Subgroups — C₁₉×#11306 #18017265

Order 4864.

530 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	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1738	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₁₉×#344	—	2	2	no	—
16	C₁₉×#344	—	2	2	no	—
17	C₁₉×#341	—	2	2	no	—
18	C₁₉×#341	—	2	2	no	—
19	C₁₉×#341	C₄	1	4	yes	complemented
20	C₁₉×#338	—	2	2	no	—
21	C₁₉×#336	—	2	2	no	—
22	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂×M₁₆×C₁₉	—	2	1	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
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	—	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	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	—	2	1	no	—
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
50	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
52	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₁₉	D₄	1	2	yes	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	M₁₆×C₁₉	—	2	2	no	—
89	M₁₆×C₁₉	—	2	2	no	—
90	M₁₆×C₁₉	—	2	2	no	—
91	M₁₆×C₁₉	—	2	2	no	—
92	M₁₆×C₁₉	—	2	2	no	—
93	M₁₆×C₁₉	—	2	2	no	—
94	M₁₆×C₁₉	—	2	2	no	—
95	M₁₆×C₁₉	—	2	2	no	—
96	M₁₆×C₁₉	—	4	1	no	—
97	M₁₆×C₁₉	—	4	1	no	—
98	M₁₆×C₁₉	—	4	1	no	—
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	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	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₂×C₈×C₁₉	—	4	1	no	—
126	C₂×C₈×C₁₉	—	4	1	no	—
127	C₂×C₈×C₁₉	—	4	1	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	2	2	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	#11306	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
139	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₁₉	#125	1	1	yes	characteristic
143	C₂³×C₁₉	#125	1	1	yes	characteristic
144	C₂³×C₁₉	#125	1	1	yes	characteristic
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
175	C₈×C₁₉	—	4	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	4	2	no	—
179	C₈×C₁₉	—	4	2	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
182	C₂×#344	C₂×C₁₉	1	1	yes	characteristic
183	#1738	C₂×C₁₉	1	1	yes	characteristic
184	C₂×#341	C₂×C₁₉	1	1	yes	characteristic
185	C₂×#341	C₂×C₁₉	1	1	yes	characteristic
186	C₂×#338	C₂×C₁₉	1	1	yes	characteristic
187	#1729	C₂×C₁₉	1	1	yes	characteristic
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	#387	1	1	yes	characteristic
196	C₂²×C₁₉	#387	1	1	yes	characteristic
197	C₂²×C₁₉	#387	1	1	yes	characteristic
198	C₂²×C₁₉	#396	1	1	yes	characteristic
199	C₂²×C₁₉	#400	1	1	yes	characteristic
200	C₂²×C₁₉	#400	1	1	yes	characteristic
201	C₂²×C₁₉	#400	1	1	yes	characteristic
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	#383	1	1	yes	characteristic
204	C₄×C₁₉	#388	1	1	yes	characteristic
205	C₄×C₁₉	#388	1	1	yes	characteristic
206	C₄×C₁₉	#388	1	1	yes	characteristic
207	C₄×C₁₉	#397	1	1	yes	characteristic
208	C₄×C₁₉	#397	1	1	yes	characteristic
209	C₄×C₁₉	#397	1	1	yes	characteristic
210	C₄×C₁₉	#401	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
218	#344	—	2	2	no	—
219	#344	—	2	2	no	—
220	#341	—	2	2	no	—
221	#341	—	2	2	no	—
222	#341	C₄×C₁₉	1	4	yes	complemented
223	#338	—	2	2	no	—
224	#336	—	2	2	no	—
225	C₂×C₁₉	—	2	1	no	—
226	C₂×C₁₉	—	2	1	no	—
227	C₂×C₁₉	—	2	1	no	—
228	C₂×C₁₉	—	2	1	no	—
229	C₂×C₁₉	—	2	1	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	#1443	1	1	yes	characteristic
232	C₂×C₁₉	#2103	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	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	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
261	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
262	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
263	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
275	C₂²×C₈	D₄×C₁₉	1	2	yes	—
276	#117	—	2	1	no	—
277	#117	—	2	1	no	—
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	Q₈×C₁₉	1	2	yes	—
282	C₂×C₄²	—	2	1	no	—
283	C₁₉	#11306	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
291	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
292	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
296	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
297	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
298	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
299	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	4	1	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	4	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₄²	—	4	1	no	—
347	C₄²	—	4	1	no	—
348	C₂³	—	4	2	no	—
349	C₂³	C₄×Q₈×C₁₉	1	1	yes	characteristic
350	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
352	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
353	C₂³	C₁₉×#125	1	1	yes	characteristic
354	C₂³	C₁₉×#125	1	1	yes	characteristic
355	C₂³	C₁₉×#125	1	1	yes	characteristic
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
359	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
360	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
361	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
363	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
365	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
366	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
367	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
368	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
369	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
370	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
371	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
372	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
373	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
374	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
375	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
376	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
377	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
378	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
379	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
380	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
381	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
382	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
383	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
384	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
385	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	C₁₉×#387	1	1	yes	characteristic
400	C₂²	C₁₉×#387	1	1	yes	characteristic
401	C₂²	C₁₉×#387	1	1	yes	characteristic
402	C₂²	C₁₉×#396	1	1	yes	characteristic
403	C₂²	C₁₉×#400	1	1	yes	characteristic
404	C₂²	C₁₉×#400	1	1	yes	characteristic
405	C₂²	C₁₉×#400	1	1	yes	characteristic
406	C₄	—	8	2	no	—
407	C₄	C₁₉×#383	1	1	yes	characteristic
408	C₄	C₁₉×#388	1	1	yes	characteristic
409	C₄	C₁₉×#388	1	1	yes	characteristic
410	C₄	C₁₉×#388	1	1	yes	characteristic
411	C₄	C₁₉×#397	1	1	yes	characteristic
412	C₄	C₁₉×#397	1	1	yes	characteristic
413	C₄	C₁₉×#397	1	1	yes	characteristic
414	C₄	C₁₉×#401	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	C₁₉×#1443	1	1	yes	characteristic
422	C₂	C₁₉×#2103	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#124
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	#400
prime radical	C₂⁴×C₁₉	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
19. C₁₉×#341	C₄	semidirect
136. #11306	C₁₉	direct (N × H)
222. #341	C₄×C₁₉	semidirect
283. C₁₉	#11306	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×#344	2
C₁₉×#1738	2
C₂×C₁₉×#341	2
C₂×C₁₉×#338	2
C₁₉×#1729	2
#11306	19

Subgroups — C19×#11306 #18017265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11306 #18017265