Subgroups — C₁₉×#9346 #18015305

Order 4864.

444 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3095	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1520	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1472	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1305	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1298	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₁₉×#485	—	2	1	no	—
11	C₁₉×#485	—	2	1	no	—
12	C₁₉×#484	—	2	1	no	—
13	C₁₉×#483	—	2	1	no	—
14	C₁₉×#433	—	2	2	no	—
15	C₁₉×#432	—	2	1	no	—
16	C₁₉×#431	—	2	1	no	—
17	C₁₉×#428	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#428	C₄	1	1	yes	characteristic, complemented
19	C₁₉×#424	—	2	1	no	—
20	C₁₉×#419	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#419	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#407	C₂²	1	1	yes	characteristic
23	C₁₉×#407	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#405	—	2	1	no	—
27	C₁₉×#380	C₂²	1	1	yes	characteristic
28	C₁₉×#340	—	2	1	no	—
29	C₁₉×#340	—	2	1	no	—
30	C₁₉×#328	—	2	1	no	—
31	C₁₉×#328	—	2	1	no	—
32	C₁₉×#324	—	2	2	no	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₁₉×C₂²⋊Q₈	—	2	1	no	—
41	C₁₉×C₂²⋊Q₈	—	2	1	no	—
42	C₁₉×C₂²⋊Q₈	—	2	1	no	—
43	C₁₉×C₂²⋊Q₈	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#117	D₄	1	1	yes	characteristic
49	C₁₉×#117	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄²×C₁₉	—	2	1	no	—
59	C₁₉×#107	—	2	1	no	—
60	C₁₉×#107	—	2	1	no	—
61	C₁₉×#106	—	2	1	no	—
62	C₁₉×#106	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	2	no	—
64	C₁₉×C₄⋊C₈	—	2	2	no	—
65	C₁₉×#103	—	2	1	no	—
66	C₁₉×#103	—	2	1	no	—
67	C₁₉×#103	—	2	1	no	—
68	C₁₉×#103	—	2	1	no	—
69	C₁₉×C₂²⋊C₈	—	2	1	no	—
70	C₁₉×C₂²⋊C₈	—	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	D₄	1	1	yes	characteristic
76	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
77	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
78	C₁₉×#97	—	2	2	no	—
79	C₄×C₈×C₁₉	—	2	2	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₂⁴×C₁₉	#41	1	1	yes	characteristic
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	4	1	no	—
85	C₂×Q₈×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	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	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	M₁₆×C₁₉	—	4	1	no	—
100	M₁₆×C₁₉	—	4	1	no	—
101	M₁₆×C₁₉	—	4	1	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₂×C₈×C₁₉	—	2	1	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂²⋊C₄×C₁₉	—	4	1	no	—
130	C₂²⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊C₄×C₁₉	—	8	1	no	—
132	C₄²×C₁₉	—	2	1	no	—
133	C₄²×C₁₉	—	2	1	no	—
134	C₄²×C₁₉	—	2	1	no	—
135	C₄²×C₁₉	—	2	1	no	—
136	#9346	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	2	1	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
142	C₂³×C₁₉	#121	1	1	yes	characteristic
143	C₂³×C₁₉	#123	1	1	yes	characteristic
144	Q₈×C₁₉	—	4	1	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	Q₈×C₁₉	—	8	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	1	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₈×C₁₉	—	4	1	no	—
175	C₈×C₁₉	—	4	1	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	1	no	—
178	C₈×C₁₉	—	4	1	no	—
179	C₈×C₁₉	—	8	1	no	—
180	#3095	C₂×C₁₉	1	1	yes	characteristic
181	#2924	C₂×C₁₉	1	1	yes	characteristic
182	#1825	C₂×C₁₉	1	1	yes	characteristic
183	#1520	C₂×C₁₉	1	1	yes	characteristic
184	#1472	C₂×C₁₉	1	1	yes	characteristic
185	#1305	C₂×C₁₉	1	1	yes	characteristic
186	#1298	C₂×C₁₉	1	1	yes	characteristic
187	C₂²×C₁₉	—	2	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	8	1	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	#386	1	1	yes	characteristic
198	C₂²×C₁₉	#471	1	1	yes	characteristic
199	C₂²×C₁₉	#473	1	1	yes	characteristic
