Subgroups — C₁₉×#9263 #18015222

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3190	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2977	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1504	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1472	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1280	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#525	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
10	C₁₉×#485	—	2	1	no	—
11	C₁₉×#483	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#480	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#467	—	2	1	no	—
14	C₁₉×#465	—	2	1	no	—
15	C₁₉×#452	—	2	1	no	—
16	C₁₉×#451	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#448	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#435	—	2	1	no	—
19	C₁₉×#435	—	2	1	no	—
20	C₈×D₄×C₁₉	—	2	1	no	—
21	C₈×D₄×C₁₉	—	2	1	no	—
22	C₁₉×#433	—	2	1	no	—
23	C₁₉×#408	—	2	1	no	—
24	C₁₉×#407	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
29	C₁₉×#328	—	2	1	no	—
30	C₁₉×#328	—	2	1	no	—
31	C₁₉×#328	—	2	1	no	—
32	C₁₉×#327	—	2	1	no	—
33	C₁₉×#324	—	2	1	no	—
34	C₁₉×#324	—	2	1	no	—
35	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×Q₁₆×C₁₉	—	2	1	no	—
40	C₂×SD₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂²×C₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₁₉×#123	—	2	1	no	—
48	C₁₉×C₂²⋊Q₈	—	2	1	no	—
49	C₁₉×C₂²⋊Q₈	—	2	1	no	—
50	C₁₉×C₂²⋊Q₈	—	2	1	no	—
51	C₁₉×C₂²⋊Q₈	—	2	1	no	—
52	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
54	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
55	C₁₉×#121	D₄	1	1	yes	characteristic
56	C₁₉×#120	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	1	no	—
58	C₄×D₄×C₁₉	—	2	1	no	—
59	C₁₉×#117	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₁₉×#107	—	2	1	no	—
64	C₁₉×#106	—	2	1	no	—
65	C₁₉×C₄⋊C₈	—	2	1	no	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×#103	—	2	1	no	—
68	C₁₉×#103	—	2	1	no	—
69	C₁₉×#103	—	2	1	no	—
70	C₁₉×#102	—	2	1	no	—
71	C₁₉×C₂²⋊C₈	—	2	1	no	—
72	C₁₉×C₂²⋊C₈	—	2	1	no	—
73	C₁₉×C₂²⋊C₈	—	2	1	no	—
74	C₁₉×C₂²⋊C₈	—	2	1	no	—
75	C₁₉×C₂²⋊C₈	—	2	1	no	—
76	C₁₉×C₂²⋊C₈	—	2	1	no	—
77	C₁₉×C₂²⋊C₈	—	2	1	no	—
78	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
81	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
84	C₁₉×#97	—	2	1	no	—
85	C₄×C₈×C₁₉	—	2	1	no	—
86	C₁₉×#95	—	2	1	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₂⁴×C₁₉	#41	1	1	yes	characteristic
89	#41×C₁₉	—	8	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×Q₈×C₁₉	—	8	1	no	—
93	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	1	no	—
97	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	8	1	no	—
105	C₂²×C₄×C₁₉	—	8	1	no	—
106	C₂²×C₄×C₁₉	—	8	1	no	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	Q₁₆×C₁₉	—	8	1	no	—
114	SD₁₆×C₁₉	—	8	1	no	—
115	M₁₆×C₁₉	—	8	1	no	—
116	M₁₆×C₁₉	—	8	1	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	1	no	—
119	C₂×C₈×C₁₉	—	2	1	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	8	1	no	—
125	C₂×C₈×C₁₉	—	8	1	no	—
126	C₂×C₈×C₁₉	—	8	1	no	—
127	C₂×C₈×C₁₉	—	8	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₁₉	—	2	1	no	—
137	C₂²⋊C₄×C₁₉	—	2	1	no	—
138	C₂²⋊C₄×C₁₉	—	2	1	no	—
139	C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₂²⋊C₄×C₁₉	—	2	1	no	—
141	C₂²⋊C₄×C₁₉	—	4	1	no	—
142	C₂²⋊C₄×C₁₉	—	4	1	no	—
143	C₄²×C₁₉	—	2	1	no	—
144	#9263	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₁₉	#121	1	1	yes	characteristic
153	C₂³×C₁₉	#123	1	1	yes	characteristic
154	Q₈×C₁₉	—	4	1	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	4	1	no	—
157	Q₈×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	4	1	no	—
159	D₄×C₁₉	—	4	1	no	—
160	D₄×C₁₉	—	4	1	no	—
161	D₄×C₁₉	—	4	1	no	—
162	D₄×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	8	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	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	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	1	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	1	no	—
183	C₂×C₄×C₁₉	—	8	1	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₈×C₁₉	—	4	1	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	—	4	1	no	—
192	C₈×C₁₉	—	4	1	no	—
193	C₈×C₁₉	—	4	1	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₈×C₁₉	—	8	1	no	—
196	#3190	C₂×C₁₉	1	1	yes	characteristic
197	#2977	C₂×C₁₉	1	1	yes	characteristic
198	#1504	C₂×C₁₉	1	1	yes	characteristic
199	C₂×#328	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#1472	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#1298	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#1280	C₂×C₁₉	1	1	yes	characteristic, complemented
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	1	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	4	1	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	#386	1	1	yes	characteristic
