Subgroups — C₁₉×#8348 #18014307

Order 4864.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3491	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1532	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1494	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#552	—	2	2	no	—
7	C₁₉×#552	—	2	2	no	—
8	C₁₉×#551	—	2	2	no	—
9	C₁₉×#551	—	2	2	no	—
10	C₁₉×#543	C₄	1	1	yes	characteristic
11	C₁₉×#539	—	2	1	no	—
12	C₁₉×#539	C₄	1	2	yes	—
13	C₁₉×#534	C₄	1	1	yes	characteristic
14	C₁₉×#529	—	2	1	no	—
15	C₁₉×#529	C₂²	1	2	yes	—
16	C₂×C₁₉×#123	—	2	1	no	—
17	C₁₉×#518	—	2	1	no	—
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	2	yes	complemented
20	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#336	—	2	1	no	—
24	C₁₉×#330	—	2	2	no	—
25	C₁₉×#329	—	2	2	no	—
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₁₉×D₄⋊C₈	—	2	2	no	—
28	C₁₉×#324	—	2	1	no	—
29	C₁₉×#323	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×#126	—	2	2	no	—
35	C₁₉×#126	—	2	2	no	—
36	C₁₉×#126	—	2	2	no	—
37	C₁₉×#126	—	2	2	no	—
38	C₁₉×#125	—	2	1	no	—
39	C₁₉×#125	—	2	2	no	—
40	C₁₉×#125	—	2	2	no	—
41	C₁₉×#125	D₄	1	2	yes	—
42	C₁₉×#124	—	2	1	no	—
43	C₁₉×#124	D₄	1	2	yes	—
44	C₁₉×#123	—	2	2	no	—
45	C₁₉×#123	—	2	2	no	—
46	C₁₉×#123	—	2	2	no	—
47	C₁₉×#123	—	2	2	no	—
48	C₁₉×#123	—	2	2	no	—
49	C₁₉×#123	—	2	2	no	—
50	C₁₉×#123	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	2	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₁₉×C₂²⋊Q₈	—	2	1	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
57	C₁₉×#121	—	2	1	no	—
58	C₁₉×#121	C₂×C₄	1	2	yes	—
59	C₁₉×#120	—	2	2	no	—
60	C₄×Q₈×C₁₉	—	2	1	no	—
61	C₄×Q₈×C₁₉	D₄	1	2	yes	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	—	2	1	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	D₄	1	2	yes	—
68	C₁₉×#117	—	2	2	no	—
69	C₁₉×#117	—	2	2	no	—
70	C₁₉×#117	—	2	2	no	—
71	C₁₉×#117	—	2	2	no	—
72	C₁₉×#117	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₂²⋊C₈	—	2	4	no	—
87	C₁₉×C₂²⋊C₈	—	2	2	no	—
88	C₁₉×#97	—	2	2	no	—
89	C₁₉×#97	—	2	2	no	—
90	C₄×C₈×C₁₉	—	2	2	no	—
91	C₂⁴×C₁₉	—	2	1	no	—
92	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	4	2	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	2	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₉	—	2	2	no	—
148	C₂²⋊C₄×C₁₉	—	2	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	1	no	—
151	C₄²×C₁₉	—	2	1	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	C₂×D₄	1	2	yes	—
154	C₄²×C₁₉	C₂×D₄	1	2	yes	—
155	#8348	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	4	1	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	8	1	no	—
163	C₂³×C₁₉	—	8	1	no	—
164	C₂³×C₁₉	#104	1	2	yes	—
165	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	Q₈×C₁₉	—	4	2	no	—
167	Q₈×C₁₉	—	8	1	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	8	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	8	2	no	—
191	C₂×C₄×C₁₉	—	8	1	no	—
192	C₂×C₄×C₁₉	—	8	2	no	—
193	C₂×C₄×C₁₉	—	8	1	no	—
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₉	#120	1	2	yes	—
196	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
198	C₈×C₁₉	—	4	2	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₈×C₁₉	—	8	2	no	—
201	#3491	C₂×C₁₉	1	1	yes	characteristic
202	#1750	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#1532	C₂×C₁₉	1	2	yes	complemented
204	#1494	C₂×C₁₉	1	2	yes	complemented
205	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	—	16	2	no	—
217	C₂²×C₁₉	#379	1	1	yes	characteristic
218	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
219	C₂²×C₁₉	#421	1	1	yes	characteristic
220	C₄×C₁₉	—	2	2	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	2	no	—
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	2	no	—
228	C₄×C₁₉	—	4	1	no	—
229	C₄×C₁₉	—	4	2	no	—
230	#552	—	2	2	no	—
