Subgroups — C₁₉×#11164 #18017123

Order 4864.

830 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×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	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#419	—	2	2	no	—
16	C₁₉×#419	—	2	2	no	—
17	C₂×C₁₉×#103	—	2	2	no	—
18	C₂×C₁₉×#103	—	2	2	no	—
19	C₂×C₁₉×#103	—	2	2	no	—
20	C₂×C₁₉×#103	—	2	2	no	—
21	C₂×C₁₉×#101	—	2	2	no	—
22	C₂×C₁₉×#101	—	2	2	no	—
23	C₂×C₁₉×#101	C₄	1	4	yes	complemented
24	C₁₉×#343	—	2	2	no	—
25	C₁₉×#341	—	2	2	no	—
26	C₁₉×#340	—	2	2	no	—
27	C₁₉×#336	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×Q₈×C₁₉	—	2	1	no	—
36	C₂²×Q₈×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
41	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	1	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	—	2	1	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	D₄	1	2	yes	—
73	C₁₉×#117	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₁₉×#117	—	2	1	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄²×C₁₉	—	2	1	no	—
86	C₁₉×#103	—	2	8	no	—
87	C₁₉×#103	—	2	8	no	—
88	C₁₉×#101	—	2	8	no	—
89	C₂⁴×C₁₉	#41	1	1	yes	characteristic
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	4	1	no	—
107	C₂×Q₈×C₁₉	—	4	1	no	—
108	C₂×Q₈×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	1	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	4	1	no	—
115	C₂×Q₈×C₁₉	—	4	1	no	—
116	C₂×Q₈×C₁₉	—	4	1	no	—
117	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	8	2	no	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
144	M₁₆×C₁₉	—	2	2	no	—
145	M₁₆×C₁₉	—	2	2	no	—
146	M₁₆×C₁₉	—	2	2	no	—
147	M₁₆×C₁₉	—	2	2	no	—
148	M₁₆×C₁₉	—	2	2	no	—
149	M₁₆×C₁₉	—	2	2	no	—
150	M₁₆×C₁₉	—	4	1	no	—
151	M₁₆×C₁₉	—	4	1	no	—
152	M₁₆×C₁₉	—	4	1	no	—
153	M₁₆×C₁₉	—	4	1	no	—
154	M₁₆×C₁₉	—	4	1	no	—
155	M₁₆×C₁₉	—	4	1	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	4	1	no	—
163	C₂×C₈×C₁₉	—	4	1	no	—
164	C₂×C₈×C₁₉	—	4	1	no	—
165	C₂×C₈×C₁₉	—	4	1	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₂×C₈×C₁₉	—	4	1	no	—
168	C₂×C₈×C₁₉	—	4	1	no	—
169	C₂×C₈×C₁₉	—	4	1	no	—
170	C₂×C₈×C₁₉	—	4	1	no	—
171	C₂×C₈×C₁₉	—	4	1	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	no	—
175	C₄⋊C₄×C₁₉	—	2	2	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₂²⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	—	4	1	no	—
181	C₄²×C₁₉	—	4	1	no	—
182	#11164	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	#117	1	1	yes	characteristic
186	C₂³×C₁₉	#121	1	1	yes	characteristic
187	C₂³×C₁₉	#123	1	1	yes	characteristic
188	C₂³×C₁₉	#123	1	1	yes	characteristic
189	C₂³×C₁₉	#123	1	1	yes	characteristic
190	C₂³×C₁₉	#124	1	1	yes	characteristic
191	C₂³×C₁₉	#126	1	1	yes	characteristic
192	Q₈×C₁₉	—	2	4	no	—
193	Q₈×C₁₉	—	2	4	no	—
194	Q₈×C₁₉	—	4	2	no	—
195	Q₈×C₁₉	—	4	2	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	—	8	2	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
242	C₈×C₁₉	—	4	2	no	—
243	C₈×C₁₉	—	4	2	no	—
244	C₈×C₁₉	—	4	2	no	—
245	C₈×C₁₉	—	4	2	no	—
246	C₂×#419	C₂×C₁₉	1	1	yes	characteristic
247	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
248	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic
249	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
250	C₂×#341	C₂×C₁₉	1	1	yes	characteristic
251	#1736	C₂×C₁₉	1	1	yes	characteristic
252	#1729	C₂×C₁₉	1	1	yes	characteristic
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	2	no	—
256	C₂²×C₁₉	—	2	2	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	#381	1	1	yes	characteristic
262	C₂²×C₁₉	#388	1	1	yes	characteristic
263	C₂²×C₁₉	#388	1	1	yes	characteristic
264	C₂²×C₁₉	#394	1	1	yes	characteristic
265	C₂²×C₁₉	#394	1	1	yes	characteristic
266	C₂²×C₁₉	#397	1	1	yes	characteristic
267	C₂²×C₁₉	#397	1	1	yes	characteristic
268	C₂²×C₁₉	#471	1	2	yes	—
269	C₂²×C₁₉	#473	1	2	yes	—
270	C₄×C₁₉	—	4	4	no	—
271	C₄×C₁₉	—	8	2	no	—
272	C₄×C₁₉	—	8	2	no	—
273	C₄×C₁₉	#386	1	1	yes	characteristic
274	C₄×C₁₉	#386	1	1	yes	characteristic
275	C₄×C₁₉	#388	1	1	yes	characteristic
276	C₄×C₁₉	#388	1	1	yes	characteristic
277	C₄×C₁₉	#394	1	1	yes	characteristic
278	C₄×C₁₉	#394	1	1	yes	characteristic
279	C₄×C₁₉	#397	1	1	yes	characteristic
280	C₄×C₁₉	#397	1	1	yes	characteristic
281	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
285	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
288	#419	—	2	2	no	—
289	#419	—	2	2	no	—
290	C₂×#103	—	2	2	no	—
291	C₂×#103	—	2	2	no	—
292	C₂×#103	—	2	2	no	—
293	C₂×#103	—	2	2	no	—
294	C₂×#101	—	2	2	no	—
295	C₂×#101	—	2	2	no	—
296	C₂×#101	C₄×C₁₉	1	4	yes	complemented
297	#343	—	2	2	no	—
298	#341	—	2	2	no	—
299	#340	—	2	2	no	—
300	#336	—	2	2	no	—
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	2	1	no	—
304	C₂×C₁₉	—	2	1	no	—
305	C₂×C₁₉	#1440	1	1	yes	characteristic
