Subgroups — C₁₉×#23562 #18029521

Order 4864.

1054 conjugacy classes of subgroups.

The subgroup lattice has 376 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	C₂×C₁₉×#428	C₂	1	2	yes	maximal
3	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2061	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2060	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1733	C₂	1	2	yes	maximal
8	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#544	—	2	2	no	—
10	C₁₉×#544	—	2	2	no	—
11	C₁₉×#544	C₂²	1	2	yes	—
12	C₁₉×#544	C₂²	1	2	yes	—
13	C₁₉×#543	—	2	2	no	—
14	C₁₉×#533	—	2	4	no	—
15	C₁₉×#533	—	2	2	no	—
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#428	—	2	4	no	—
21	C₁₉×#428	C₂²	1	8	yes	—
22	C₂×C₁₉×#107	—	2	2	no	—
23	C₂×C₁₉×#106	—	2	2	no	—
24	C₁₉×#389	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#384	C₂²	1	2	yes	—
27	C₁₉×#382	C₂²	1	2	yes	—
28	C₁₉×#343	C₂²	1	2	yes	—
29	C₁₉×#343	C₂²	1	2	yes	—
30	C₁₉×#339	C₂²	1	8	yes	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂×M₁₆×C₁₉	—	2	4	no	—
35	C₂×M₁₆×C₁₉	Q₈	1	8	yes	complemented
36	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
37	C₂²×C₈×C₁₉	—	2	2	no	—
38	C₁₉×C₄⋊Q₈	—	2	2	no	—
39	C₁₉×C₄⋊Q₈	—	2	2	no	—
40	C₁₉×C₄⋊Q₈	—	2	4	no	—
41	C₁₉×C₄⋊Q₈	—	2	4	no	—
42	C₁₉×#125	—	2	4	no	—
43	C₁₉×#125	—	2	4	no	—
44	C₁₉×#125	—	2	4	no	—
45	C₁₉×C₂²⋊Q₈	—	2	8	no	—
46	C₁₉×C₂²⋊Q₈	—	2	8	no	—
47	C₁₉×C₂²⋊Q₈	—	2	4	no	—
48	C₁₉×C₂²⋊Q₈	—	2	4	no	—
49	C₄×Q₈×C₁₉	—	2	4	no	—
50	C₄×Q₈×C₁₉	—	2	4	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	—	2	2	no	—
54	C₁₉×#117	—	2	2	no	—
55	C₁₉×#117	—	2	2	no	—
56	C₁₉×#117	D₄	1	4	yes	—
57	C₁₉×#117	Q₈	1	4	yes	complemented
58	C₁₉×#117	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₉	—	2	2	no	—
73	C₂×C₄²×C₁₉	D₄	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
75	C₁₉×#107	—	2	8	no	—
76	C₁₉×#106	—	2	8	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₉	—	2	4	no	—
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	—	8	2	no	—
87	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₁₉	#41	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₁₉	—	2	8	no	—
97	M₁₆×C₁₉	—	2	4	no	—
98	M₁₆×C₁₉	C₂×Q₈	1	8	yes	—
99	C₂×C₈×C₁₉	—	2	8	no	—
100	C₂×C₈×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	2	8	no	—
102	C₄⋊C₄×C₁₉	—	2	8	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	8	4	no	—
114	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
115	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
116	C₂²⋊C₄×C₁₉	—	2	4	no	—
117	C₂²⋊C₄×C₁₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₉	—	2	4	no	—
120	C₄²×C₁₉	—	2	4	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	2	4	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
126	#23562	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	#120	1	2	yes	—
130	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
131	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
132	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₁₉	—	8	4	no	—
134	Q₈×C₁₉	—	8	4	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	8	2	no	—
147	C₂×C₄×C₁₉	—	8	2	no	—
148	C₂×C₄×C₁₉	—	8	4	no	—
149	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
152	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
153	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
155	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
156	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
159	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
161	C₈×C₁₉	—	2	8	no	—
162	#3458	C₂×C₁₉	1	1	yes	characteristic
163	C₂×#428	C₂×C₁₉	1	2	yes	—
164	#2317	C₂×C₁₉	1	1	yes	characteristic
165	#2061	C₂×C₁₉	1	4	yes	complemented
166	#2060	C₂×C₁₉	1	4	yes	complemented
167	#1742	C₂×C₁₉	1	1	yes	characteristic
168	#1733	C₂×C₁₉	1	2	yes	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	#395	1	4	yes	—
176	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
179	C₄×C₁₉	—	4	4	no	—
180	C₄×C₁₉	—	4	2	no	—
181	C₄×C₁₉	—	4	4	no	—
182	C₄×C₁₉	—	4	2	no	—
183	C₄×C₁₉	—	4	4	no	—
184	C₄×C₁₉	—	8	2	no	—
185	C₄×C₁₉	#395	1	2	yes	—
186	C₄×C₁₉	#395	1	2	yes	—
187	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
188	C₄×C₁₉	C₂×C₄⋊Q₈	1	2	yes	—
189	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
190	#544	—	2	2	no	—
191	#544	—	2	2	no	—
192	#544	C₂²×C₁₉	1	2	yes	—
