Subgroups — C₁₉×#9331 #18015290

Order 4864.

438 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3196	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2978	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1516	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1511	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1472	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1306	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1293	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×#484	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#481	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#470	—	2	1	no	—
14	C₁₉×#468	—	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×#436	—	2	1	no	—
19	C₁₉×#436	—	2	1	no	—
20	C₁₉×#435	—	2	1	no	—
21	C₁₉×#435	—	2	1	no	—
22	C₁₉×#433	—	2	1	no	—
23	C₁₉×#408	—	2	1	no	—
24	C₁₉×#407	C₂²	1	1	yes	characteristic
25	C₁₉×#407	C₂²	1	1	yes	characteristic
26	C₁₉×#407	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#381	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	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₁₉	—	2	1	no	—
39	C₂×SD₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₁₉×#123	—	2	1	no	—
47	C₁₉×C₂²⋊Q₈	—	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	C₂×C₄	1	1	yes	characteristic
52	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
53	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
54	C₁₉×#121	D₄	1	1	yes	characteristic
55	C₁₉×#120	—	2	1	no	—
56	C₄×D₄×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	1	no	—
58	C₁₉×#117	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	8	1	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	Q₁₆×C₁₉	—	8	1	no	—
110	SD₁₆×C₁₉	—	8	1	no	—
111	M₁₆×C₁₉	—	8	1	no	—
112	M₁₆×C₁₉	—	8	1	no	—
113	M₁₆×C₁₉	—	8	1	no	—
114	M₁₆×C₁₉	—	8	1	no	—
115	C₂×C₈×C₁₉	—	2	1	no	—
116	C₂×C₈×C₁₉	—	2	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	—	4	1	no	—
122	C₂×C₈×C₁₉	—	8	1	no	—
123	C₂×C₈×C₁₉	—	8	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂²⋊C₄×C₁₉	—	2	1	no	—
135	C₂²⋊C₄×C₁₉	—	2	1	no	—
136	C₂²⋊C₄×C₁₉	—	2	1	no	—
137	C₂²⋊C₄×C₁₉	—	4	1	no	—
138	C₂²⋊C₄×C₁₉	—	4	1	no	—
139	C₂²⋊C₄×C₁₉	—	8	1	no	—
140	C₄²×C₁₉	—	2	1	no	—
141	#9331	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₁₉	#121	1	1	yes	characteristic
148	C₂³×C₁₉	#123	1	1	yes	characteristic
149	Q₈×C₁₉	—	4	1	no	—
150	Q₈×C₁₉	—	4	1	no	—
151	Q₈×C₁₉	—	4	1	no	—
152	Q₈×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	D₄×C₁₉	—	8	1	no	—
155	D₄×C₁₉	—	8	1	no	—
156	D₄×C₁₉	—	8	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	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	8	1	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	4	1	no	—
183	C₈×C₁₉	—	4	1	no	—
184	C₈×C₁₉	—	4	1	no	—
185	C₈×C₁₉	—	8	1	no	—
186	#3196	C₂×C₁₉	1	1	yes	characteristic
187	#2978	C₂×C₁₉	1	1	yes	characteristic
188	#1516	C₂×C₁₉	1	1	yes	characteristic
189	#1511	C₂×C₁₉	1	1	yes	characteristic, complemented
190	#1472	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1306	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#1293	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	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	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	8	2	no	—
206	C₂²×C₁₉	#386	1	1	yes	characteristic
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	4	1	no	—
213	C₄×C₁₉	—	4	1	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	—	16	1	no	—
217	#525	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
219	#485	—	2	1	no	—
220	#484	C₄×C₁₉	1	1	yes	characteristic, complemented
221	#481	C₄×C₁₉	1	1	yes	characteristic, complemented
222	#470	—	2	1	no	—
223	#468	—	2	1	no	—
224	#452	—	2	1	no	—
225	#451	C₄×C₁₉	1	1	yes	characteristic, complemented
