Subgroups — C₁₉×#21046 #18027005

Order 4864.

1178 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1923	C₂	1	8	yes	maximal, complemented
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#424	—	2	4	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
18	C₁₉×#408	—	2	4	no	—
19	C₁₉×#408	—	2	4	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₁₉	—	2	4	no	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	—
24	C₁₉×#391	C₄	1	2	yes	—
25	C₁₉×#390	C₄	1	2	yes	—
26	C₁₉×#386	C₄	1	4	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
28	C₁₉×#336	C₂²	1	4	yes	—
29	C₁₉×#336	C₂²	1	4	yes	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂²×C₈×C₁₉	—	2	2	no	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₂²×C₈×C₁₉	D₄	1	4	yes	—
53	C₂²×C₈×C₁₉	D₄	1	4	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
62	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₉	—	2	2	no	—
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
68	C₁₉×C₄⋊C₈	—	2	8	no	—
69	C₁₉×C₂²⋊C₈	—	2	8	no	—
70	C₁₉×C₂²⋊C₈	—	2	8	no	—
71	C₄×C₈×C₁₉	—	2	8	no	—
72	C₁₉×#95	C₂×C₄	1	8	yes	—
73	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₉	—	4	4	no	—
76	#41×C₁₉	—	4	4	no	—
77	#41×C₁₉	—	4	4	no	—
78	#41×C₁₉	—	4	4	no	—
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	4	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	#41	1	2	yes	—
103	C₂²×C₄×C₁₉	#41	1	2	yes	—
104	C₂²×C₄×C₁₉	#41	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₁₉	—	4	4	no	—
108	M₁₆×C₁₉	—	4	4	no	—
109	C₂×C₈×C₁₉	—	2	8	no	—
110	C₂×C₈×C₁₉	—	2	8	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
122	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₂²⋊C₄×C₁₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₉	—	2	16	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	#21046	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	8	no	—
137	C₂³×C₁₉	#117	1	2	yes	—
138	C₂³×C₁₉	C₄×D₄	1	2	yes	—
139	C₂³×C₁₉	C₄×D₄	1	2	yes	—
140	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
141	Q₈×C₁₉	—	4	4	no	—
142	D₄×C₁₉	—	4	8	no	—
143	D₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	2	16	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	8	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	#117	1	2	yes	—
157	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₁₉	#121	1	4	yes	—
160	C₂×C₄×C₁₉	#123	1	4	yes	—
161	C₂×C₄×C₁₉	#124	1	4	yes	—
162	C₂×C₄×C₁₉	#126	1	4	yes	—
163	C₂×C₄×C₁₉	#131	1	8	yes	—
164	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
170	C₈×C₁₉	—	2	4	no	—
171	C₈×C₁₉	—	2	4	no	—
172	C₈×C₁₉	—	4	2	no	—
173	C₈×C₁₉	—	4	2	no	—
174	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
175	C₂×#408	C₂×C₁₉	1	1	yes	characteristic
176	C₂×#408	C₂×C₁₉	1	1	yes	characteristic
177	C₂²×C₄×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
178	#2297	C₂×C₁₉	1	1	yes	characteristic
179	#1923	C₂×C₁₉	1	8	yes	complemented
180	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#1728	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	#388	1	4	yes	—
190	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#131	1	4	yes	—
194	C₄×C₁₉	—	2	8	no	—
195	C₄×C₁₉	—	4	4	no	—
196	C₄×C₁₉	—	4	2	no	—
197	C₄×C₁₉	#388	1	4	yes	—
198	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
199	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
200	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
201	C₄×C₁₉	C₂×#126	1	1	yes	characteristic
202	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
203	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
204	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
205	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
206	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
208	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
209	#424	—	2	4	no	—
210	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
