Subgroups — C₁₉×#18303 #18024262

Order 4864.

912 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3458	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3209	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2628	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1605	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1602	C₂	1	4	yes	maximal
6	C₁₉×#1518	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1458	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#544	—	2	2	no	—
9	C₁₉×#544	—	2	2	no	—
10	C₁₉×#544	—	2	1	no	—
11	C₁₉×#544	C₂²	1	2	yes	—
12	C₁₉×#543	—	2	1	no	—
13	C₁₉×#543	C₂²	1	2	yes	—
14	C₁₉×#533	—	2	4	no	—
15	C₁₉×#533	—	2	1	no	—
16	C₁₉×#533	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	—	2	1	no	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₁₉×#494	—	2	2	no	—
21	C₁₉×#487	—	2	2	no	—
22	C₁₉×#462	—	2	4	no	—
23	C₁₉×#451	C₂²	1	8	yes	—
24	C₁₉×#431	C₂²	1	2	yes	—
25	C₁₉×#400	—	2	1	no	—
26	C₁₉×#399	—	2	1	no	—
27	C₁₉×#395	C₂²	1	2	yes	—
28	C₁₉×#393	C₂²	1	2	yes	—
29	C₁₉×#389	—	2	1	no	—
30	C₁₉×#382	C₂²	1	1	yes	characteristic
31	C₁₉×#380	—	2	1	no	—
32	C₁₉×#328	C₂²	1	8	yes	—
33	C₁₉×#324	C₂²	1	2	yes	—
34	C₁₉×#323	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂×Q₁₆×C₁₉	—	2	8	no	—
38	C₁₉×C₄⋊Q₈	—	2	4	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	4	no	—
42	C₁₉×C₄⋊Q₈	—	2	2	no	—
43	C₁₉×C₄⋊Q₈	—	2	2	no	—
44	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
45	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₉×#125	—	2	4	no	—
47	C₁₉×#125	—	2	2	no	—
48	C₁₉×#125	—	2	4	no	—
49	C₁₉×#125	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	—	2	4	no	—
51	C₁₉×C₂²⋊Q₈	—	2	4	no	—
52	C₁₉×C₂²⋊Q₈	—	2	4	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₁₉×C₂²⋊Q₈	—	2	2	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	—	2	2	no	—
60	C₄×Q₈×C₁₉	—	2	2	no	—
61	C₄×Q₈×C₁₉	D₄	1	4	yes	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	—	2	2	no	—
84	C₁₉×#103	—	2	8	no	—
85	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
86	C₄×C₈×C₁₉	—	2	2	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	C₂³	1	2	yes	—
91	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	4	no	—
96	C₂×Q₈×C₁₉	—	8	2	no	—
97	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	complemented
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₁₉	—	8	8	no	—
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	4	no	—
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	2	no	—
131	C₄⋊C₄×C₁₉	—	8	2	no	—
132	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₂²⋊C₄×C₁₉	—	2	2	no	—
137	C₂²⋊C₄×C₁₉	—	8	2	no	—
138	C₄²×C₁₉	—	2	4	no	—
139	C₄²×C₁₉	—	2	4	no	—
140	C₄²×C₁₉	—	2	1	no	—
141	C₄²×C₁₉	—	2	1	no	—
142	C₄²×C₁₉	C₂×D₄	1	2	yes	—
143	C₄²×C₁₉	C₂×D₄	1	2	yes	—
144	#18303	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₉	—	4	4	no	—
152	Q₈×C₁₉	—	4	8	no	—
153	Q₈×C₁₉	—	8	2	no	—
154	Q₈×C₁₉	—	8	2	no	—
155	Q₈×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	8	2	no	—
175	C₂×C₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	#120	1	2	yes	—
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
180	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₁₉	#137	1	2	yes	—
182	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
183	C₈×C₁₉	—	4	4	no	—
184	#3458	C₂×C₁₉	1	1	yes	characteristic
185	#3209	C₂×C₁₉	1	2	yes	complemented
186	#2628	C₂×C₁₉	1	1	yes	characteristic
187	#1605	C₂×C₁₉	1	4	yes	complemented
188	#1602	C₂×C₁₉	1	4	yes	—
189	#1518	C₂×C₁₉	1	2	yes	complemented
190	#1458	C₂×C₁₉	1	1	yes	characteristic
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
199	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
200	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	8	2	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	#451	1	2	yes	—
211	C₄×C₁₉	#451	1	2	yes	—
212	#544	—	2	2	no	—
213	#544	—	2	2	no	—
214	#544	—	2	1	no	—