193	#544	C₂²×C₁₉	1	2	yes	—
194	#543	—	2	2	no	—
195	#533	—	2	4	no	—
196	#533	—	2	2	no	—
197	C₂×#117	C₂²×C₁₉	1	2	yes	—
198	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
199	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
201	#428	—	2	4	no	—
202	#428	C₂²×C₁₉	1	8	yes	—
203	C₂×#107	—	2	2	no	—
204	C₂×#106	—	2	2	no	—
205	#389	—	2	2	no	—
206	#385	—	2	2	no	—
207	#384	C₂²×C₁₉	1	2	yes	—
208	#382	C₂²×C₁₉	1	2	yes	—
209	#343	C₂²×C₁₉	1	2	yes	—
210	#343	C₂²×C₁₉	1	2	yes	—
211	#339	C₂²×C₁₉	1	8	yes	—
212	C₂×C₁₉	—	2	1	no	—
213	C₂×C₁₉	—	2	1	no	—
214	C₂×C₁₉	—	2	4	no	—
215	C₂×C₁₉	C₂×#395	1	1	yes	characteristic
216	C₂×C₁₉	#3021	1	1	yes	characteristic
217	C₂×C₁₉	#3022	1	1	yes	characteristic
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	Q₈×C₁₉	1	8	yes	complemented
223	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
224	C₂²×C₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	—	2	4	no	—
229	#125	—	2	4	no	—
230	#125	—	2	4	no	—
231	#125	—	2	4	no	—
232	C₂²⋊Q₈	—	2	8	no	—
233	C₂²⋊Q₈	—	2	8	no	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	#117	—	2	2	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	D₄×C₁₉	1	4	yes	—
244	#117	Q₈×C₁₉	1	4	yes	complemented
245	#117	C₂³×C₁₉	1	4	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
252	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	D₄×C₁₉	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
262	#107	—	2	8	no	—
263	#106	—	2	8	no	—
264	#95	—	2	4	no	—
265	C₁₉	#23562	1	1	yes	characteristic, direct product factor, Sylow
266	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	8	2	no	—
275	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
280	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
282	C₂²×C₄	#41×C₁₉	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
284	M₁₆	—	2	8	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	C₂×Q₈×C₁₉	1	8	yes	—
287	C₂×C₈	—	2	8	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	8	4	no	—
302	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
303	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	C₁₉×#120	1	2	yes	—
317	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
318	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
319	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
320	Q₈	—	8	4	no	—
321	Q₈	—	8	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
337	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
338	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
339	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
340	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
341	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
342	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
343	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
344	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
345	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
346	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
348	C₈	—	2	8	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	C₁₉×#395	1	4	yes	—
356	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
357	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
358	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	4	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	4	no	—
364	C₄	—	8	2	no	—
365	C₄	C₁₉×#395	1	2	yes	—
366	C₄	C₁₉×#395	1	2	yes	—
367	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
368	C₄	C₂×C₁₉×C₄⋊Q₈	1	2	yes	—
369	C₂	—	2	1	no	—
370	C₂	—	2	4	no	—
371	C₂	—	2	1	no	—
372	C₂	C₂×C₁₉×#395	1	1	yes	characteristic
373	C₂	C₁₉×#3021	1	1	yes	characteristic
374	C₂	C₁₉×#3022	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 ▷ C₂ ▷ 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
4. C₁₉×#2061	C₂	semidirect
5. C₁₉×#2060	C₂	semidirect
35. C₂×M₁₆×C₁₉	Q₈	semidirect
57. C₁₉×#117	Q₈	semidirect
126. #23562	C₁₉	direct (N × H)
165. #2061	C₂×C₁₉	semidirect
166. #2060	C₂×C₁₉	semidirect
222. C₂×M₁₆	Q₈×C₁₉	semidirect
244. #117	Q₈×C₁₉	semidirect
265. C₁₉	#23562	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×#3458	2
C₂×C₁₉×#428	2
C₁₉×#2317	2
C₁₉×#2061	2
C₁₉×#2060	2
C₁₉×#1742	2
C₁₉×#1733	2
#23562	19

Subgroups — C19×#23562 #18029521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23562 #18029521