Subgroups — C₂×C₁₉×#2020 #18029396

Order 4864.

1902 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	2	yes	maximal
2	C₂³×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#101	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2020	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₁₉×#137	—	2	4	no	—
10	C₂×C₁₉×#137	—	2	8	no	—
11	C₂×C₁₉×#137	—	2	8	no	—
12	C₂×C₁₉×#137	C₂²	1	8	yes	—
13	C₂²×Q₁₆×C₁₉	—	2	8	no	—
14	C₂²×Q₁₆×C₁₉	—	2	2	no	—
15	C₂²×Q₁₆×C₁₉	—	2	2	no	—
16	C₂²×Q₁₆×C₁₉	—	2	2	no	—
17	C₂²×Q₁₆×C₁₉	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₁₉	—	2	2	no	—
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#101	—	2	8	no	—
23	C₂×C₁₉×#101	C₂²	1	8	yes	complemented
24	C₁₉×#408	—	2	2	no	—
25	C₁₉×#408	C₂²	1	4	yes	—
26	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
27	C₁₉×#341	C₂²	1	4	yes	complemented
28	C₂×#41×C₁₉	—	2	1	no	—
29	C₂×#41×C₁₉	—	2	1	no	—
30	C₂×#41×C₁₉	—	2	4	no	—
31	C₂×#41×C₁₉	—	2	4	no	—
32	C₂×#41×C₁₉	D₄	1	2	yes	—
33	C₂×#41×C₁₉	C₂³	1	2	yes	—
34	C₂²×Q₈×C₁₉	—	2	4	no	—
35	C₂²×Q₈×C₁₉	—	2	2	no	—
36	C₂²×Q₈×C₁₉	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	4	no	—
38	C₂²×Q₈×C₁₉	—	2	2	no	—
39	C₂²×Q₈×C₁₉	—	2	2	no	—
40	C₂²×Q₈×C₁₉	—	2	2	no	—
41	C₂²×Q₈×C₁₉	—	2	4	no	—
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	D₄	1	8	yes	—
44	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×#137	—	2	32	no	—
51	C₁₉×#137	—	2	16	no	—
52	C₁₉×#137	—	2	16	no	—
53	C₂×Q₁₆×C₁₉	—	2	16	no	—
54	C₂×Q₁₆×C₁₉	—	2	16	no	—
55	C₂×Q₁₆×C₁₉	—	2	16	no	—
56	C₂×Q₁₆×C₁₉	—	2	16	no	—
57	C₂×Q₁₆×C₁₉	—	2	8	no	—
58	C₂×Q₁₆×C₁₉	—	2	8	no	—
59	C₂×SD₁₆×C₁₉	—	2	16	no	—
60	C₂×SD₁₆×C₁₉	—	2	8	no	—
61	C₂×M₁₆×C₁₉	—	2	4	no	—
62	C₂×M₁₆×C₁₉	—	2	2	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₂×M₁₆×C₁₉	—	2	4	no	—
65	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
67	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₉	—	2	4	no	—
69	C₂²×C₈×C₁₉	—	2	2	no	—
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	D₄	1	2	yes	—
72	C₂²×C₈×C₁₉	D₄	1	2	yes	—
73	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
74	C₁₉×#101	—	2	16	no	—
75	C₁₉×C₂²⋊C₈	—	2	8	no	—
76	C₂⁴×C₁₉	—	2	1	no	—
77	C₂⁴×C₁₉	#41	1	1	yes	characteristic
78	#41×C₁₉	—	2	8	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	4	2	no	—
82	#41×C₁₉	—	4	4	no	—
83	#41×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	—	2	8	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	4	no	—
87	C₂×Q₈×C₁₉	—	2	8	no	—
88	C₂×Q₈×C₁₉	—	2	8	no	—
89	C₂×Q₈×C₁₉	—	2	8	no	—
90	C₂×Q₈×C₁₉	—	2	4	no	—
91	C₂×Q₈×C₁₉	—	2	8	no	—
92	C₂×Q₈×C₁₉	—	2	4	no	—
93	C₂×Q₈×C₁₉	—	2	4	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	—	2	4	no	—
96	C₂×Q₈×C₁₉	—	4	4	no	—
97	C₂×Q₈×C₁₉	—	4	4	no	—
98	C₂×Q₈×C₁₉	—	4	2	no	—
99	C₂×Q₈×C₁₉	—	4	2	no	—
100	C₂×Q₈×C₁₉	—	4	4	no	—
101	C₂×Q₈×C₁₉	—	4	4	no	—
102	C₂×Q₈×C₁₉	—	4	4	no	—
103	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	—	2	8	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	2	no	—
120	C₂²×C₄×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₁₉	—	2	32	no	—
130	Q₁₆×C₁₉	—	2	32	no	—
131	SD₁₆×C₁₉	—	2	32	no	—
132	M₁₆×C₁₉	—	2	8	no	—
133	M₁₆×C₁₉	—	2	4	no	—
134	M₁₆×C₁₉	—	2	4	no	—
135	M₁₆×C₁₉	—	4	2	no	—
136	M₁₆×C₁₉	C₂×D₄	1	8	yes	—
137	C₂×C₈×C₁₉	—	2	4	no	—
138	C₂×C₈×C₁₉	—	2	4	no	—
139	C₂×C₈×C₁₉	—	2	8	no	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	4	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	4	2	no	—
144	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
145	C₂×#2020	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	4	4	no	—
