Subgroups — C₁₉×#8330 #18014289

Order 4864.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#328	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#327	C₂	1	2	yes	maximal
5	C₁₉×#1434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#529	—	2	4	no	—
7	C₁₉×#529	—	2	4	no	—
8	C₂×C₁₉×#126	—	2	1	no	—
9	C₂×C₁₉×#125	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×#124	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₉×#123	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₄×C₁₉	—	2	1	no	—
16	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₉×#117	—	2	1	no	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂×C₁₉×#95	—	2	1	no	—
22	C₂×C₁₉×#95	C₂²	1	2	yes	—
23	C₁₉×#336	—	2	1	no	—
24	C₁₉×#336	—	2	1	no	—
25	C₁₉×#328	—	2	4	no	—
26	C₁₉×#327	—	2	4	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	—	2	2	no	—
36	C₁₉×#126	—	2	8	no	—
37	C₁₉×#125	—	2	2	no	—
38	C₁₉×#125	—	2	2	no	—
39	C₁₉×#124	—	2	2	no	—
40	C₁₉×#124	—	2	2	no	—
41	C₁₉×#123	—	2	8	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
44	C₁₉×#121	—	2	2	no	—
45	C₁₉×#121	D₄	1	4	yes	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×Q₈×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	2	no	—
50	C₄×D₄×C₁₉	—	2	2	no	—
51	C₁₉×#117	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
70	C₁₉×C₂²⋊C₈	—	2	2	no	—
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×#95	—	2	4	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	4	2	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂×D₄×C₁₉	—	2	4	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₉	—	4	2	no	—
121	C₂×C₈×C₁₉	—	4	2	no	—
122	C₂×C₈×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	4	no	—
137	C₄²×C₁₉	—	2	1	no	—
138	C₄²×C₁₉	—	2	1	no	—
139	C₄²×C₁₉	—	2	1	no	—
140	C₄²×C₁₉	—	2	1	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	#8330	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	—	4	1	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂³×C₁₉	#120	1	2	yes	—
157	C₂³×C₁₉	#135	1	2	yes	—
158	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂³×C₁₉	#137	1	1	yes	characteristic
160	Q₈×C₁₉	—	4	2	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	4	2	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	—	4	4	no	—
165	D₄×C₁₉	—	4	4	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	1	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	8	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	4	4	no	—
198	C₂×C₄×C₁₉	—	4	4	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	#104	1	2	yes	—
204	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#120	1	2	yes	—
207	C₈×C₁₉	—	8	2	no	—
208	C₂×#529	C₂×C₁₉	1	1	yes	characteristic
209	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
210	C₂×#328	C₂×C₁₉	1	2	yes	complemented
211	C₂×#327	C₂×C₁₉	1	2	yes	—
212	#1434	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	8	1	no	—
225	C₂²×C₁₉	—	8	1	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	#379	1	1	yes	characteristic
229	C₂²×C₁₉	#410	1	1	yes	characteristic
230	C₂²×C₁₉	#410	1	1	yes	characteristic
231	C₂²×C₁₉	#416	1	1	yes	characteristic
232	C₂²×C₁₉	#417	1	1	yes	characteristic
233	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
234	C₂²×C₁₉	#421	1	1	yes	characteristic
235	C₂²×C₁₉	#449	1	2	yes	—
236	C₂²×C₁₉	#452	1	2	yes	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	1	no	—
243	C₄×C₁₉	—	4	1	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	1	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	8	4	no	—
248	#529	—	2	4	no	—
249	#529	—	2	4	no	—
250	C₂×#126	—	2	1	no	—
