Subgroups — C₁₉×#20836 #18026795

Order 4864.

1542 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1851	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1850	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1729	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	—	2	4	no	—
10	C₂²×M₁₆×C₁₉	—	2	8	no	—
11	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₁₉×#424	—	2	8	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	8	yes	complemented
19	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₁₉×#381	C₄	1	2	yes	—
23	C₁₉×#380	C₄	1	2	yes	—
24	C₁₉×#380	C₄	1	2	yes	—
25	C₁₉×#379	C₄	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#336	C₂²	1	8	yes	complemented
29	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	4	no	—
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	4	yes	—
36	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	—	2	32	no	—
41	C₂×M₁₆×C₁₉	—	2	4	no	—
42	C₂×M₁₆×C₁₉	—	2	4	no	—
43	C₂×M₁₆×C₁₉	—	2	4	no	—
44	C₂×M₁₆×C₁₉	—	2	8	no	—
45	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
46	C₂²×C₈×C₁₉	—	2	4	no	—
47	C₂²×C₈×C₁₉	—	2	8	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	4	no	—
51	C₂²×C₈×C₁₉	—	2	4	no	—
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
55	C₁₉×#117	—	2	4	no	—
56	C₁₉×#117	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
62	C₁₉×C₄⋊C₈	—	2	16	no	—
63	C₁₉×C₂²⋊C₈	—	2	4	no	—
64	C₁₉×C₂²⋊C₈	—	2	4	no	—
65	C₁₉×#95	C₂×C₄	1	4	yes	—
66	C₁₉×#95	C₂×C₄	1	4	yes	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	4	2	no	—
70	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
71	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	8	no	—
78	C₂²×C₄×C₁₉	—	2	16	no	—
79	C₂²×C₄×C₁₉	—	2	8	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	2	no	—
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₉	#41	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₁₉	—	2	16	no	—
101	M₁₆×C₁₉	—	2	16	no	—
102	C₂×C₈×C₁₉	—	2	16	no	—
103	C₂×C₈×C₁₉	—	2	4	no	—
104	C₂×C₈×C₁₉	—	2	4	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	4	no	—
108	C₂×C₈×C₁₉	—	2	4	no	—
109	C₂×C₈×C₁₉	—	4	4	no	—
110	C₂×C₈×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₂²⋊C₄×C₁₉	—	2	8	no	—
114	C₂²⋊C₄×C₁₉	—	2	8	no	—
115	C₂²⋊C₄×C₁₉	—	4	4	no	—
116	C₄²×C₁₉	—	2	4	no	—
117	C₄²×C₁₉	—	2	4	no	—
118	#20836	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	8	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	4	4	no	—
129	C₂³×C₁₉	—	4	16	no	—
130	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
131	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
132	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₁₉	C₄×D₄	1	4	yes	—
134	C₂³×C₁₉	#131	1	4	yes	—
135	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	8	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	8	no	—
146	C₂×C₄×C₁₉	—	2	8	no	—
147	C₂×C₄×C₁₉	—	2	8	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
154	C₂×C₄×C₁₉	#120	1	4	yes	—
155	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
156	C₂×C₄×C₁₉	#123	1	4	yes	—
157	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
161	C₈×C₁₉	—	2	8	no	—
162	C₈×C₁₉	—	4	2	no	—
163	C₈×C₁₉	—	4	2	no	—
164	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic
165	C₂×#424	C₂×C₁₉	1	2	yes	complemented
166	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
167	#2280	C₂×C₁₉	1	1	yes	characteristic
168	#1851	C₂×C₁₉	1	4	yes	complemented
169	#1850	C₂×C₁₉	1	4	yes	complemented
170	#1729	C₂×C₁₉	1	2	yes	complemented
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	8	no	—
175	C₂²×C₁₉	—	2	8	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	4	16	no	—
181	C₂²×C₁₉	—	4	4	no	—
182	C₂²×C₁₉	#385	1	4	yes	—
183	C₂²×C₁₉	#424	1	4	yes	complemented
184	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
186	C₂²×C₁₉	C₂×#131	1	2	yes	—
187	C₂²×C₁₉	#568	1	2	yes	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	—	4	8	no	—
191	C₄×C₁₉	#385	1	4	yes	—
192	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
193	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
194	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
195	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
196	C₂²×M₁₆	—	2	4	no	—
197	C₂²×M₁₆	—	2	8	no	—
198	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
199	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
200	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
201	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
202	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×#117	C₂²×C₁₉	1	2	yes	—
204	#424	—	2	8	no	—
205	C₂×C₄⋊C₈	C₂²×C₁₉	1	8	yes	complemented
206	C₂×C₂²⋊C₈	—	2	4	no	—
207	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
209	#381	C₄×C₁₉	1	2	yes	—
210	#380	C₄×C₁₉	1	2	yes	—
211	#380	C₄×C₁₉	1	2	yes	—
212	#379	C₄×C₁₉	1	2	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