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	1	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	—	8	1	no	—
209	C₄×C₁₉	—	16	1	no	—
210	C₄×C₁₉	#410	1	1	yes	characteristic
211	C₄×C₁₉	#410	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
214	#485	—	2	1	no	—
215	#485	—	2	1	no	—
216	#484	—	2	1	no	—
217	#483	—	2	1	no	—
218	#433	—	2	2	no	—
219	#432	—	2	1	no	—
220	#431	—	2	1	no	—
221	#428	C₄×C₁₉	1	1	yes	characteristic, complemented
222	#428	C₄×C₁₉	1	1	yes	characteristic, complemented
223	#424	—	2	1	no	—
224	#419	C₄×C₁₉	1	1	yes	characteristic, complemented
225	#419	C₄×C₁₉	1	1	yes	characteristic, complemented
226	#407	C₂²×C₁₉	1	1	yes	characteristic
227	#407	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
230	#405	—	2	1	no	—
231	#380	C₂²×C₁₉	1	1	yes	characteristic
232	#340	—	2	1	no	—
233	#340	—	2	1	no	—
234	#328	—	2	1	no	—
235	#328	—	2	1	no	—
236	#324	—	2	2	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	4	1	no	—
240	C₂×C₁₉	—	4	1	no	—
241	C₂×C₁₉	#1881	1	1	yes	characteristic
242	C₂×C₁₉	#1899	1	1	yes	characteristic
243	C₂×C₁₉	#1908	1	1	yes	characteristic
244	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
248	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²⋊Q₈	—	2	1	no	—
252	C₂²⋊Q₈	—	2	1	no	—
253	C₂²⋊Q₈	—	2	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
258	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
259	#117	D₄×C₁₉	1	1	yes	characteristic
260	#117	D₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	#107	—	2	1	no	—
271	#107	—	2	1	no	—
272	#106	—	2	1	no	—
273	#106	—	2	1	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	2	no	—
276	#103	—	2	1	no	—
277	#103	—	2	1	no	—
278	#103	—	2	1	no	—
279	#103	—	2	1	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
287	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
288	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
289	#97	—	2	2	no	—
290	C₄×C₈	—	2	2	no	—
291	#95	—	2	1	no	—
292	C₁₉	#9346	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	#41×C₁₉	1	1	yes	characteristic
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
311	M₁₆	—	4	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
334	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
335	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
336	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	8	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
353	C₂³	C₁₉×#121	1	1	yes	characteristic
354	C₂³	C₁₉×#123	1	1	yes	characteristic
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	8	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	—	8	1	no	—
380	C₂×C₄	—	8	1	no	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	8	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₁₉×#386	1	1	yes	characteristic
402	C₂²	C₁₉×#471	1	1	yes	characteristic
403	C₂²	C₁₉×#473	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	—	16	1	no	—
414	C₄	C₁₉×#410	1	1	yes	characteristic
415	C₄	C₁₉×#410	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	4	1	no	—
419	C₂	—	4	1	no	—
420	C₂	C₁₉×#1881	1	1	yes	characteristic
421	C₂	C₁₉×#1899	1	1	yes	characteristic
422	C₂	C₁₉×#1908	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	C₂⁴×C₁₉	#41
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
17. C₁₉×#428	C₄	semidirect
18. C₁₉×#428	C₄	semidirect
20. C₁₉×#419	C₄	semidirect
21. C₁₉×#419	C₄	semidirect
136. #9346	C₁₉	direct (N × H)
221. #428	C₄×C₁₉	semidirect
222. #428	C₄×C₁₉	semidirect
224. #419	C₄×C₁₉	semidirect
225. #419	C₄×C₁₉	semidirect
292. C₁₉	#9346	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×#3095	2
C₁₉×#2924	2
C₁₉×#1825	2
C₁₉×#1520	2
C₁₉×#1472	2
C₁₉×#1305	2
C₁₉×#1298	2
#9346	19

Subgroups — C19×#9346 #18015305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9346 #18015305