Subgroups — C₁₉×#21622 #18027581

Order 4864.

792 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#479	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2330	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2276	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#479	C₄	1	8	yes	complemented
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#387	—	2	1	no	—
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₁₉×#376	—	2	1	no	—
49	C₁₉×#376	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₁₉	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₁₉	Q₈	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂×C₄	1	4	yes	—
101	C₁₉×#106	—	2	2	no	—
102	C₁₉×#106	—	2	2	no	—
103	C₁₉×#106	C₂×C₄	1	4	yes	—
104	C₁₉×C₄⋊C₈	—	2	2	no	—
105	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	C₂×C₄	1	4	yes	—
109	C₁₉×#103	C₂×C₄	1	4	yes	—
110	C₁₉×#97	—	2	2	no	—
111	C₄×C₈×C₁₉	—	2	2	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	D₄	1	1	yes	characteristic
120	C₁₉×#95	D₄	1	1	yes	characteristic
121	C₁₉×#95	D₄	1	1	yes	characteristic
122	C₁₉×#95	D₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
128	C₂×Q₈×C₁₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	4	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	8	1	no	—
171	C₄⋊C₄×C₁₉	—	8	1	no	—
172	C₄⋊C₄×C₁₉	—	8	1	no	—
173	C₄⋊C₄×C₁₉	—	8	1	no	—
174	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
175	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
176	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
178	C₄⋊C₄×C₁₉	#41	1	2	yes	—
179	C₄²×C₁₉	—	2	4	no	—
180	C₄²×C₁₉	—	2	4	no	—
181	C₄²×C₁₉	—	2	4	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	8	1	no	—
185	C₄²×C₁₉	—	8	1	no	—
186	C₄²×C₁₉	—	8	1	no	—
187	C₄²×C₁₉	—	8	1	no	—
188	C₄²×C₁₉	—	8	1	no	—
189	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
190	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
191	C₄²×C₁₉	#41	1	2	yes	—
192	C₄²×C₁₉	#41	1	2	yes	—
193	#21622	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₉	—	2	2	no	—
196	Q₈×C₁₉	—	2	2	no	—
197	Q₈×C₁₉	—	2	2	no	—
198	Q₈×C₁₉	C₄×Q₈	1	4	yes	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
239	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
240	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
241	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₈×C₁₉	—	2	2	no	—
248	C₈×C₁₉	—	2	2	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	1	no	—
251	C₂×#479	C₂×C₁₉	1	1	yes	characteristic
252	#2330	C₂×C₁₉	1	1	yes	characteristic
253	#2276	C₂×C₁₉	1	1	yes	characteristic
254	#1989	C₂×C₁₉	1	1	yes	characteristic
255	#1948	C₂×C₁₉	1	1	yes	characteristic
256	#1921	C₂×C₁₉	1	1	yes	characteristic
257	#1920	C₂×C₁₉	1	1	yes	characteristic
258	#1865	C₂×C₁₉	1	1	yes	characteristic
259	#1865	C₂×C₁₉	1	1	yes	characteristic
260	#1803	C₂×C₁₉	1	1	yes	characteristic
261	#1776	C₂×C₁₉	1	1	yes	characteristic
262	C₄×#106	C₂×C₁₉	1	1	yes	characteristic
263	#1768	C₂×C₁₉	1	1	yes	characteristic
264	#1763	C₂×C₁₉	1	1	yes	characteristic
265	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
266	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	C₂²×C₁₉	#525	1	1	yes	characteristic
269	C₂²×C₁₉	#577	1	1	yes	characteristic
270	C₂²×C₁₉	#577	1	1	yes	characteristic
271	C₂²×C₁₉	#577	1	1	yes	characteristic
272	C₂²×C₁₉	#578	1	1	yes	characteristic
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	2	2	no	—
276	C₄×C₁₉	—	2	2	no	—
277	C₄×C₁₉	—	2	4	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
288	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
289	C₄×C₁₉	#529	1	1	yes	characteristic
290	C₄×C₁₉	#533	1	1	yes	characteristic
291	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
295	#479	C₄×C₁₉	1	8	yes	complemented
296	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
308	#389	—	2	1	no	—
309	#389	—	2	1	no	—
310	#389	C₂²×C₁₉	1	1	yes	characteristic
311	#389	C₂²×C₁₉	1	1	yes	characteristic
312	#387	—	2	1	no	—
313	#387	—	2	1	no	—
314	#384	C₂²×C₁₉	1	1	yes	characteristic
315	C₄×C₄⋊C₄	—	2	1	no	—
316	C₄×C₄⋊C₄	—	2	1	no	—
317	C₄×C₄⋊C₄	—	2	1	no	—
318	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
320	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
321	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
322	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