226	#448	C₄×C₁₉	1	1	yes	characteristic, complemented
227	#436	—	2	1	no	—
228	#436	—	2	1	no	—
229	#435	—	2	1	no	—
230	#435	—	2	1	no	—
231	#433	—	2	1	no	—
232	#408	—	2	1	no	—
233	#407	C₂²×C₁₉	1	1	yes	characteristic
234	#407	C₂²×C₁₉	1	1	yes	characteristic
235	#407	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
237	#381	C₂²×C₁₉	1	1	yes	characteristic
238	#328	—	2	1	no	—
239	#328	—	2	1	no	—
240	#328	—	2	1	no	—
241	#327	—	2	1	no	—
242	#324	—	2	1	no	—
243	#324	—	2	1	no	—
244	C₂×C₁₉	—	4	1	no	—
245	C₂×C₁₉	—	4	1	no	—
246	C₂×C₁₉	—	4	1	no	—
247	C₂×C₁₉	—	8	1	no	—
248	C₂×C₁₉	#1881	1	1	yes	characteristic
249	C₂×C₁₉	#1902	1	1	yes	characteristic
250	C₂×C₁₉	#1913	1	1	yes	characteristic
251	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
252	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	#123	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
268	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
269	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
270	#121	D₄×C₁₉	1	1	yes	characteristic
271	#120	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	#117	D₄×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	#107	—	2	1	no	—
280	#106	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#103	—	2	1	no	—
286	#102	—	2	1	no	—
287	C₂²⋊C₈	—	2	1	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
296	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
297	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
298	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
299	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
300	#97	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	C₁₉	#9331	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	#41×C₁₉	1	1	yes	characteristic
306	#41	—	8	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	8	1	no	—
310	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	8	1	no	—
320	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
326	Q₁₆	—	8	1	no	—
327	SD₁₆	—	8	1	no	—
328	M₁₆	—	8	1	no	—
329	M₁₆	—	8	1	no	—
330	M₁₆	—	8	1	no	—
331	M₁₆	—	8	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	8	1	no	—
340	C₂×C₈	—	8	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
348	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	8	1	no	—
357	C₄²	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
363	C₂³	C₁₉×#121	1	1	yes	characteristic
364	C₂³	C₁₉×#123	1	1	yes	characteristic
365	Q₈	—	4	1	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	8	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	8	1	no	—
371	D₄	—	8	1	no	—
372	D₄	—	8	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
394	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	8	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	C₁₉×#386	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	1	no	—
425	C₄	—	16	1	no	—
426	C₂	—	4	1	no	—
427	C₂	—	4	1	no	—
428	C₂	—	4	1	no	—
429	C₂	—	8	1	no	—
430	C₂	C₁₉×#1881	1	1	yes	characteristic
431	C₂	C₁₉×#1902	1	1	yes	characteristic
432	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. C₁₉×#1511	C₂	semidirect
5. C₁₉×#1472	C₂	semidirect
6. C₁₉×#1306	C₂	semidirect
7. C₁₉×#1293	C₂	semidirect
11. C₁₉×#484	C₄	semidirect
12. C₁₉×#481	C₄	semidirect
16. C₁₉×#451	C₄	semidirect
17. C₁₉×#448	C₄	semidirect
141. #9331	C₁₉	direct (N × H)
189. #1511	C₂×C₁₉	semidirect
190. #1472	C₂×C₁₉	semidirect
191. #1306	C₂×C₁₉	semidirect
192. #1293	C₂×C₁₉	semidirect
220. #484	C₄×C₁₉	semidirect
221. #481	C₄×C₁₉	semidirect
225. #451	C₄×C₁₉	semidirect
226. #448	C₄×C₁₉	semidirect
304. C₁₉	#9331	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×#3196	2
C₁₉×#2978	2
C₁₉×#1516	2
C₁₉×#1511	2
C₁₉×#1472	2
C₁₉×#1306	2
C₁₉×#1293	2
#9331	19

Subgroups — C19×#9331 #18015290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9331 #18015290