Subgroups — C₁₉×#18383 #18024342

Order 4864.

986 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3189	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2564	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1617	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1614	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1605	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1602	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#328	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#554	—	2	4	no	—
11	C₁₉×#554	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	2	no	—
13	C₁₉×#544	C₂²	1	2	yes	—
14	C₁₉×#543	—	2	1	no	—
15	C₁₉×#543	C₂²	1	2	yes	—
16	C₁₉×#533	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#518	—	2	1	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#484	—	2	2	no	—
23	C₁₉×#484	C₂²	1	4	yes	—
24	C₁₉×#467	—	2	4	no	—
25	C₁₉×#451	—	2	2	no	—
26	C₁₉×#451	C₂²	1	4	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₁₉×#400	C₂²	1	1	yes	characteristic
29	C₁₉×#399	C₂²	1	1	yes	characteristic
30	C₁₉×#395	C₂²	1	1	yes	characteristic
31	C₁₉×#393	C₂²	1	1	yes	characteristic
32	C₁₉×#387	—	2	1	no	—
33	C₁₉×#386	—	2	1	no	—
34	C₁₉×#385	—	2	1	no	—
35	C₁₉×#380	—	2	1	no	—
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#328	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#323	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₁₉	—	2	4	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	1	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	4	no	—
53	C₁₉×#125	—	2	2	no	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×C₂²⋊Q₈	—	2	2	no	—
56	C₁₉×C₂²⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×C₂²⋊Q₈	—	2	2	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	4	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
68	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₁₉×#117	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	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	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
93	C₁₉×#107	—	2	4	no	—
94	C₁₉×#103	—	2	4	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
98	C₁₉×#95	—	2	1	no	—
99	C₁₉×#95	—	2	1	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	—	2	1	no	—
103	C₁₉×#95	C₂³	1	1	yes	characteristic
104	C₁₉×#95	C₂³	1	1	yes	characteristic
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	8	1	no	—
112	C₂×Q₈×C₁₉	—	8	2	no	—
113	C₂×Q₈×C₁₉	—	8	2	no	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	Q₁₆	1	4	yes	complemented
118	C₂²×C₄×C₁₉	—	2	1	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	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	4	2	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	8	1	no	—
131	C₂²×C₄×C₁₉	—	8	1	no	—
132	C₂²×C₄×C₁₉	—	8	1	no	—
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	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₁₉	—	8	4	no	—
141	C₂×C₈×C₁₉	—	2	4	no	—
142	C₂×C₈×C₁₉	—	8	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	4	2	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	—	8	1	no	—
158	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	4	no	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	4	2	no	—
165	C₂²⋊C₄×C₁₉	—	4	2	no	—
166	C₂²⋊C₄×C₁₉	—	8	1	no	—
167	C₄²×C₁₉	—	2	4	no	—
168	C₄²×C₁₉	—	2	1	no	—
169	C₄²×C₁₉	—	2	1	no	—
170	#18383	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	#120	1	2	yes	—
178	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
179	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
180	C₂³×C₁₉	#137	1	2	yes	—
181	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₉	—	4	4	no	—
183	Q₈×C₁₉	—	4	4	no	—
184	Q₈×C₁₉	—	4	4	no	—
185	Q₈×C₁₉	—	8	2	no	—
186	Q₈×C₁₉	—	8	2	no	—
187	D₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	8	1	no	—
214	C₂×C₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	8	2	no	—
216	C₂×C₄×C₁₉	—	8	2	no	—
217	C₂×C₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	—	8	4	no	—
219	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
222	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
223	C₈×C₁₉	—	4	4	no	—
224	#3501	C₂×C₁₉	1	1	yes	characteristic
225	#3189	C₂×C₁₉	1	2	yes	complemented
226	#2564	C₂×C₁₉	1	1	yes	characteristic
227	#1617	C₂×C₁₉	1	2	yes	complemented
228	#1614	C₂×C₁₉	1	2	yes	complemented
229	#1605	C₂×C₁₉	1	2	yes	complemented
230	#1602	C₂×C₁₉	1	2	yes	complemented
231	C₂×#328	C₂×C₁₉	1	2	yes	complemented
232	#1459	C₂×C₁₉	1	1	yes	characteristic
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	8	1	no	—
244	C₂²×C₁₉	#451	1	4	yes	—
245	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
246	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
247	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
248	C₄×C₁₉	—	2	2	no	—
249	C₄×C₁₉	—	2	2	no	—