251	C₂×#125	C₄×C₁₉	1	1	yes	characteristic, complemented
252	C₂×#124	C₄×C₁₉	1	1	yes	characteristic, complemented
253	C₂×#123	—	2	1	no	—
254	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
257	C₂×C₄×D₄	—	2	1	no	—
258	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
259	C₂×#117	—	2	1	no	—
260	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
262	C₂×#95	—	2	1	no	—
263	C₂×#95	—	2	1	no	—
264	C₂×#95	C₂²×C₁₉	1	2	yes	—
265	#336	—	2	1	no	—
266	#336	—	2	1	no	—
267	#328	—	2	4	no	—
268	#327	—	2	4	no	—
269	C₂×C₁₉	—	2	2	no	—
270	C₂×C₁₉	—	2	2	no	—
271	C₂×C₁₉	—	8	2	no	—
272	C₂×C₁₉	#1500	1	1	yes	characteristic
273	C₂×C₁₉	#1509	1	1	yes	characteristic
274	C₂×C₁₉	#1512	1	1	yes	characteristic
275	C₂×C₁₉	#1521	1	1	yes	characteristic
276	C₂×C₁₉	#1782	1	1	yes	characteristic
277	C₂×C₁₉	#1788	1	1	yes	characteristic
278	C₂×C₁₉	#1789	1	1	yes	characteristic
279	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	#126	—	2	8	no	—
289	#125	—	2	2	no	—
290	#125	—	2	2	no	—
291	#124	—	2	2	no	—
292	#124	—	2	2	no	—
293	#123	—	2	8	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
296	#121	—	2	2	no	—
297	#121	D₄×C₁₉	1	4	yes	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×D₄	—	2	8	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	#117	—	2	8	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
319	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	#95	—	2	4	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	4	2	no	—
328	C₁₉	#8330	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁴	—	2	1	no	—
330	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	4	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
408	C₂³	C₁₉×#120	1	2	yes	—
409	C₂³	C₁₉×#135	1	2	yes	—
410	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂³	C₁₉×#137	1	1	yes	characteristic
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	4	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	C₁₉×#104	1	2	yes	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
458	C₂×C₄	C₁₉×#120	1	2	yes	—
459	C₈	—	8	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₁₉×#379	1	1	yes	characteristic
476	C₂²	C₁₉×#410	1	1	yes	characteristic
477	C₂²	C₁₉×#410	1	1	yes	characteristic
478	C₂²	C₁₉×#416	1	1	yes	characteristic
479	C₂²	C₁₉×#417	1	1	yes	characteristic
480	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
481	C₂²	C₁₉×#421	1	1	yes	characteristic
482	C₂²	C₁₉×#449	1	2	yes	—
483	C₂²	C₁₉×#452	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	8	4	no	—
495	C₂	—	2	2	no	—
496	C₂	—	2	2	no	—
497	C₂	—	8	2	no	—
498	C₂	C₁₉×#1500	1	1	yes	characteristic
499	C₂	C₁₉×#1509	1	1	yes	characteristic
500	C₂	C₁₉×#1512	1	1	yes	characteristic
501	C₂	C₁₉×#1521	1	1	yes	characteristic
502	C₂	C₁₉×#1782	1	1	yes	characteristic
503	C₂	C₁₉×#1788	1	1	yes	characteristic
504	C₂	C₁₉×#1789	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1817	C₂	semidirect
3. C₂×C₁₉×#328	C₂	semidirect
5. C₁₉×#1434	C₂	semidirect
9. C₂×C₁₉×#125	C₄	semidirect
10. C₂×C₁₉×#124	C₄	semidirect
14. C₂×C₄×Q₈×C₁₉	C₄	semidirect
16. C₂×C₄×D₄×C₁₉	C₄	semidirect
143. #8330	C₁₉	direct (N × H)
209. #1817	C₂×C₁₉	semidirect
210. C₂×#328	C₂×C₁₉	semidirect
212. #1434	C₂×C₁₉	semidirect
251. C₂×#125	C₄×C₁₉	semidirect
252. C₂×#124	C₄×C₁₉	semidirect
256. C₂×C₄×Q₈	C₄×C₁₉	semidirect
258. C₂×C₄×D₄	C₄×C₁₉	semidirect
328. C₁₉	#8330	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×#529	2
C₁₉×#1817	2
C₂×C₁₉×#328	2
C₂×C₁₉×#327	2
C₁₉×#1434	2
#8330	19

Subgroups — C19×#8330 #18014289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8330 #18014289