Subgroups — C₁₉×#21947 #18027906

Order 4864.

1010 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2311	C₂	1	2	yes	maximal
3	C₁₉×#1854	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1852	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1809	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1808	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#117	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×#107	C₂²	1	2	yes	—
13	C₂×C₁₉×#107	C₂²	1	2	yes	—
14	C₂×C₁₉×#107	C₂²	1	2	yes	—
15	C₂×C₁₉×#106	C₂²	1	2	yes	—
16	C₁₉×#408	C₄	1	8	yes	complemented
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
18	C₁₉×#391	—	2	2	no	—
19	C₁₉×#390	—	2	2	no	—
20	C₁₉×#386	—	2	2	no	—
21	C₁₉×#386	—	2	2	no	—
22	C₁₉×#380	C₂²	1	4	yes	—
23	C₁₉×#380	C₂²	1	4	yes	—
24	C₁₉×#340	C₂²	1	4	yes	—
25	C₁₉×#340	C₂²	1	4	yes	—
26	C₂×#41×C₁₉	—	4	1	no	—
27	C₂×#41×C₁₉	—	4	1	no	—
28	C₂×#41×C₁₉	—	4	1	no	—
29	C₂×#41×C₁₉	—	4	1	no	—
30	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
31	C₂×#41×C₁₉	Q₈	1	4	yes	—
32	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	D₄	1	2	yes	—
35	C₂³×C₄×C₁₉	—	2	2	no	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂×M₁₆×C₁₉	—	4	1	no	—
39	C₂×M₁₆×C₁₉	—	4	1	no	—
40	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
41	C₂²×C₈×C₁₉	—	4	1	no	—
42	C₂²×C₈×C₁₉	—	4	1	no	—
43	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₁₉×#117	—	4	2	no	—
47	C₁₉×#117	—	4	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄²×C₁₉	—	2	2	no	—
57	C₁₉×#107	—	4	2	no	—
58	C₁₉×#107	—	4	2	no	—
59	C₁₉×#107	—	4	2	no	—
60	C₁₉×#106	—	4	2	no	—
61	C₁₉×C₂²⋊C₈	C₂×C₄	1	16	yes	complemented
62	C₁₉×#95	—	2	4	no	—
63	C₁₉×#95	—	2	4	no	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
66	#41×C₁₉	—	4	4	no	—
67	#41×C₁₉	—	4	4	no	—
68	#41×C₁₉	—	4	4	no	—
69	#41×C₁₉	—	4	4	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
73	C₂×D₄×C₁₉	—	4	2	no	—
74	C₂×D₄×C₁₉	—	4	2	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
78	C₂×D₄×C₁₉	C₄⋊C₄	1	8	yes	—
79	C₂²×C₄×C₁₉	—	2	2	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	—	8	4	no	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₁₉	—	4	4	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	4	4	no	—
104	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
105	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	4	4	no	—
111	C₂²⋊C₄×C₁₉	—	4	4	no	—
112	C₂²⋊C₄×C₁₉	—	8	4	no	—
113	C₂²⋊C₄×C₁₉	—	8	4	no	—
114	C₄²×C₁₉	—	4	4	no	—
115	#21947	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
125	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
126	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₁₉	—	4	4	no	—
128	D₄×C₁₉	—	4	8	no	—
129	D₄×C₁₉	—	4	4	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	4	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	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	8	8	no	—
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
157	C₈×C₁₉	—	2	4	no	—
158	C₈×C₁₉	—	2	4	no	—
159	C₂×#408	C₂×C₁₉	1	1	yes	characteristic
160	#2311	C₂×C₁₉	1	2	yes	—
161	#1854	C₂×C₁₉	1	4	yes	complemented
162	#1852	C₂×C₁₉	1	4	yes	complemented
163	#1809	C₂×C₁₉	1	2	yes	complemented
164	#1808	C₂×C₁₉	1	2	yes	complemented
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	4	no	—
167	C₂²×C₁₉	—	2	4	no	—
168	C₂²×C₁₉	—	2	8	no	—
169	C₂²×C₁₉	—	4	2	no	—
170	C₂²×C₁₉	—	4	1	no	—
171	C₂²×C₁₉	—	4	2	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₉	#534	1	1	yes	characteristic
177	C₂²×C₁₉	#534	1	1	yes	characteristic
178	C₂²×C₁₉	#576	1	2	yes	—
179	C₂²×C₁₉	#578	1	2	yes	—
180	C₄×C₁₉	—	2	4	no	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	8	4	no	—
183	C₄×C₁₉	—	8	4	no	—
184	C₄×C₁₉	#518	1	1	yes	characteristic
185	C₄×C₁₉	#518	1	1	yes	characteristic
186	C₄×C₁₉	#543	1	1	yes	characteristic
187	C₄×C₁₉	#543	1	1	yes	characteristic
188	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
189	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
190	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
191	C₂×#117	C₂²×C₁₉	1	2	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
193	C₂×#107	C₂²×C₁₉	1	2	yes	—
194	C₂×#107	C₂²×C₁₉	1	2	yes	—
195	C₂×#107	C₂²×C₁₉	1	2	yes	—
196	C₂×#106	C₂²×C₁₉	1	2	yes	—
197	#408	C₄×C₁₉	1	8	yes	complemented
198	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
199	#391	—	2	2	no	—
200	#390	—	2	2	no	—
201	#386	—	2	2	no	—
202	#386	—	2	2	no	—
203	#380	C₂²×C₁₉	1	4	yes	—
204	#380	C₂²×C₁₉	1	4	yes	—
205	#340	C₂²×C₁₉	1	4	yes	—
206	#340	C₂²×C₁₉	1	4	yes	—
207	C₂×C₁₉	—	4	4	no	—
208	C₂×C₁₉	—	4	2	no	—