250	C₄×C₁₉	—	2	1	no	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	4	1	no	—
254	C₄×C₁₉	—	4	4	no	—
255	C₄×C₁₉	—	4	1	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	—	8	1	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	—	8	1	no	—
260	#554	—	2	4	no	—
261	#554	—	2	2	no	—
262	D₄×Q₈	—	2	2	no	—
263	#544	C₂²×C₁₉	1	2	yes	—
264	#543	—	2	1	no	—
265	#543	C₂²×C₁₉	1	2	yes	—
266	#533	—	2	1	no	—
267	C₂×C₂²⋊Q₈	—	2	1	no	—
268	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
270	#518	—	2	1	no	—
271	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
272	#484	—	2	2	no	—
273	#484	C₂²×C₁₉	1	4	yes	—
274	#467	—	2	4	no	—
275	#451	—	2	2	no	—
276	#451	C₂²×C₁₉	1	4	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
278	#400	C₂²×C₁₉	1	1	yes	characteristic
279	#399	C₂²×C₁₉	1	1	yes	characteristic
280	#395	C₂²×C₁₉	1	1	yes	characteristic
281	#393	C₂²×C₁₉	1	1	yes	characteristic
282	#387	—	2	1	no	—
283	#386	—	2	1	no	—
284	#385	—	2	1	no	—
285	#380	—	2	1	no	—
286	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
287	#328	C₂²×C₁₉	1	4	yes	—
288	#328	C₂²×C₁₉	1	4	yes	—
289	#324	C₂²×C₁₉	1	2	yes	—
290	#323	C₂²×C₁₉	1	2	yes	—
291	C₂×C₁₉	—	2	1	no	—
292	C₂×C₁₉	—	2	1	no	—
293	C₂×C₁₉	—	2	4	no	—
294	C₂×C₁₉	—	4	2	no	—
295	C₂×C₁₉	C₂×#451	1	1	yes	characteristic
296	C₂×C₁₉	#3018	1	1	yes	characteristic
297	C₂×C₁₉	#3026	1	1	yes	characteristic
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
300	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
301	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×Q₁₆	—	2	4	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	4	no	—
310	#125	—	2	2	no	—
311	#125	—	2	4	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
325	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	#117	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
349	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
350	#107	—	2	4	no	—
351	#103	—	2	4	no	—
352	#103	—	2	4	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	C₂³×C₁₉	1	1	yes	characteristic
361	#95	C₂³×C₁₉	1	1	yes	characteristic
362	C₁₉	#18383	1	1	yes	characteristic, direct product factor, Sylow
363	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
364	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	8	1	no	—
370	C₂×Q₈	—	8	2	no	—
371	C₂×Q₈	—	8	2	no	—
372	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	Q₁₆×C₁₉	1	4	yes	complemented
376	C₂²×C₄	—	2	1	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	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	8	1	no	—
389	C₂²×C₄	—	8	1	no	—
390	C₂²×C₄	—	8	1	no	—
391	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
398	Q₁₆	—	8	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	8	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	8	1	no	—
416	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	8	1	no	—
425	C₄²	—	2	4	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	C₁₉×#120	1	2	yes	—
435	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
436	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
437	C₂³	C₁₉×#137	1	2	yes	—
438	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
439	Q₈	—	4	4	no	—
440	Q₈	—	4	4	no	—
441	Q₈	—	4	4	no	—
442	Q₈	—	8	2	no	—
443	Q₈	—	8	2	no	—
444	D₄	—	2	8	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	2	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
477	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
478	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
480	C₈	—	4	4	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	C₁₉×#451	1	4	yes	—
493	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
494	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
495	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	4	no	—
505	C₄	—	8	1	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	1	no	—
508	C₂	—	2	1	no	—
509	C₂	—	2	1	no	—
510	C₂	—	2	4	no	—
511	C₂	—	4	2	no	—
512	C₂	C₂×C₁₉×#451	1	1	yes	characteristic
513	C₂	C₁₉×#3018	1	1	yes	characteristic
514	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3189	C₂	semidirect
4. C₁₉×#1617	C₂	semidirect
5. C₁₉×#1614	C₂	semidirect
6. C₁₉×#1605	C₂	semidirect
7. C₁₉×#1602	C₂	semidirect
8. C₂×C₁₉×#328	C₂	semidirect
117. C₂×D₄×C₁₉	Q₁₆	semidirect
170. #18383	C₁₉	direct (N × H)
225. #3189	C₂×C₁₉	semidirect
227. #1617	C₂×C₁₉	semidirect
228. #1614	C₂×C₁₉	semidirect
229. #1605	C₂×C₁₉	semidirect
230. #1602	C₂×C₁₉	semidirect
231. C₂×#328	C₂×C₁₉	semidirect
362. C₁₉	#18383	direct (N × H)
375. C₂×D₄	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×#3501	2
C₁₉×#3189	2
C₁₉×#2564	2
C₁₉×#1617	2
C₁₉×#1614	2
C₁₉×#1605	2
C₁₉×#1602	2
C₂×C₁₉×#328	2
C₁₉×#1459	2
#18383	19

Subgroups — C19×#18383 #18024342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18383 #18024342