215	#544	C₂²×C₁₉	1	2	yes	—
216	#543	—	2	1	no	—
217	#543	C₂²×C₁₉	1	2	yes	—
218	#533	—	2	4	no	—
219	#533	—	2	1	no	—
220	#533	C₂²×C₁₉	1	2	yes	—
221	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₂×#117	—	2	1	no	—
223	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
224	#494	—	2	2	no	—
225	#487	—	2	2	no	—
226	#462	—	2	4	no	—
227	#451	C₂²×C₁₉	1	8	yes	—
228	#431	C₂²×C₁₉	1	2	yes	—
229	#400	—	2	1	no	—
230	#399	—	2	1	no	—
231	#395	C₂²×C₁₉	1	2	yes	—
232	#393	C₂²×C₁₉	1	2	yes	—
233	#389	—	2	1	no	—
234	#382	C₂²×C₁₉	1	1	yes	characteristic
235	#380	—	2	1	no	—
236	#328	C₂²×C₁₉	1	8	yes	—
237	#324	C₂²×C₁₉	1	2	yes	—
238	#323	C₂²×C₁₉	1	2	yes	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	4	2	no	—
242	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
243	C₂×C₁₉	#3022	1	1	yes	characteristic
244	C₂×C₁₉	#3027	1	1	yes	characteristic
245	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
246	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
247	C₂×Q₁₆	—	2	8	no	—
248	C₄⋊Q₈	—	2	4	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	4	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
255	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
256	#125	—	2	4	no	—
257	#125	—	2	2	no	—
258	#125	—	2	4	no	—
259	#125	—	2	2	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	C₂²⋊Q₈	—	2	2	no	—
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	D₄×C₁₉	1	4	yes	—
272	#117	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
293	C₄⋊C₈	—	2	2	no	—
294	#103	—	2	8	no	—
295	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
296	C₄×C₈	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	2	no	—
300	#95	C₂³×C₁₉	1	2	yes	—
301	C₁₉	#18303	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	8	2	no	—
308	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	Q₁₆×C₁₉	1	4	yes	complemented
317	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
323	Q₁₆	—	8	8	no	—
324	C₂×C₈	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	8	2	no	—
343	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	4	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	C₂×D₄×C₁₉	1	2	yes	—
354	C₄²	C₂×D₄×C₁₉	1	2	yes	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
360	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
361	Q₈	—	4	4	no	—
362	Q₈	—	4	8	no	—
363	Q₈	—	8	2	no	—
364	Q₈	—	8	2	no	—
365	Q₈	—	8	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	C₁₉×#120	1	2	yes	—
387	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
388	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
389	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
390	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
391	C₂×C₄	C₁₉×#137	1	2	yes	—
392	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
393	C₈	—	4	4	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
402	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
403	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	4	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₁₉×#451	1	2	yes	—
414	C₄	C₁₉×#451	1	2	yes	—
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	4	2	no	—
418	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
419	C₂	C₁₉×#3022	1	1	yes	characteristic
420	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
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×#3209	C₂	semidirect
4. C₁₉×#1605	C₂	semidirect
6. C₁₉×#1518	C₂	semidirect
105. C₂²×C₄×C₁₉	Q₁₆	semidirect
144. #18303	C₁₉	direct (N × H)
185. #3209	C₂×C₁₉	semidirect
187. #1605	C₂×C₁₉	semidirect
189. #1518	C₂×C₁₉	semidirect
301. C₁₉	#18303	direct (N × H)
316. C₂²×C₄	Q₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3458	2
C₁₉×#3209	2
C₁₉×#2628	2
C₁₉×#1605	2
C₁₉×#1602	2
C₁₉×#1518	2
C₁₉×#1458	2
#18303	19

Subgroups — C19×#18303 #18024262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18303 #18024262