209	C₂×C₁₉	#2315	1	1	yes	characteristic
210	C₂×C₁₉	#2913	1	2	yes	—
211	C₂×C₁₉	#3199	1	1	yes	characteristic
212	C₂×C₁₉	#3202	1	1	yes	characteristic
213	C₂×C₁₉	#3203	1	2	yes	—
214	C₂×#41	—	4	1	no	—
215	C₂×#41	—	4	1	no	—
216	C₂×#41	—	4	1	no	—
217	C₂×#41	—	4	1	no	—
218	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
219	C₂×#41	Q₈×C₁₉	1	4	yes	—
220	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
221	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
222	C₂²×D₄	D₄×C₁₉	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
225	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
226	C₂×M₁₆	—	4	1	no	—
227	C₂×M₁₆	—	4	1	no	—
228	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
229	C₂²×C₈	—	4	1	no	—
230	C₂²×C₈	—	4	1	no	—
231	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
232	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
233	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
234	#117	—	4	2	no	—
235	#117	—	4	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	4	2	no	—
238	C₂×C₄⋊C₄	—	4	2	no	—
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₄²	—	2	2	no	—
245	#107	—	4	2	no	—
246	#107	—	4	2	no	—
247	#107	—	4	2	no	—
248	#106	—	4	2	no	—
249	C₂²⋊C₈	C₂×C₄×C₁₉	1	16	yes	complemented
250	#95	—	2	4	no	—
251	#95	—	2	4	no	—
252	C₁₉	#21947	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
254	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
255	#41	—	4	4	no	—
256	#41	—	4	4	no	—
257	#41	—	4	4	no	—
258	#41	—	4	4	no	—
259	C₂×Q₈	—	4	1	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×Q₈	C₄⋊C₄×C₁₉	1	4	yes	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
267	C₂×D₄	C₄⋊C₄×C₁₉	1	8	yes	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	—	8	4	no	—
280	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
284	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
285	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
287	M₁₆	—	4	4	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	4	4	no	—
293	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
294	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	8	4	no	—
302	C₂²⋊C₄	—	8	4	no	—
303	C₄²	—	4	4	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	4	no	—
312	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
313	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
314	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
315	Q₈	—	4	4	no	—
316	D₄	—	4	8	no	—
317	D₄	—	4	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	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	—	2	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	8	8	no	—
337	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
338	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
339	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
341	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
345	C₈	—	2	4	no	—
346	C₈	—	2	4	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	2	no	—
357	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
358	C₂²	C₁₉×#534	1	1	yes	characteristic
359	C₂²	C₁₉×#534	1	1	yes	characteristic
360	C₂²	C₁₉×#576	1	2	yes	—
361	C₂²	C₁₉×#578	1	2	yes	—
362	C₄	—	2	4	no	—
363	C₄	—	2	2	no	—
364	C₄	—	8	4	no	—
365	C₄	—	8	4	no	—
366	C₄	C₁₉×#518	1	1	yes	characteristic
367	C₄	C₁₉×#518	1	1	yes	characteristic
368	C₄	C₁₉×#543	1	1	yes	characteristic
369	C₄	C₁₉×#543	1	1	yes	characteristic
370	C₂	—	4	4	no	—
371	C₂	—	4	2	no	—
372	C₂	C₁₉×#2315	1	1	yes	characteristic
373	C₂	C₁₉×#2913	1	2	yes	—
374	C₂	C₁₉×#3199	1	1	yes	characteristic
375	C₂	C₁₉×#3202	1	1	yes	characteristic
376	C₂	C₁₉×#3203	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1854	C₂	semidirect
4. C₁₉×#1852	C₂	semidirect
5. C₁₉×#1809	C₂	semidirect
6. C₁₉×#1808	C₂	semidirect
16. C₁₉×#408	C₄	semidirect
40. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
43. C₂²×C₈×C₁₉	C₂×C₄	semidirect
61. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
115. #21947	C₁₉	direct (N × H)
161. #1854	C₂×C₁₉	semidirect
162. #1852	C₂×C₁₉	semidirect
163. #1809	C₂×C₁₉	semidirect
164. #1808	C₂×C₁₉	semidirect
197. #408	C₄×C₁₉	semidirect
228. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
231. C₂²×C₈	C₂×C₄×C₁₉	semidirect
249. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
252. C₁₉	#21947	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×#408	2
C₁₉×#2311	2
C₁₉×#1854	2
C₁₉×#1852	2
C₁₉×#1809	2
C₁₉×#1808	2
#21947	19

Subgroups — C19×#21947 #18027906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21947 #18027906