214	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
215	#336	C₂²×C₁₉	1	8	yes	complemented
216	C₂×C₁₉	—	2	4	no	—
217	C₂×C₁₉	—	2	4	no	—
218	C₂×C₁₉	—	4	2	no	—
219	C₂×C₁₉	C₂×#385	1	1	yes	characteristic
220	C₂×C₁₉	C₂×#424	1	1	yes	characteristic
221	C₂×C₁₉	#2905	1	1	yes	characteristic
222	C₂×C₁₉	#2933	1	4	yes	—
223	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
224	C₂³×C₄	—	2	4	no	—
225	C₂³×C₄	—	2	4	no	—
226	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
228	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₁₉	1	4	yes	—
230	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
231	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₂×M₁₆	—	2	32	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	—	2	4	no	—
237	C₂×M₁₆	—	2	4	no	—
238	C₂×M₁₆	—	2	8	no	—
239	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
240	C₂²×C₈	—	2	4	no	—
241	C₂²×C₈	—	2	8	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	—	2	4	no	—
246	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
249	#117	—	2	4	no	—
250	#117	—	2	4	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
252	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
255	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
256	C₄⋊C₈	—	2	16	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₂²⋊C₈	—	2	4	no	—
259	#95	C₂×C₄×C₁₉	1	4	yes	—
260	#95	C₂×C₄×C₁₉	1	4	yes	—
261	C₁₉	#20836	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	4	2	no	—
265	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
266	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
267	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
268	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
280	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
281	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
283	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
290	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
291	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
292	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
293	C₂²×C₄	#41×C₁₉	1	4	yes	—
294	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
295	M₁₆	—	2	16	no	—
296	M₁₆	—	2	16	no	—
297	C₂×C₈	—	2	16	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
307	C₄⋊C₄	—	2	8	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	4	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	16	no	—
324	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
325	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
326	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
327	C₂³	C₄×D₄×C₁₉	1	4	yes	—
328	C₂³	C₁₉×#131	1	4	yes	—
329	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
345	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
346	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
347	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
348	C₂×C₄	C₁₉×#120	1	4	yes	—
349	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
350	C₂×C₄	C₁₉×#123	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
352	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
354	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
355	C₈	—	2	8	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	2	8	no	—
359	C₂²	—	2	8	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	16	no	—
368	C₂²	—	4	4	no	—
369	C₂²	C₁₉×#385	1	4	yes	—
370	C₂²	C₁₉×#424	1	4	yes	complemented
371	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
372	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
373	C₂²	C₂×C₁₉×#131	1	2	yes	—
374	C₂²	C₁₉×#568	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	8	no	—
378	C₄	C₁₉×#385	1	4	yes	—
379	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
380	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
381	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
382	C₂	—	2	4	no	—
383	C₂	—	2	4	no	—
384	C₂	—	4	2	no	—
385	C₂	C₂×C₁₉×#385	1	1	yes	characteristic
386	C₂	C₂×C₁₉×#424	1	1	yes	characteristic
387	C₂	C₁₉×#2905	1	1	yes	characteristic
388	C₂	C₁₉×#2933	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#424	C₂	semidirect
5. C₁₉×#1851	C₂	semidirect
6. C₁₉×#1850	C₂	semidirect
7. C₁₉×#1729	C₂	semidirect
18. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
28. C₁₉×#336	C₂²	semidirect
118. #20836	C₁₉	direct (N × H)
165. C₂×#424	C₂×C₁₉	semidirect
168. #1851	C₂×C₁₉	semidirect
169. #1850	C₂×C₁₉	semidirect
170. #1729	C₂×C₁₉	semidirect
183. C₂²×C₁₉	#424	semidirect
205. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
215. #336	C₂²×C₁₉	semidirect
261. C₁₉	#20836	direct (N × H)
370. C₂²	C₁₉×#424	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂×C₁₉×#424	2
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#2280	2
C₁₉×#1851	2
C₁₉×#1850	2
C₁₉×#1729	2
#20836	19

Subgroups — C19×#20836 #18026795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20836 #18026795