Subgroups — C₁₉×#9522 #18015481

Order 4864.

472 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×#3092	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2976	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1821	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1513	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1305	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	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#484	C₄	1	2	yes	complemented
11	C₁₉×#483	—	2	1	no	—
12	C₁₉×#481	C₄	1	2	yes	complemented
13	C₁₉×#480	—	2	1	no	—
14	C₁₉×#436	—	2	1	no	—
15	C₁₉×#435	—	2	1	no	—
16	C₁₉×#435	—	2	1	no	—
17	C₈×D₄×C₁₉	—	2	1	no	—
18	C₁₉×#433	—	2	1	no	—
19	C₁₉×#428	—	2	1	no	—
20	C₁₉×#417	—	2	1	no	—
21	C₁₉×#408	—	2	1	no	—
22	C₁₉×#407	C₂²	1	1	yes	characteristic
23	C₁₉×#407	C₂²	1	1	yes	characteristic
24	C₁₉×#407	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#380	C₂²	1	1	yes	characteristic
27	C₁₉×#343	—	2	1	no	—
28	C₁₉×#343	—	2	1	no	—
29	C₁₉×#340	—	2	1	no	—
30	C₁₉×#340	—	2	1	no	—
31	C₁₉×#328	—	2	1	no	—
32	C₁₉×#327	—	2	1	no	—
33	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	1	no	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×#123	—	2	1	no	—
45	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
46	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
47	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
48	C₁₉×#121	D₄	1	1	yes	characteristic
49	C₁₉×#120	—	2	1	no	—
50	C₄×D₄×C₁₉	—	2	1	no	—
51	C₄×D₄×C₁₉	—	2	1	no	—
52	C₁₉×#117	D₄	1	1	yes	characteristic
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	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₁₉×#107	—	2	2	no	—
62	C₁₉×#106	—	2	2	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×#103	—	2	2	no	—
66	C₁₉×#102	—	2	2	no	—
67	C₁₉×C₂²⋊C₈	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	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	—	2	1	no	—
76	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₉×#97	—	2	1	no	—
78	C₄×C₈×C₁₉	—	2	1	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₂⁴×C₁₉	#41	1	1	yes	characteristic
81	#41×C₁₉	—	4	1	no	—
82	#41×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	2	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	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	8	1	no	—
96	C₂²×C₄×C₁₉	—	8	1	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	8	1	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	2	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	8	1	no	—
119	C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	4	1	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂²⋊C₄×C₁₉	—	2	1	no	—
132	C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂²⋊C₄×C₁₉	—	8	1	no	—
135	C₄²×C₁₉	—	2	1	no	—
136	#9522	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	—	2	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂³×C₁₉	#121	1	1	yes	characteristic
144	C₂³×C₁₉	#123	1	1	yes	characteristic
145	Q₈×C₁₉	—	4	1	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	4	1	no	—
148	D₄×C₁₉	—	4	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	8	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	—	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	2	no	—
166	C₂×C₄×C₁₉	—	8	2	no	—
167	C₂×C₄×C₁₉	—	8	1	no	—
168	C₂×C₄×C₁₉	—	8	1	no	—
169	C₂×C₄×C₁₉	—	8	2	no	—
170	C₂×C₄×C₁₉	—	8	1	no	—
171	C₂×C₄×C₁₉	—	8	1	no	—
172	C₂×C₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	1	no	—
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	1	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₈×C₁₉	—	8	1	no	—
183	#3092	C₂×C₁₉	1	1	yes	characteristic
184	#2976	C₂×C₁₉	1	1	yes	characteristic
185	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#1821	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#1513	C₂×C₁₉	1	1	yes	characteristic
188	#1305	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#1293	C₂×C₁₉	1	1	yes	characteristic, complemented
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	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	4	1	no	—
