Subgroups — C₁₉×#9651 #18015610

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#388	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#324	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#323	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	—	2	1	no	—
15	C₁₉×#388	—	2	1	no	—
16	C₁₉×#388	—	2	1	no	—
17	C₁₉×#388	—	2	1	no	—
18	C₁₉×#388	—	2	1	no	—
19	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
20	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#324	—	2	4	no	—
24	C₁₉×#323	—	2	4	no	—
25	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	C₈	1	4	yes	complemented
49	C₂×C₄²×C₁₉	—	4	2	no	—
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
54	C₁₉×C₄⋊C₈	—	4	2	no	—
55	C₁₉×C₂²⋊C₈	—	2	2	no	—
56	C₁₉×C₂²⋊C₈	—	2	2	no	—
57	C₁₉×C₂²⋊C₈	—	2	2	no	—
58	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
59	C₄×C₈×C₁₉	—	4	2	no	—
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉×#95	—	2	1	no	—
64	C₂⁴×C₁₉	—	2	1	no	—
65	C₂⁴×C₁₉	—	2	1	no	—
66	C₂⁴×C₁₉	—	2	2	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂⁴×C₁₉	—	4	1	no	—
69	C₂⁴×C₁₉	—	4	1	no	—
70	C₂⁴×C₁₉	—	4	1	no	—
71	C₂⁴×C₁₉	—	4	1	no	—
72	C₂⁴×C₁₉	C₂×C₈	1	2	yes	—
73	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
99	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	#41	1	2	yes	—
104	C₂×C₈×C₁₉	—	2	4	no	—
105	C₂×C₈×C₁₉	—	4	2	no	—
106	C₂×C₈×C₁₉	—	4	2	no	—
107	C₂×C₈×C₁₉	—	4	2	no	—
108	C₂×C₈×C₁₉	—	4	2	no	—
109	C₂×C₈×C₁₉	—	4	2	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	—	4	1	no	—
124	#9651	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	2	1	no	—
128	C₂³×C₁₉	—	2	1	no	—
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	8	2	no	—
143	C₂³×C₁₉	—	8	2	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	—	8	2	no	—
146	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₉	C₄×D₄	1	2	yes	—
148	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
149	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
150	C₂³×C₁₉	#131	1	2	yes	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	8	2	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
183	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
184	C₂×C₄×C₁₉	#99	1	2	yes	—
185	C₂×C₄×C₁₉	#121	1	2	yes	—
186	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
188	C₈×C₁₉	—	4	4	no	—
189	C₈×C₁₉	—	8	2	no	—
190	C₂×#388	C₂×C₁₉	1	1	yes	characteristic
191	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂×#324	C₂×C₁₉	1	2	yes	complemented
194	C₂×#323	C₂×C₁₉	1	2	yes	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	8	4	no	—
207	C₂²×C₁₉	—	8	4	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	#390	1	1	yes	characteristic
213	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
214	C₂²×C₁₉	#408	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
216	C₂²×C₁₉	#410	1	1	yes	characteristic
217	C₂²×C₁₉	#413	1	1	yes	characteristic
218	C₂²×C₁₉	#413	1	1	yes	characteristic
219	C₂²×C₁₉	C₈×D₄	1	2	yes	—
220	C₂²×C₁₉	#436	1	2	yes	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	2	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	8	1	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	2	1	no	—
237	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
239	C₂×C₄×C₈	—	2	1	no	—
240	#388	—	2	1	no	—
241	#388	—	2	1	no	—
242	#388	—	2	1	no	—
243	#388	—	2	1	no	—
244	C₂×#95	C₄×C₁₉	1	1	yes	characteristic
245	C₂×#95	C₄×C₁₉	1	1	yes	characteristic
246	#336	—	2	1	no	—
247	#336	—	2	1	no	—
248	#324	—	2	4	no	—
249	#323	—	2	4	no	—
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	8	2	no	—
253	C₂×C₁₉	#1458	1	1	yes	characteristic
254	C₂×C₁₉	#1459	1	1	yes	characteristic
255	C₂×C₁₉	#1468	1	1	yes	characteristic
256	C₂×C₁₉	#1473	1	1	yes	characteristic
257	C₂×C₁₉	#1954	1	1	yes	characteristic
258	C₂×C₁₉	#1964	1	1	yes	characteristic
259	C₂×C₁₉	#1967	1	1	yes	characteristic
260	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
261	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
263	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	4	2	no	—
283	C₂×C₂²⋊C₄	C₈×C₁₉	1	4	yes	complemented
284	C₂×C₄²	—	4	2	no	—
285	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
289	C₄⋊C₈	—	4	2	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
294	C₄×C₈	—	4	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	1	no	—
297	#95	—	2	1	no	—
298	#95	—	2	1	no	—
299	C₁₉	#9651	1	1	yes	characteristic, direct product factor, Sylow
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	2	1	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	4	1	no	—
305	C₂⁴	—	4	1	no	—
306	C₂⁴	—	4	1	no	—
307	C₂⁴	—	4	1	no	—
308	C₂⁴	C₂×C₈×C₁₉	1	2	yes	—
309	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
335	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
339	C₂²×C₄	#41×C₁₉	1	2	yes	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	4	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂³	C₄×D₄×C₁₉	1	2	yes	—
383	C₂³	C₂²×C₈×C₁₉	1	1	yes	characteristic
384	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
385	C₂³	C₁₉×#131	1	2	yes	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
418	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
419	C₂×C₄	C₁₉×#99	1	2	yes	—
420	C₂×C₄	C₁₉×#121	1	2	yes	—
421	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
422	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
423	C₈	—	4	4	no	—
424	C₈	—	8	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	1	no	—
442	C₂²	C₁₉×#390	1	1	yes	characteristic
443	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
444	C₂²	C₁₉×#408	1	1	yes	characteristic
445	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
446	C₂²	C₁₉×#410	1	1	yes	characteristic
447	C₂²	C₁₉×#413	1	1	yes	characteristic
448	C₂²	C₁₉×#413	1	1	yes	characteristic
449	C₂²	C₈×D₄×C₁₉	1	2	yes	—
450	C₂²	C₁₉×#436	1	2	yes	—
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₂	—	2	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	8	2	no	—
464	C₂	C₁₉×#1458	1	1	yes	characteristic
465	C₂	C₁₉×#1459	1	1	yes	characteristic
466	C₂	C₁₉×#1468	1	1	yes	characteristic
467	C₂	C₁₉×#1473	1	1	yes	characteristic
468	C₂	C₁₉×#1954	1	1	yes	characteristic
469	C₂	C₁₉×#1964	1	1	yes	characteristic
470	C₂	C₁₉×#1967	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1797	C₂	semidirect
3. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
4. C₂×C₁₉×#324	C₂	semidirect
48. C₂×C₂²⋊C₄×C₁₉	C₈	semidirect
124. #9651	C₁₉	direct (N × H)
191. #1797	C₂×C₁₉	semidirect
192. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
193. C₂×#324	C₂×C₁₉	semidirect
283. C₂×C₂²⋊C₄	C₈×C₁₉	semidirect
299. C₁₉	#9651	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×#388	2
C₁₉×#1797	2
C₄×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#324	2
C₂×C₁₉×#323	2
#9651	19

Subgroups — C19×#9651 #18015610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9651 #18015610