211	#408	—	2	4	no	—
212	#408	—	2	4	no	—
213	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
215	C₂×C₄×C₈	—	2	4	no	—
216	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	—
217	#391	C₄×C₁₉	1	2	yes	—
218	#390	C₄×C₁₉	1	2	yes	—
219	#386	C₄×C₁₉	1	4	yes	—
220	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
221	#336	C₂²×C₁₉	1	4	yes	—
222	#336	C₂²×C₁₉	1	4	yes	—
223	C₂×C₁₉	—	2	4	no	—
224	C₂×C₁₉	—	8	2	no	—
225	C₂×C₁₉	C₂×#388	1	1	yes	characteristic
226	C₂×C₁₉	#2922	1	2	yes	—
227	C₂×C₁₉	#2929	1	2	yes	—
228	C₂×C₁₉	#2931	1	2	yes	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
236	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
237	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
240	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	D₄×C₁₉	1	4	yes	—
252	C₂²×C₈	D₄×C₁₉	1	4	yes	—
253	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
267	C₄⋊C₈	—	2	8	no	—
268	C₂²⋊C₈	—	2	8	no	—
269	C₂²⋊C₈	—	2	8	no	—
270	C₄×C₈	—	2	8	no	—
271	#95	C₂×C₄×C₁₉	1	8	yes	—
272	C₁₉	#21046	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
274	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
275	#41	—	4	4	no	—
276	#41	—	4	4	no	—
277	#41	—	4	4	no	—
278	#41	—	4	4	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
298	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
302	C₂²×C₄	#41×C₁₉	1	2	yes	—
303	C₂²×C₄	#41×C₁₉	1	2	yes	—
304	C₂²×C₄	#41×C₁₉	1	2	yes	—
305	C₂²×C₄	#41×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
307	M₁₆	—	4	4	no	—
308	M₁₆	—	4	4	no	—
309	C₂×C₈	—	2	8	no	—
310	C₂×C₈	—	2	8	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
322	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	16	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	8	no	—
336	C₂³	C₁₉×#117	1	2	yes	—
337	C₂³	C₄×D₄×C₁₉	1	2	yes	—
338	C₂³	C₄×D₄×C₁₉	1	2	yes	—
339	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
340	Q₈	—	4	4	no	—
341	D₄	—	4	8	no	—
342	D₄	—	4	4	no	—
343	C₂×C₄	—	2	16	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	C₁₉×#117	1	2	yes	—
356	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
357	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
358	C₂×C₄	C₁₉×#121	1	4	yes	—
359	C₂×C₄	C₁₉×#123	1	4	yes	—
360	C₂×C₄	C₁₉×#124	1	4	yes	—
361	C₂×C₄	C₁₉×#126	1	4	yes	—
362	C₂×C₄	C₁₉×#131	1	8	yes	—
363	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	2	4	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	C₁₉×#388	1	4	yes	—
381	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
382	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
383	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
384	C₂²	C₂×C₁₉×#131	1	4	yes	—
385	C₄	—	2	8	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	C₁₉×#388	1	4	yes	—
389	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
390	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
391	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
392	C₄	C₂×C₁₉×#126	1	1	yes	characteristic
393	C₂	—	2	4	no	—
394	C₂	—	8	2	no	—
395	C₂	C₂×C₁₉×#388	1	1	yes	characteristic
396	C₂	C₁₉×#2922	1	2	yes	—
397	C₂	C₁₉×#2929	1	2	yes	—
398	C₂	C₁₉×#2931	1	2	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	C₂²×#41×C₁₉	C₂²
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
1. C₂×C₁₉×#424	C₂	semidirect
4. C₂²×C₄×C₈×C₁₉	C₂	semidirect
6. C₁₉×#1923	C₂	semidirect
7. C₁₉×#1729	C₂	semidirect
8. C₁₉×#1728	C₂	semidirect
131. #21046	C₁₉	direct (N × H)
174. C₂×#424	C₂×C₁₉	semidirect
177. C₂²×C₄×C₈	C₂×C₁₉	semidirect
179. #1923	C₂×C₁₉	semidirect
180. #1729	C₂×C₁₉	semidirect
181. #1728	C₂×C₁₉	semidirect
272. C₁₉	#21046	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×#424	2
C₂×C₁₉×#408	2
C₂²×C₄×C₈×C₁₉	2
C₁₉×#2297	2
C₁₉×#1923	2
C₁₉×#1729	2
C₁₉×#1728	2
#21046	19

Subgroups — C19×#21046 #18027005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21046 #18027005