150	C₂³×C₁₉	#121	1	4	yes	—
151	C₂³×C₁₉	#121	1	1	yes	characteristic
152	C₂³×C₁₉	#121	1	1	yes	characteristic
153	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
154	Q₈×C₁₉	—	2	8	no	—
155	Q₈×C₁₉	—	2	8	no	—
156	Q₈×C₁₉	—	2	4	no	—
157	Q₈×C₁₉	—	4	4	no	—
158	Q₈×C₁₉	—	4	4	no	—
159	Q₈×C₁₉	—	4	8	no	—
160	Q₈×C₁₉	—	4	8	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	D₄×C₁₉	—	2	4	no	—
163	D₄×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	4	4	no	—
165	D₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	8	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	8	no	—
172	C₂×C₄×C₁₉	—	4	8	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	#120	1	2	yes	—
177	C₂×C₄×C₁₉	#120	1	4	yes	—
178	C₂×C₄×C₁₉	#120	1	2	yes	—
179	C₂×C₄×C₁₉	#120	1	4	yes	—
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	4	yes	—
183	C₂×C₄×C₁₉	#127	1	2	yes	—
184	C₂×C₄×C₁₉	#127	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
189	C₈×C₁₉	—	2	4	no	—
190	C₈×C₁₉	—	2	8	no	—
191	C₈×C₁₉	—	4	2	no	—
192	C₂²×#137	C₂×C₁₉	1	2	yes	—
193	C₂³×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×#101	C₂×C₁₉	1	2	yes	complemented
195	C₂×#408	C₂×C₁₉	1	1	yes	characteristic
196	#2020	C₂×C₁₉	1	8	yes	direct product factor
197	C₂×#341	C₂×C₁₉	1	1	yes	characteristic, complemented
198	C₂²×C₁₉	—	2	8	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	—	8	4	no	—
204	C₂²×C₁₉	#392	1	2	yes	—
205	C₂²×C₁₉	#392	1	2	yes	—
206	C₂²×C₁₉	#473	1	4	yes	—
207	C₂²×C₁₉	C₂×#121	1	2	yes	—
208	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	8	no	—
211	C₄×C₁₉	#392	1	2	yes	—
212	C₄×C₁₉	#392	1	2	yes	—
213	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
214	C₄×C₁₉	C₂×#120	1	2	yes	—
215	C₄×C₁₉	C₂×#127	1	1	yes	characteristic
216	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
217	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
218	C₂×#137	—	2	4	no	—
219	C₂×#137	—	2	8	no	—
220	C₂×#137	—	2	8	no	—
221	C₂×#137	C₂²×C₁₉	1	8	yes	—
222	C₂²×Q₁₆	—	2	8	no	—
223	C₂²×Q₁₆	—	2	2	no	—
224	C₂²×Q₁₆	—	2	2	no	—
225	C₂²×Q₁₆	—	2	2	no	—
226	C₂²×Q₁₆	C₂²×C₁₉	1	4	yes	complemented
227	C₂²×SD₁₆	—	2	2	no	—
228	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
230	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×#101	—	2	8	no	—
232	C₂×#101	C₂²×C₁₉	1	8	yes	complemented
233	#408	—	2	2	no	—
234	#408	C₂²×C₁₉	1	4	yes	—
235	C₂×C₂²⋊C₈	—	2	2	no	—
236	#341	C₂²×C₁₉	1	4	yes	complemented
237	C₂×C₁₉	—	2	2	no	—
238	C₂×C₁₉	—	2	2	no	—
239	C₂×C₁₉	—	8	2	no	—
240	C₂×C₁₉	#2020	1	4	yes	direct product factor
241	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
242	C₂×C₁₉	C₂×#473	1	2	yes	—
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	2	1	no	—
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	D₄×C₁₉	1	2	yes	—
248	C₂×#41	C₂³×C₁₉	1	2	yes	—
249	C₂²×Q₈	—	2	4	no	—
250	C₂²×Q₈	—	2	2	no	—
251	C₂²×Q₈	—	2	2	no	—
252	C₂²×Q₈	—	2	4	no	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	4	no	—
257	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
258	C₂²×Q₈	D₄×C₁₉	1	8	yes	—
259	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	#137	—	2	32	no	—
266	#137	—	2	16	no	—
267	#137	—	2	16	no	—
268	C₂×Q₁₆	—	2	16	no	—
269	C₂×Q₁₆	—	2	16	no	—
270	C₂×Q₁₆	—	2	16	no	—
271	C₂×Q₁₆	—	2	16	no	—
272	C₂×Q₁₆	—	2	8	no	—
273	C₂×Q₁₆	—	2	8	no	—
274	C₂×SD₁₆	—	2	16	no	—
275	C₂×SD₁₆	—	2	8	no	—
276	C₂×M₁₆	—	2	4	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
281	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
282	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
