
395	C₄	C₁₉×#519	1	1	yes	characteristic
396	C₄	C₁₉×#552	1	2	yes	—
397	C₂	—	4	2	no	—
398	C₂	C₁₉×#2344	1	1	yes	characteristic
399	C₂	C₁₉×#2943	1	1	yes	characteristic
400	C₂	C₁₉×#2951	1	1	yes	characteristic
401	C₂	C₁₉×#3347	1	2	yes	—
402	C₂	C₁₉×#3349	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₁₉×#1944	C₂	semidirect
5. C₁₉×#1921	C₂	semidirect
6. C₁₉×#1918	C₂	semidirect
10. C₁₉×#1776	C₂	semidirect
15. C₁₉×#427	C₄	semidirect
133. #22616	C₁₉	direct (N × H)
177. #1944	C₂×C₁₉	semidirect
178. #1921	C₂×C₁₉	semidirect
179. #1918	C₂×C₁₉	semidirect
183. #1776	C₂×C₁₉	semidirect
210. #427	C₄×C₁₉	semidirect
286. C₁₉	#22616	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#427	2
C₁₉×#2347	2
C₁₉×#2346	2
C₁₉×#1944	2
C₁₉×#1921	2
C₁₉×#1918	2
C₁₉×#1825	2
C₁₉×#1808	2
C₁₉×#1776	2
C₁₉×#1752	2
#22616	19

Subgroups — C19×#22616 #18028575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22616 #18028575