Subgroups — C₁₉×#8523 #18014482

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#542	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1556	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1533	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#542	—	2	4	no	—
7	C₁₉×#542	—	2	4	no	—
8	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#126	—	2	1	no	—
10	C₂×C₁₉×#124	—	2	1	no	—
11	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#123	—	2	1	no	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	2	yes	—
20	C₁₉×#432	C₂²	1	2	yes	—
21	C₁₉×#332	—	2	4	no	—
22	C₁₉×#329	—	2	4	no	—
23	C₁₉×#324	—	2	1	no	—
24	C₁₉×#324	—	2	1	no	—
25	C₁₉×#323	—	2	1	no	—
26	C₁₉×#323	—	2	1	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₁₉×C₄⋊Q₈	—	2	2	no	—
34	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
35	C₁₉×#126	—	2	8	no	—
36	C₁₉×#124	—	2	8	no	—
37	C₁₉×#124	—	2	2	no	—
38	C₁₉×#124	D₄	1	4	yes	—
39	C₁₉×#123	—	2	8	no	—
40	C₁₉×C₂²⋊Q₈	—	2	8	no	—
41	C₁₉×C₂²⋊Q₈	—	2	2	no	—
42	C₁₉×C₂²⋊Q₈	—	2	2	no	—
43	C₁₉×#121	—	2	2	no	—
44	C₁₉×#121	—	2	2	no	—
45	C₄×Q₈×C₁₉	—	2	2	no	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₁₉×#117	—	2	2	no	—
50	C₁₉×#117	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	D₄	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×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×C₄⋊C₈	—	2	2	no	—
69	C₁₉×C₄⋊C₈	—	2	2	no	—
70	C₁₉×C₂²⋊C₈	—	2	2	no	—
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×#97	—	2	2	no	—
73	C₁₉×#97	—	2	2	no	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	4	2	no	—
79	C₂×Q₈×C₁₉	—	8	2	no	—
80	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	4	2	no	—
84	C₂×D₄×C₁₉	—	8	2	no	—
85	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	8	2	no	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₁₉	—	4	2	no	—
101	C₂×C₈×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
111	C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₉	—	2	4	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	2	4	no	—
119	C₄²×C₁₉	—	2	1	no	—
120	C₄²×C₁₉	—	2	1	no	—
121	C₄²×C₁₉	C₂×D₄	1	2	yes	—
122	C₄²×C₁₉	C₂×D₄	1	2	yes	—
123	#8523	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	Q₈×C₁₉	—	4	2	no	—
134	Q₈×C₁₉	—	4	2	no	—
135	Q₈×C₁₉	—	8	4	no	—
136	D₄×C₁₉	—	4	2	no	—
137	D₄×C₁₉	—	4	2	no	—
138	D₄×C₁₉	—	8	4	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	8	4	no	—
157	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#120	1	2	yes	—
160	C₂×C₄×C₁₉	#120	1	2	yes	—
161	C₈×C₁₉	—	8	2	no	—
162	C₈×C₁₉	—	8	2	no	—
163	C₂×#542	C₂×C₁₉	1	1	yes	characteristic
164	#1556	C₂×C₁₉	1	2	yes	complemented
165	#1533	C₂×C₁₉	1	2	yes	complemented
166	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
167	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	4	2	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	—	4	2	no	—
176	C₂²×C₁₉	—	8	2	no	—
177	C₂²×C₁₉	—	8	4	no	—
178	C₂²×C₁₉	#379	1	1	yes	characteristic
179	C₂²×C₁₉	#413	1	2	yes	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	4	2	no	—
185	C₄×C₁₉	—	4	2	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	1	no	—
188	C₄×C₁₉	—	4	1	no	—
189	C₄×C₁₉	—	4	2	no	—
190	#542	—	2	4	no	—
191	#542	—	2	4	no	—
192	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×#126	—	2	1	no	—
194	C₂×#124	—	2	1	no	—
195	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#123	—	2	1	no	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₂²⋊Q₈	C₄×C₁₉	1	1	yes	characteristic
199	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
200	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
201	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
202	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
203	#432	C₂²×C₁₉	1	2	yes	—
204	#432	C₂²×C₁₉	1	2	yes	—
205	#332	—	2	4	no	—
206	#329	—	2	4	no	—
207	#324	—	2	1	no	—
208	#324	—	2	1	no	—
209	#323	—	2	1	no	—
210	#323	—	2	1	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	—	8	1	no	—
213	C₂×C₁₉	—	8	2	no	—
214	C₂×C₁₉	#1785	1	1	yes	characteristic
215	C₂×C₁₉	#1795	1	1	yes	characteristic
216	C₂×C₁₉	#1796	1	1	yes	characteristic
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
221	C₂³×C₄	—	2	1	no	—
222	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	D₄×C₁₉	1	4	yes	—
225	#126	—	2	8	no	—
226	#124	—	2	8	no	—
227	#124	—	2	2	no	—
228	#124	D₄×C₁₉	1	4	yes	—
229	#123	—	2	8	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	#121	—	2	2	no	—
234	#121	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	#97	—	2	2	no	—
263	#97	—	2	2	no	—
264	C₁₉	#8523	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	2	1	no	—
266	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	—	8	2	no	—
271	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	8	2	no	—
276	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	8	2	no	—
285	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
301	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₄²	—	2	4	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	C₂×D₄×C₁₉	1	2	yes	—
313	C₄²	C₂×D₄×C₁₉	1	2	yes	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	2	no	—
322	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
323	Q₈	—	4	2	no	—
324	Q₈	—	4	2	no	—
325	Q₈	—	8	4	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄	C₁₉×#120	1	2	yes	—
350	C₂×C₄	C₁₉×#120	1	2	yes	—
351	C₈	—	8	2	no	—
352	C₈	—	8	2	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	C₁₉×#379	1	1	yes	characteristic
364	C₂²	C₁₉×#413	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₂	—	2	2	no	—
376	C₂	—	8	2	no	—
377	C₂	—	8	1	no	—
378	C₂	C₁₉×#1785	1	1	yes	characteristic
379	C₂	C₁₉×#1795	1	1	yes	characteristic
380	C₂	C₁₉×#1796	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	C₂×C₁₉×#121	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×#1556	C₂	semidirect
3. C₁₉×#1533	C₂	semidirect
4. C₁₉×#1464	C₂	semidirect
5. C₁₉×#1464	C₂	semidirect
123. #8523	C₁₉	direct (N × H)
164. #1556	C₂×C₁₉	semidirect
165. #1533	C₂×C₁₉	semidirect
166. #1464	C₂×C₁₉	semidirect
167. #1464	C₂×C₁₉	semidirect
264. C₁₉	#8523	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×#542	2
C₁₉×#1556	2
C₁₉×#1533	2
C₁₉×#1464	2
#8523	19

Subgroups — C19×#8523 #18014482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8523 #18014482