Subgroups — C₁₉×#11070 #18017029

Order 4864.

1202 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2315	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#381	C₂	1	2	yes	maximal
3	C₂×C₁₉×#381	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#342	C₂	1	2	yes	maximal
5	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#385	—	2	4	no	—
12	C₁₉×#381	—	2	4	no	—
13	C₁₉×#381	—	2	4	no	—
14	C₁₉×#381	—	2	2	no	—
15	C₁₉×#381	C₄	1	4	yes	complemented
16	C₁₉×#380	—	2	2	no	—
17	C₂×C₁₉×#95	—	2	4	no	—
18	C₂×C₁₉×#95	—	2	2	no	—
19	C₁₉×#342	—	2	2	no	—
20	C₁₉×#342	—	2	4	no	—
21	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	—	2	2	no	—
24	C₂³×C₄×C₁₉	—	2	1	no	—
25	C₂³×C₄×C₁₉	—	2	2	no	—
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	2	2	no	—
29	C₂³×C₄×C₁₉	—	2	2	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₉	D₄	1	4	yes	—
35	C₂³×C₄×C₁₉	D₄	1	2	yes	—
36	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
58	C₁₉×#95	—	2	16	no	—
59	C₁₉×#95	—	2	4	no	—
60	C₁₉×#95	—	2	8	no	—
61	C₂⁴×C₁₉	—	4	4	no	—
62	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
65	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
68	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
69	C₂⁴×C₁₉	#41	1	1	yes	characteristic
70	C₂⁴×C₁₉	#41	1	1	yes	characteristic
71	C₂⁴×C₁₉	#41	1	2	yes	—
72	C₂⁴×C₁₉	#41	1	2	yes	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	4	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
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	4	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	4	no	—
103	C₂²×C₄×C₁₉	—	4	8	no	—
104	C₂²×C₄×C₁₉	—	4	4	no	—
105	C₂²×C₄×C₁₉	—	4	8	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
111	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
112	C₄⋊C₄×C₁₉	—	8	4	no	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂²⋊C₄×C₁₉	—	2	4	no	—
117	C₂²⋊C₄×C₁₉	—	2	4	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	—	4	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	2	no	—
125	#11070	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	4	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₉	#117	1	1	yes	characteristic
140	C₂³×C₁₉	C₄×D₄	1	2	yes	—
141	C₂³×C₁₉	C₄×D₄	1	2	yes	—
142	C₂³×C₁₉	#120	1	2	yes	—
143	C₂³×C₁₉	#120	1	1	yes	characteristic
144	C₂³×C₁₉	#121	1	1	yes	characteristic
145	C₂³×C₁₉	#121	1	2	yes	—
146	C₂³×C₁₉	#121	1	2	yes	—
147	C₂³×C₁₉	#121	1	1	yes	characteristic
148	C₂³×C₁₉	#121	1	2	yes	—
149	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
151	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
153	C₂³×C₁₉	#123	1	1	yes	characteristic
154	C₂³×C₁₉	#123	1	2	yes	—
155	C₂³×C₁₉	#123	1	2	yes	—
156	C₂³×C₁₉	#124	1	2	yes	—
157	C₂³×C₁₉	#124	1	1	yes	characteristic
158	C₂³×C₁₉	#126	1	2	yes	—
159	C₂³×C₁₉	#127	1	1	yes	characteristic
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	8	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	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	2	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	4	4	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	8	no	—
176	C₂×C₄×C₁₉	—	4	8	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	8	no	—
181	C₂×C₄×C₁₉	—	8	2	no	—
182	C₂×C₄×C₁₉	—	8	4	no	—
183	C₂×C₄×C₁₉	—	8	2	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	—	8	4	no	—
186	C₂×C₄×C₁₉	—	8	4	no	—
187	#2315	C₂×C₁₉	1	1	yes	characteristic
188	C₂×#381	C₂×C₁₉	1	2	yes	—
189	C₂×#381	C₂×C₁₉	1	1	yes	characteristic
190	C₂×#342	C₂×C₁₉	1	2	yes	—
191	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	2	4	no	—
197	C₂²×C₁₉	—	2	4	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	4	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	4	no	—
204	C₂²×C₁₉	—	4	1	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	#380	1	1	yes	characteristic
215	C₂²×C₁₉	#385	1	2	yes	—
216	C₂²×C₁₉	#386	1	1	yes	characteristic
217	C₂²×C₁₉	#388	1	2	yes	—
218	C₂²×C₁₉	#390	1	1	yes	characteristic
219	C₂²×C₁₉	#392	1	1	yes	characteristic
220	C₂²×C₁₉	#393	1	1	yes	characteristic
221	C₂²×C₁₉	#394	1	2	yes	—
222	C₂²×C₁₉	#396	1	2	yes	—
223	C₂²×C₁₉	#397	1	1	yes	characteristic
224	C₂²×C₁₉	#399	1	1	yes	characteristic
225	C₂²×C₁₉	#458	1	4	yes	—
226	C₄×C₁₉	—	4	4	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	4	no	—
230	C₄×C₁₉	—	8	4	no	—
