Subgroups — C₁₉×#8336 #18014295

Order 4864.

846 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1749	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1749	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#330	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#329	C₂	1	2	yes	maximal, complemented
6	C₁₉×#529	—	2	4	no	—
7	C₁₉×#529	—	2	4	no	—
8	C₂×C₁₉×#126	—	2	1	no	—
9	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#123	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#117	—	2	1	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₁₉×#97	C₂²	1	2	yes	—
22	C₂×C₁₉×#97	C₂²	1	2	yes	—
23	C₁₉×#336	—	2	1	no	—
24	C₁₉×#336	—	2	1	no	—
25	C₁₉×#330	—	2	4	no	—
26	C₁₉×#329	—	2	4	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	—	2	2	no	—
35	C₂²×C₈×C₁₉	—	2	2	no	—
36	C₁₉×#126	—	2	8	no	—
37	C₁₉×#125	—	2	2	no	—
38	C₁₉×#125	D₄	1	4	yes	—
39	C₁₉×#124	—	2	2	no	—
40	C₁₉×#124	D₄	1	4	yes	—
41	C₁₉×#123	—	2	8	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×C₂²⋊Q₈	—	2	2	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₁₉×#121	—	2	2	no	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×Q₈×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	2	no	—
50	C₄×D₄×C₁₉	—	2	2	no	—
51	C₁₉×#117	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₂²⋊C₈	—	2	4	no	—
71	C₁₉×C₂²⋊C₈	—	2	4	no	—
72	C₁₉×#97	—	2	2	no	—
73	C₁₉×#97	—	2	2	no	—
74	C₁₉×#97	—	2	2	no	—
75	C₁₉×#97	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂×D₄×C₁₉	—	2	4	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₉	—	2	4	no	—
112	C₂×C₈×C₁₉	—	2	4	no	—
113	C₂×C₈×C₁₉	—	4	2	no	—
114	C₂×C₈×C₁₉	—	4	2	no	—
115	C₂×C₈×C₁₉	—	4	2	no	—
116	C₂×C₈×C₁₉	—	4	2	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	4	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
125	C₂²⋊C₄×C₁₉	—	2	4	no	—
126	C₂²⋊C₄×C₁₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₉	—	2	4	no	—
128	C₂²⋊C₄×C₁₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₉	—	2	4	no	—
130	C₄²×C₁₉	—	2	4	no	—
131	C₄²×C₁₉	—	2	1	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	C₂×D₄	1	2	yes	—
136	C₄²×C₁₉	C₂×D₄	1	2	yes	—
137	#8336	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	#104	1	2	yes	—
152	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	D₄×C₁₉	—	4	2	no	—
156	D₄×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	8	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	1	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	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	8	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	#104	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#120	1	2	yes	—
190	C₂×C₄×C₁₉	#120	1	2	yes	—
191	C₈×C₁₉	—	4	4	no	—
192	C₈×C₁₉	—	4	4	no	—
193	C₂×#529	C₂×C₁₉	1	1	yes	characteristic
194	#1749	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1749	C₂×C₁₉	1	1	yes	characteristic, complemented
196	C₂×#330	C₂×C₁₉	1	2	yes	complemented
197	C₂×#329	C₂×C₁₉	1	2	yes	complemented
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	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	#379	1	1	yes	characteristic
213	C₂²×C₁₉	#413	1	1	yes	characteristic
214	C₂²×C₁₉	#413	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
217	C₂²×C₁₉	#421	1	1	yes	characteristic
218	C₂²×C₁₉	#421	1	1	yes	characteristic
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	2	no	—
229	#529	—	2	4	no	—
230	#529	—	2	4	no	—
231	C₂×#126	—	2	1	no	—
232	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#123	—	2	1	no	—
235	C₂×C₂²⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
236	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
238	C₂×C₄×D₄	—	2	1	no	—
239	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
240	C₂×#117	—	2	1	no	—
241	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	2	1	no	—
243	C₂×C₂²⋊C₈	—	2	1	no	—
244	C₂×#97	C₂²×C₁₉	1	2	yes	—
245	C₂×#97	C₂²×C₁₉	1	2	yes	—
246	#336	—	2	1	no	—
247	#336	—	2	1	no	—
248	#330	—	2	4	no	—
249	#329	—	2	4	no	—
250	C₂×C₁₉	—	4	2	no	—
251	C₂×C₁₉	—	8	2	no	—
252	C₂×C₁₉	#1524	1	1	yes	characteristic
253	C₂×C₁₉	#1529	1	1	yes	characteristic
254	C₂×C₁₉	#1532	1	1	yes	characteristic
255	C₂×C₁₉	#1535	1	1	yes	characteristic
256	C₂×C₁₉	#1785	1	1	yes	characteristic
257	C₂×C₁₉	#1789	1	1	yes	characteristic
258	C₂×C₁₉	#1789	1	1	yes	characteristic
259	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	#126	—	2	8	no	—
269	#125	—	2	2	no	—
270	#125	D₄×C₁₉	1	4	yes	—
271	#124	—	2	2	no	—
272	#124	D₄×C₁₉	1	4	yes	—
273	#123	—	2	8	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	#121	—	2	2	no	—
277	#121	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×D₄	—	2	8	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	#117	—	2	8	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
302	C₂²⋊C₈	—	2	4	no	—
303	C₂²⋊C₈	—	2	4	no	—
304	#97	—	2	2	no	—
305	#97	—	2	2	no	—
306	#97	—	2	2	no	—
307	#97	—	2	2	no	—
308	C₁₉	#8336	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	—	2	1	no	—
310	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
357	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	C₂×D₄×C₁₉	1	2	yes	—
369	C₄²	C₂×D₄×C₁₉	1	2	yes	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	C₁₉×#104	1	2	yes	—
384	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	8	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	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	C₁₉×#104	1	2	yes	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#120	1	2	yes	—
422	C₂×C₄	C₁₉×#120	1	2	yes	—
423	C₈	—	4	4	no	—
424	C₈	—	4	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₁₉×#379	1	1	yes	characteristic
440	C₂²	C₁₉×#413	1	1	yes	characteristic
441	C₂²	C₁₉×#413	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
443	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
444	C₂²	C₁₉×#421	1	1	yes	characteristic
445	C₂²	C₁₉×#421	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₂	—	4	2	no	—
457	C₂	—	8	2	no	—
458	C₂	C₁₉×#1524	1	1	yes	characteristic
459	C₂	C₁₉×#1529	1	1	yes	characteristic
460	C₂	C₁₉×#1532	1	1	yes	characteristic
461	C₂	C₁₉×#1535	1	1	yes	characteristic
462	C₂	C₁₉×#1785	1	1	yes	characteristic
463	C₂	C₁₉×#1789	1	1	yes	characteristic
464	C₂	C₁₉×#1789	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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×#1749	C₂	semidirect
3. C₁₉×#1749	C₂	semidirect
4. C₂×C₁₉×#330	C₂	semidirect
5. C₂×C₁₉×#329	C₂	semidirect
137. #8336	C₁₉	direct (N × H)
194. #1749	C₂×C₁₉	semidirect
195. #1749	C₂×C₁₉	semidirect
196. C₂×#330	C₂×C₁₉	semidirect
197. C₂×#329	C₂×C₁₉	semidirect
308. C₁₉	#8336	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×#529	2
C₁₉×#1749	2
C₂×C₁₉×#330	2
C₂×C₁₉×#329	2
#8336	19

Subgroups — C19×#8336 #18014295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8336 #18014295