283	C₂²×C₈	—	2	4	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	D₄×C₁₉	1	2	yes	—
287	C₂²×C₈	D₄×C₁₉	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
289	#101	—	2	16	no	—
290	C₂²⋊C₈	—	2	8	no	—
291	C₁₉	C₂×#2020	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	—	2	1	no	—
293	C₂⁴	#41×C₁₉	1	1	yes	characteristic
294	#41	—	2	8	no	—
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	4	2	no	—
298	#41	—	4	4	no	—
299	#41	—	4	2	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	8	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	8	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	4	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	4	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	—	4	4	no	—
319	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
320	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
339	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
343	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	Q₁₆	—	2	32	no	—
346	Q₁₆	—	2	32	no	—
347	SD₁₆	—	2	32	no	—
348	M₁₆	—	2	8	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	4	2	no	—
352	M₁₆	C₂×D₄×C₁₉	1	8	yes	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	8	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	C₁₉×#121	1	4	yes	—
366	C₂³	C₁₉×#121	1	1	yes	characteristic
367	C₂³	C₁₉×#121	1	1	yes	characteristic
368	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
369	Q₈	—	2	8	no	—
370	Q₈	—	2	8	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	8	no	—
373	Q₈	—	4	8	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	4	no	—
376	Q₈	—	4	4	no	—
377	D₄	—	2	4	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	C₁₉×#120	1	2	yes	—
392	C₂×C₄	C₁₉×#120	1	4	yes	—
393	C₂×C₄	C₁₉×#120	1	2	yes	—
394	C₂×C₄	C₁₉×#120	1	4	yes	—
395	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
396	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
397	C₂×C₄	C₁₉×#121	1	4	yes	—
398	C₂×C₄	C₁₉×#127	1	2	yes	—
399	C₂×C₄	C₁₉×#127	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
404	C₈	—	2	4	no	—
405	C₈	—	2	8	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	C₁₉×#392	1	2	yes	—
414	C₂²	C₁₉×#392	1	2	yes	—
415	C₂²	C₁₉×#473	1	4	yes	—
416	C₂²	C₂×C₁₉×#121	1	2	yes	—
417	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
418	C₄	—	4	2	no	—
419	C₄	—	4	8	no	—
420	C₄	C₁₉×#392	1	2	yes	—
421	C₄	C₁₉×#392	1	2	yes	—
422	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
423	C₄	C₂×C₁₉×#120	1	2	yes	—
424	C₄	C₂×C₁₉×#127	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	2	2	no	—
427	C₂	—	8	2	no	—
428	C₂	C₁₉×#2020	1	4	yes	direct product factor
429	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
430	C₂	C₂×C₁₉×#473	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×Q₁₆×C₁₉	C₂	semidirect
3. C₂²×C₁₉×#101	C₂	semidirect
5. C₁₉×#2020	C₂	direct (N × H)
6. C₂×C₁₉×#341	C₂	semidirect
17. C₂²×Q₁₆×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#101	C₂²	semidirect
27. C₁₉×#341	C₂²	semidirect
145. C₂×#2020	C₁₉	direct (N × H)
193. C₂³×Q₁₆	C₂×C₁₉	semidirect
194. C₂²×#101	C₂×C₁₉	semidirect
196. #2020	C₂×C₁₉	direct (N × H)
197. C₂×#341	C₂×C₁₉	semidirect
226. C₂²×Q₁₆	C₂²×C₁₉	semidirect
232. C₂×#101	C₂²×C₁₉	semidirect
236. #341	C₂²×C₁₉	semidirect
240. C₂×C₁₉	#2020	direct (N × H)
291. C₁₉	C₂×#2020	direct (N × H)
428. C₂	C₁₉×#2020	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₂³×Q₁₆×C₁₉	2
C₂²×C₁₉×#101	2
C₂×C₁₉×#408	2
C₁₉×#2020	2
C₂×C₁₉×#341	2
C₂×#2020	19

Subgroups — C2×C19×#2020 #18029396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2020 #18029396