231	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
236	#385	—	2	4	no	—
237	#381	—	2	4	no	—
238	#381	—	2	4	no	—
239	#381	—	2	2	no	—
240	#381	C₄×C₁₉	1	4	yes	complemented
241	#380	—	2	2	no	—
242	C₂×#95	—	2	4	no	—
243	C₂×#95	—	2	2	no	—
244	#342	—	2	2	no	—
245	#342	—	2	4	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	—	2	2	no	—
248	C₂×C₁₉	—	2	1	no	—
249	C₂×C₁₉	—	2	2	no	—
250	C₂×C₁₉	—	2	2	no	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	#1439	1	1	yes	characteristic
255	C₂×C₁₉	#1890	1	2	yes	—
256	C₂×C₁₉	#2022	1	2	yes	—
257	C₂×C₁₉	#2030	1	2	yes	—
258	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	2	2	no	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
270	C₂³×C₄	D₄×C₁₉	1	2	yes	—
271	C₂³×C₄	D₄×C₁₉	1	4	yes	—
272	C₂³×C₄	D₄×C₁₉	1	2	yes	—
273	C₂³×C₄	Q₈×C₁₉	1	2	yes	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
293	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
294	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
295	#95	—	2	16	no	—
296	#95	—	2	4	no	—
297	#95	—	2	8	no	—
298	C₁₉	#11070	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	4	4	no	—
300	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
301	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
302	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
303	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
305	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
306	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
307	C₂⁴	#41×C₁₉	1	1	yes	characteristic
308	C₂⁴	#41×C₁₉	1	1	yes	characteristic
309	C₂⁴	#41×C₁₉	1	2	yes	—
310	C₂⁴	#41×C₁₉	1	2	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	8	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	8	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
349	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	complemented
350	C₄⋊C₄	—	8	4	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	4	no	—
374	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
375	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
376	C₂³	C₁₉×#117	1	1	yes	characteristic
377	C₂³	C₄×D₄×C₁₉	1	2	yes	—
378	C₂³	C₄×D₄×C₁₉	1	2	yes	—
379	C₂³	C₁₉×#120	1	2	yes	—
380	C₂³	C₁₉×#120	1	1	yes	characteristic
381	C₂³	C₁₉×#121	1	1	yes	characteristic
382	C₂³	C₁₉×#121	1	2	yes	—
383	C₂³	C₁₉×#121	1	2	yes	—
384	C₂³	C₁₉×#121	1	1	yes	characteristic
385	C₂³	C₁₉×#121	1	2	yes	—
386	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
387	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
388	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
389	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
390	C₂³	C₁₉×#123	1	1	yes	characteristic
391	C₂³	C₁₉×#123	1	2	yes	—
392	C₂³	C₁₉×#123	1	2	yes	—
393	C₂³	C₁₉×#124	1	2	yes	—
394	C₂³	C₁₉×#124	1	1	yes	characteristic
395	C₂³	C₁₉×#126	1	2	yes	—
396	C₂³	C₁₉×#127	1	1	yes	characteristic
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	4	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	4	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	C₁₉×#380	1	1	yes	characteristic
447	C₂²	C₁₉×#385	1	2	yes	—
448	C₂²	C₁₉×#386	1	1	yes	characteristic
449	C₂²	C₁₉×#388	1	2	yes	—
450	C₂²	C₁₉×#390	1	1	yes	characteristic
451	C₂²	C₁₉×#392	1	1	yes	characteristic
452	C₂²	C₁₉×#393	1	1	yes	characteristic
453	C₂²	C₁₉×#394	1	2	yes	—
454	C₂²	C₁₉×#396	1	2	yes	—
455	C₂²	C₁₉×#397	1	1	yes	characteristic
456	C₂²	C₁₉×#399	1	1	yes	characteristic
457	C₂²	C₁₉×#458	1	4	yes	—
458	C₄	—	4	4	no	—
459	C₄	—	4	4	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	4	no	—
462	C₄	—	8	4	no	—
463	C₂	—	2	1	no	—
464	C₂	—	2	2	no	—
465	C₂	—	2	1	no	—
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	2	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	C₁₉×#1439	1	1	yes	characteristic
472	C₂	C₁₉×#1890	1	2	yes	—
473	C₂	C₁₉×#2022	1	2	yes	—
474	C₂	C₁₉×#2030	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₉×#381	C₄	semidirect
111. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
125. #11070	C₁₉	direct (N × H)
240. #381	C₄×C₁₉	semidirect
298. C₁₉	#11070	direct (N × H)
349. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2315	2
C₂×C₁₉×#381	2
C₂×C₁₉×#342	2
#11070	19

Subgroups — C19×#11070 #18017029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11070 #18017029