306	C₂×C₁₉	#1930	1	2	yes	—
307	C₂×C₁₉	#2046	1	1	yes	characteristic
308	C₂×C₁₉	#2047	1	1	yes	characteristic
309	C₂×C₁₉	#2052	1	2	yes	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×Q₈	—	2	1	no	—
321	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
322	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
323	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
343	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
344	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	—	2	1	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	D₄×C₁₉	1	2	yes	—
355	#117	—	2	1	no	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
365	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	#103	—	2	8	no	—
369	#103	—	2	8	no	—
370	#101	—	2	8	no	—
371	C₁₉	#11164	1	1	yes	characteristic, direct product factor, Sylow
372	C₂⁴	#41×C₁₉	1	1	yes	characteristic
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	4	1	no	—
389	C₂×Q₈	—	4	1	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	—	4	1	no	—
400	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	1	no	—
407	C₂²×C₄	—	4	1	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	4	1	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	8	2	no	—
413	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	4	1	no	—
434	M₁₆	—	4	1	no	—
435	M₁₆	—	4	1	no	—
436	M₁₆	—	4	1	no	—
437	M₁₆	—	4	1	no	—
438	M₁₆	—	4	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	1	no	—
446	C₂×C₈	—	4	1	no	—
447	C₂×C₈	—	4	1	no	—
448	C₂×C₈	—	4	1	no	—
449	C₂×C₈	—	4	1	no	—
450	C₂×C₈	—	4	1	no	—
451	C₂×C₈	—	4	1	no	—
452	C₂×C₈	—	4	1	no	—
453	C₂×C₈	—	4	1	no	—
454	C₂×C₈	—	4	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₄²	—	4	1	no	—
464	C₄²	—	4	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	C₁₉×#117	1	1	yes	characteristic
468	C₂³	C₁₉×#121	1	1	yes	characteristic
469	C₂³	C₁₉×#123	1	1	yes	characteristic
470	C₂³	C₁₉×#123	1	1	yes	characteristic
471	C₂³	C₁₉×#123	1	1	yes	characteristic
472	C₂³	C₁₉×#124	1	1	yes	characteristic
473	C₂³	C₁₉×#126	1	1	yes	characteristic
474	Q₈	—	2	4	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
498	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
503	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
507	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
508	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
509	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
510	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
511	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
512	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
513	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
514	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
515	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
517	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
518	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
519	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
520	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
521	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
522	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
523	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
524	C₈	—	4	2	no	—
525	C₈	—	4	2	no	—
526	C₈	—	4	2	no	—
527	C₈	—	4	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	C₁₉×#381	1	1	yes	characteristic
537	C₂²	C₁₉×#388	1	1	yes	characteristic
538	C₂²	C₁₉×#388	1	1	yes	characteristic
539	C₂²	C₁₉×#394	1	1	yes	characteristic
540	C₂²	C₁₉×#394	1	1	yes	characteristic
541	C₂²	C₁₉×#397	1	1	yes	characteristic
542	C₂²	C₁₉×#397	1	1	yes	characteristic
543	C₂²	C₁₉×#471	1	2	yes	—
544	C₂²	C₁₉×#473	1	2	yes	—
545	C₄	—	4	4	no	—
546	C₄	—	8	2	no	—
547	C₄	—	8	2	no	—
548	C₄	C₁₉×#386	1	1	yes	characteristic
549	C₄	C₁₉×#386	1	1	yes	characteristic
550	C₄	C₁₉×#388	1	1	yes	characteristic
551	C₄	C₁₉×#388	1	1	yes	characteristic
552	C₄	C₁₉×#394	1	1	yes	characteristic
553	C₄	C₁₉×#394	1	1	yes	characteristic
554	C₄	C₁₉×#397	1	1	yes	characteristic
555	C₄	C₁₉×#397	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	2	1	no	—
559	C₂	—	2	1	no	—
560	C₂	C₁₉×#1440	1	1	yes	characteristic
561	C₂	C₁₉×#1930	1	2	yes	—
562	C₂	C₁₉×#2046	1	1	yes	characteristic
563	C₂	C₁₉×#2047	1	1	yes	characteristic
564	C₂	C₁₉×#2052	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
23. C₂×C₁₉×#101	C₄	semidirect
182. #11164	C₁₉	direct (N × H)
296. C₂×#101	C₄×C₁₉	semidirect
371. C₁₉	#11164	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×#419	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×#101	2
C₂×C₁₉×#343	2
C₂×C₁₉×#341	2
C₁₉×#1736	2
C₁₉×#1729	2
#11164	19

Subgroups — C19×#11164 #18017123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11164 #18017123