201	C₂²×C₁₉	—	4	1	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	#386	1	1	yes	characteristic
204	C₂²×C₁₉	#471	1	1	yes	characteristic
205	C₂²×C₁₉	#472	1	1	yes	characteristic
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	—	16	1	no	—
214	C₄×C₁₉	#458	1	1	yes	characteristic
215	C₄×C₁₉	#458	1	1	yes	characteristic
216	#525	C₂²×C₁₉	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
218	#484	C₄×C₁₉	1	2	yes	complemented
219	#483	—	2	1	no	—
220	#481	C₄×C₁₉	1	2	yes	complemented
221	#480	—	2	1	no	—
222	#436	—	2	1	no	—
223	#435	—	2	1	no	—
224	#435	—	2	1	no	—
225	C₈×D₄	—	2	1	no	—
226	#433	—	2	1	no	—
227	#428	—	2	1	no	—
228	#417	—	2	1	no	—
229	#408	—	2	1	no	—
230	#407	C₂²×C₁₉	1	1	yes	characteristic
231	#407	C₂²×C₁₉	1	1	yes	characteristic
232	#407	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
234	#380	C₂²×C₁₉	1	1	yes	characteristic
235	#343	—	2	1	no	—
236	#343	—	2	1	no	—
237	#340	—	2	1	no	—
238	#340	—	2	1	no	—
239	#328	—	2	1	no	—
240	#327	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	4	1	no	—
244	C₂×C₁₉	—	4	1	no	—
245	C₂×C₁₉	—	8	1	no	—
246	C₂×C₁₉	#1890	1	1	yes	characteristic
247	C₂×C₁₉	#1902	1	1	yes	characteristic
248	C₂×C₁₉	#1907	1	1	yes	characteristic
249	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
256	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
259	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
260	#123	—	2	1	no	—
261	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
263	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
264	#121	D₄×C₁₉	1	1	yes	characteristic
265	#120	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	#117	D₄×C₁₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	#107	—	2	2	no	—
278	#106	—	2	2	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	#103	—	2	2	no	—
282	#102	—	2	2	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	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	C₂×C₄×C₁₉	1	2	yes	—
293	#97	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	#95	—	2	1	no	—
296	C₁₉	#9522	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁴	#41×C₁₉	1	1	yes	characteristic
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	8	1	no	—
313	C₂²×C₄	—	8	1	no	—
314	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
320	M₁₆	—	4	1	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	8	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	8	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	8	1	no	—
352	C₄²	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
359	C₂³	C₁₉×#121	1	1	yes	characteristic
360	C₂³	C₁₉×#123	1	1	yes	characteristic
361	Q₈	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	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	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	8	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	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	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	C₁₉×#386	1	1	yes	characteristic
413	C₂²	C₁₉×#471	1	1	yes	characteristic
414	C₂²	C₁₉×#472	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	16	1	no	—
423	C₄	C₁₉×#458	1	1	yes	characteristic
424	C₄	C₁₉×#458	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	4	1	no	—
428	C₂	—	4	1	no	—
429	C₂	—	8	1	no	—
430	C₂	C₁₉×#1890	1	1	yes	characteristic
431	C₂	C₁₉×#1902	1	1	yes	characteristic
432	C₂	C₁₉×#1907	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
3. C₁₉×#1823	C₂	semidirect
4. C₁₉×#1821	C₂	semidirect
6. C₁₉×#1305	C₂	semidirect
7. C₁₉×#1293	C₂	semidirect
10. C₁₉×#484	C₄	semidirect
12. C₁₉×#481	C₄	semidirect
136. #9522	C₁₉	direct (N × H)
185. #1823	C₂×C₁₉	semidirect
186. #1821	C₂×C₁₉	semidirect
188. #1305	C₂×C₁₉	semidirect
189. #1293	C₂×C₁₉	semidirect
218. #484	C₄×C₁₉	semidirect
220. #481	C₄×C₁₉	semidirect
296. C₁₉	#9522	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×#3092	2
C₁₉×#2976	2
C₁₉×#1823	2
C₁₉×#1821	2
C₁₉×#1513	2
C₁₉×#1305	2
C₁₉×#1293	2
#9522	19

Subgroups — C19×#9522 #18015481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9522 #18015481