218	C₂²×C₁₉	#443	1	1	yes	characteristic
219	C₂²×C₁₉	#444	1	1	yes	characteristic
220	C₂²×C₁₉	#471	1	1	yes	characteristic
221	C₂²×C₁₉	#473	1	1	yes	characteristic
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	2	1	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	—	8	1	no	—
231	C₄×C₁₉	—	8	1	no	—
232	#525	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
234	#485	—	2	1	no	—
235	#483	C₄×C₁₉	1	1	yes	characteristic, complemented
236	#480	C₄×C₁₉	1	1	yes	characteristic, complemented
237	#467	—	2	1	no	—
238	#465	—	2	1	no	—
239	#452	—	2	1	no	—
240	#451	C₄×C₁₉	1	1	yes	characteristic, complemented
241	#448	C₄×C₁₉	1	1	yes	characteristic, complemented
242	#435	—	2	1	no	—
243	#435	—	2	1	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	#433	—	2	1	no	—
247	#408	—	2	1	no	—
248	#407	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
253	#328	—	2	1	no	—
254	#328	—	2	1	no	—
255	#328	—	2	1	no	—
256	#327	—	2	1	no	—
257	#324	—	2	1	no	—
258	#324	—	2	1	no	—
259	C₂×C₁₉	—	2	1	no	—
260	C₂×C₁₉	—	2	1	no	—
261	C₂×C₁₉	—	2	1	no	—
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	—	4	1	no	—
264	C₂×C₁₉	—	8	1	no	—
265	C₂×C₁₉	#1876	1	1	yes	characteristic
266	C₂×C₁₉	#1908	1	1	yes	characteristic
267	C₂×C₁₉	#1913	1	1	yes	characteristic
268	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
269	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	C₂×Q₁₆	—	2	1	no	—
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	#123	—	2	1	no	—
281	C₂²⋊Q₈	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
287	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
288	#121	D₄×C₁₉	1	1	yes	characteristic
289	#120	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	#117	D₄×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	#107	—	2	1	no	—
297	#106	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	#103	—	2	1	no	—
301	#103	—	2	1	no	—
302	#103	—	2	1	no	—
303	#102	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
312	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
313	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
314	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
315	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
316	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
317	#97	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	C₁₉	#9263	1	1	yes	characteristic, direct product factor, Sylow
322	C₂⁴	#41×C₁₉	1	1	yes	characteristic
323	#41	—	8	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	8	1	no	—
339	C₂²×C₄	—	8	1	no	—
340	C₂²×C₄	—	8	1	no	—
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	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
347	Q₁₆	—	8	1	no	—
348	SD₁₆	—	8	1	no	—
349	M₁₆	—	8	1	no	—
350	M₁₆	—	8	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	8	1	no	—
359	C₂×C₈	—	8	1	no	—
360	C₂×C₈	—	8	1	no	—
361	C₂×C₈	—	8	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₄²	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
385	C₂³	C₁₉×#121	1	1	yes	characteristic
386	C₂³	C₁₉×#123	1	1	yes	characteristic
387	Q₈	—	4	1	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	8	1	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	8	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	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	—	8	1	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	8	1	no	—
416	C₂×C₄	—	8	1	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
421	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	1	no	—
428	C₈	—	8	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	C₁₉×#386	1	1	yes	characteristic
444	C₂²	C₁₉×#443	1	1	yes	characteristic
445	C₂²	C₁₉×#444	1	1	yes	characteristic
446	C₂²	C₁₉×#471	1	1	yes	characteristic
447	C₂²	C₁₉×#473	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	4	1	no	—
463	C₂	—	8	1	no	—
464	C₂	C₁₉×#1876	1	1	yes	characteristic
465	C₂	C₁₉×#1908	1	1	yes	characteristic
466	C₂	C₁₉×#1913	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#328	C₂	semidirect
5. C₁₉×#1472	C₂	semidirect
6. C₁₉×#1298	C₂	semidirect
7. C₁₉×#1280	C₂	semidirect
11. C₁₉×#483	C₄	semidirect
12. C₁₉×#480	C₄	semidirect
16. C₁₉×#451	C₄	semidirect
17. C₁₉×#448	C₄	semidirect
144. #9263	C₁₉	direct (N × H)
199. C₂×#328	C₂×C₁₉	semidirect
200. #1472	C₂×C₁₉	semidirect
201. #1298	C₂×C₁₉	semidirect
202. #1280	C₂×C₁₉	semidirect
235. #483	C₄×C₁₉	semidirect
236. #480	C₄×C₁₉	semidirect
240. #451	C₄×C₁₉	semidirect
241. #448	C₄×C₁₉	semidirect
321. C₁₉	#9263	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3190	2
C₁₉×#2977	2
C₁₉×#1504	2
C₂×C₁₉×#328	2
C₁₉×#1472	2
C₁₉×#1298	2
C₁₉×#1280	2
#9263	19

Subgroups — C19×#9263 #18015222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9263 #18015222