323	#376	—	2	1	no	—
324	#376	C₂²×C₁₉	1	1	yes	characteristic
325	#340	C₂²×C₁₉	1	1	yes	characteristic
326	#340	C₂²×C₁₉	1	1	yes	characteristic
327	#340	C₂²×C₁₉	1	1	yes	characteristic
328	#340	C₂²×C₁₉	1	1	yes	characteristic
329	#340	C₂²×C₁₉	1	1	yes	characteristic
330	#340	C₂²×C₁₉	1	1	yes	characteristic
331	#340	C₂²×C₁₉	1	1	yes	characteristic
332	#340	C₂²×C₁₉	1	1	yes	characteristic
333	#336	C₂²×C₁₉	1	1	yes	characteristic
334	#336	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₁₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
336	C₂×C₁₉	#2947	1	1	yes	characteristic
337	C₂×C₁₉	#2952	1	1	yes	characteristic
338	C₂×C₁₉	#3082	1	1	yes	characteristic
339	C₂×C₁₉	#3084	1	1	yes	characteristic
340	C₂×C₁₉	#3120	1	1	yes	characteristic
341	C₂×C₁₉	#3126	1	1	yes	characteristic
342	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
347	#125	—	2	2	no	—
348	#125	C₂×C₄×C₁₉	1	4	yes	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
354	C₄×Q₈	Q₈×C₁₉	1	4	yes	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
382	#107	C₂×C₄×C₁₉	1	4	yes	—
383	#106	—	2	2	no	—
384	#106	—	2	2	no	—
385	#106	C₂×C₄×C₁₉	1	4	yes	—
386	C₄⋊C₈	—	2	2	no	—
387	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	C₂×C₄×C₁₉	1	4	yes	—
391	#103	C₂×C₄×C₁₉	1	4	yes	—
392	#97	—	2	2	no	—
393	C₄×C₈	—	2	2	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	D₄×C₁₉	1	1	yes	characteristic
402	#95	D₄×C₁₉	1	1	yes	characteristic
403	#95	D₄×C₁₉	1	1	yes	characteristic
404	#95	D₄×C₁₉	1	1	yes	characteristic
405	C₁₉	#21622	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
410	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
411	C₂×Q₈	#41×C₁₉	1	2	yes	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
438	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₄⋊C₄	—	8	1	no	—
455	C₄⋊C₄	—	8	1	no	—
456	C₄⋊C₄	—	8	1	no	—
457	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
458	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
459	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
460	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
461	C₄⋊C₄	#41×C₁₉	1	2	yes	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	8	1	no	—
468	C₄²	—	8	1	no	—
469	C₄²	—	8	1	no	—
470	C₄²	—	8	1	no	—
471	C₄²	—	8	1	no	—
472	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
473	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
474	C₄²	#41×C₁₉	1	2	yes	—
475	C₄²	#41×C₁₉	1	2	yes	—
476	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	C₄×Q₈×C₁₉	1	4	yes	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
520	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
521	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
522	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
523	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
526	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
527	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
529	C₈	—	2	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
534	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
535	C₂²	C₁₉×#525	1	1	yes	characteristic
536	C₂²	C₁₉×#577	1	1	yes	characteristic
537	C₂²	C₁₉×#577	1	1	yes	characteristic
538	C₂²	C₁₉×#577	1	1	yes	characteristic
539	C₂²	C₁₉×#578	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	4	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
555	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
556	C₄	C₁₉×#529	1	1	yes	characteristic
557	C₄	C₁₉×#533	1	1	yes	characteristic
558	C₂	C₄×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
559	C₂	C₁₉×#2947	1	1	yes	characteristic
560	C₂	C₁₉×#2952	1	1	yes	characteristic
561	C₂	C₁₉×#3082	1	1	yes	characteristic
562	C₂	C₁₉×#3084	1	1	yes	characteristic
563	C₂	C₁₉×#3120	1	1	yes	characteristic
564	C₂	C₁₉×#3126	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
20. C₁₉×#479	C₄	semidirect
193. #21622	C₁₉	direct (N × H)
295. #479	C₄×C₁₉	semidirect
405. C₁₉	#21622	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×#479	2
C₁₉×#2330	2
C₁₉×#2276	2
C₁₉×#1989	2
C₁₉×#1948	2
C₁₉×#1921	2
C₁₉×#1920	2
C₁₉×#1865	2
C₁₉×#1803	2
C₁₉×#1776	2
C₄×C₁₉×#106	2
C₁₉×#1768	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#21622	19

Subgroups — C19×#21622 #18027581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21622 #18027581