231	#552	—	2	2	no	—
232	#551	—	2	2	no	—
233	#551	—	2	2	no	—
234	#543	C₄×C₁₉	1	1	yes	characteristic
235	#539	—	2	1	no	—
236	#539	C₄×C₁₉	1	2	yes	—
237	#534	C₄×C₁₉	1	1	yes	characteristic
238	#529	—	2	1	no	—
239	#529	C₂²×C₁₉	1	2	yes	—
240	C₂×#123	—	2	1	no	—
241	#518	—	2	1	no	—
242	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
243	#432	C₂²×C₁₉	1	2	yes	complemented
244	C₂×C₂²⋊C₈	—	2	1	no	—
245	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
246	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
247	#336	—	2	1	no	—
248	#330	—	2	2	no	—
249	#329	—	2	2	no	—
250	Q₈⋊C₈	—	2	2	no	—
251	D₄⋊C₈	—	2	2	no	—
252	#324	—	2	1	no	—
253	#323	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	4	2	no	—
257	C₂×C₁₉	—	8	2	no	—
258	C₂×C₁₉	#1789	1	1	yes	characteristic
259	C₂×C₁₉	#1791	1	1	yes	characteristic
260	C₂×C₁₉	#1794	1	1	yes	characteristic
261	C₂²×D₄	—	2	1	no	—
262	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	#126	—	2	2	no	—
266	#126	—	2	2	no	—
267	#126	—	2	2	no	—
268	#126	—	2	2	no	—
269	#125	—	2	1	no	—
270	#125	—	2	2	no	—
271	#125	—	2	2	no	—
272	#125	D₄×C₁₉	1	2	yes	—
273	#124	—	2	1	no	—
274	#124	D₄×C₁₉	1	2	yes	—
275	#123	—	2	2	no	—
276	#123	—	2	2	no	—
277	#123	—	2	2	no	—
278	#123	—	2	2	no	—
279	#123	—	2	2	no	—
280	#123	—	2	2	no	—
281	#123	—	2	2	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
288	#121	—	2	1	no	—
289	#121	C₂×C₄×C₁₉	1	2	yes	—
290	#120	—	2	2	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	D₄×C₁₉	1	2	yes	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	D₄×C₁₉	1	2	yes	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	4	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	#97	—	2	2	no	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₁₉	#8348	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	2	1	no	—
324	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
343	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	C₂×D₄×C₁₉	1	2	yes	—
386	C₄²	C₂×D₄×C₁₉	1	2	yes	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	1	no	—
394	C₂³	—	8	1	no	—
395	C₂³	C₁₉×#104	1	2	yes	—
396	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	Q₈	—	4	2	no	—
398	Q₈	—	8	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	8	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	2	no	—
423	C₂×C₄	—	8	1	no	—
424	C₂×C₄	—	8	1	no	—
425	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
426	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#120	1	2	yes	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₈	—	8	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	16	2	no	—
443	C₂²	C₁₉×#379	1	1	yes	characteristic
444	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
445	C₂²	C₁₉×#421	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	2	no	—
456	C₂	—	2	1	no	—
457	C₂	—	2	1	no	—
458	C₂	—	4	2	no	—
459	C₂	—	8	2	no	—
460	C₂	C₁₉×#1789	1	1	yes	characteristic
461	C₂	C₁₉×#1791	1	1	yes	characteristic
462	C₂	C₁₉×#1794	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#534	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1750	C₂	semidirect
3. C₁₉×#1532	C₂	semidirect
4. C₁₉×#1494	C₂	semidirect
5. C₁₉×#1464	C₂	semidirect
19. C₁₉×#432	C₂²	semidirect
21. C₂×C₁₉×#97	C₂²	semidirect
22. C₂×C₄×C₈×C₁₉	C₂²	semidirect
155. #8348	C₁₉	direct (N × H)
202. #1750	C₂×C₁₉	semidirect
203. #1532	C₂×C₁₉	semidirect
204. #1494	C₂×C₁₉	semidirect
205. #1464	C₂×C₁₉	semidirect
243. #432	C₂²×C₁₉	semidirect
245. C₂×#97	C₂²×C₁₉	semidirect
246. C₂×C₄×C₈	C₂²×C₁₉	semidirect
322. C₁₉	#8348	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×#3491	2
C₁₉×#1750	2
C₁₉×#1532	2
C₁₉×#1494	2
C₁₉×#1464	2
#8348	19

Subgroups — C19×#8348 #18014307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8348 #18014307