Subgroups — C₁₉×#22871 #18028830

Order 4864.

1098 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2360	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1852	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#451	C₄	1	8	yes	complemented
26	C₄×Q₁₆×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	—	2	4	no	—
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#391	—	2	1	no	—
42	C₁₉×#391	—	2	1	no	—
43	C₁₉×#391	C₂²	1	1	yes	characteristic
44	C₁₉×#391	C₂²	1	1	yes	characteristic
45	C₁₉×#391	C₂²	1	1	yes	characteristic
46	C₁₉×#389	—	2	1	no	—
47	C₁₉×#389	C₂²	1	1	yes	characteristic
48	C₁₉×#387	—	2	1	no	—
49	C₁₉×#385	—	2	1	no	—
50	C₁₉×#380	—	2	1	no	—
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₁₉×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	—	2	1	no	—
63	C₂²×Q₈×C₁₉	—	2	2	no	—
64	C₂²×Q₈×C₁₉	—	2	2	no	—
65	C₂²×Q₈×C₁₉	—	2	2	no	—
66	C₂²×Q₈×C₁₉	—	4	1	no	—
67	C₂²×Q₈×C₁₉	—	4	1	no	—
68	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
69	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	—	2	1	no	—
73	C₂³×C₄×C₁₉	—	2	1	no	—
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×Q₁₆×C₁₉	—	2	2	no	—
76	C₂×Q₁₆×C₁₉	—	2	2	no	—
77	C₂×Q₁₆×C₁₉	—	4	1	no	—
78	C₂×Q₁₆×C₁₉	—	4	1	no	—
79	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
80	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
81	C₂²×C₈×C₁₉	—	2	2	no	—
82	C₂²×C₈×C₁₉	—	2	2	no	—
83	C₂²×C₈×C₁₉	—	4	1	no	—
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	—	2	2	no	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×Q₈×C₁₉	—	4	1	no	—
94	C₄×Q₈×C₁₉	—	4	1	no	—
95	C₄×Q₈×C₁₉	—	4	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₉	—	2	1	no	—
114	C₂×C₄²×C₁₉	—	2	1	no	—
115	C₂×C₄²×C₁₉	—	2	1	no	—
116	C₂×C₄²×C₁₉	—	2	1	no	—
117	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
119	C₁₉×#107	—	2	2	no	—
120	C₁₉×#107	—	4	1	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#103	—	2	2	no	—
125	C₁₉×#103	—	4	1	no	—
126	C₁₉×#103	C₂×C₄	1	4	yes	complemented
127	C₁₉×#103	C₂×C₄	1	4	yes	complemented
128	C₁₉×#103	D₄	1	4	yes	—
129	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
130	C₄×C₈×C₁₉	—	2	2	no	—
131	C₄×C₈×C₁₉	—	4	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	—	2	1	no	—
137	C₁₉×#95	—	2	1	no	—
138	C₁₉×#95	—	2	1	no	—
139	C₁₉×#95	—	2	1	no	—
140	C₁₉×#95	—	2	1	no	—
141	C₁₉×#95	D₄	1	1	yes	characteristic
142	C₁₉×#95	D₄	1	1	yes	characteristic
143	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₁₉	—	2	4	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	8	no	—
151	C₂×Q₈×C₁₉	—	2	1	no	—
152	C₂×Q₈×C₁₉	—	2	1	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	2	1	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	4	2	no	—
160	C₂×Q₈×C₁₉	—	4	2	no	—
161	C₂×Q₈×C₁₉	—	4	4	no	—
162	C₂×Q₈×C₁₉	—	4	4	no	—
163	C₂×Q₈×C₁₉	—	4	4	no	—
164	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
165	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
166	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
167	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
168	C₂×Q₈×C₁₉	#41	1	2	yes	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	4	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	4	2	no	—
183	C₂²×C₄×C₁₉	—	4	2	no	—
184	C₂²×C₄×C₁₉	—	4	2	no	—
185	C₂²×C₄×C₁₉	—	4	2	no	—
186	C₂²×C₄×C₁₉	—	8	1	no	—
187	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	#41	1	2	yes	—
194	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
195	Q₁₆×C₁₉	—	2	8	no	—
196	Q₁₆×C₁₉	—	4	4	no	—
197	C₂×C₈×C₁₉	—	2	1	no	—
198	C₂×C₈×C₁₉	—	2	1	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₂×C₈×C₁₉	—	2	1	no	—
202	C₂×C₈×C₁₉	—	2	1	no	—
203	C₂×C₈×C₁₉	—	2	1	no	—
204	C₂×C₈×C₁₉	—	2	1	no	—
205	C₂×C₈×C₁₉	—	2	1	no	—
206	C₂×C₈×C₁₉	—	4	4	no	—
207	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
208	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
209	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₁₉	—	2	4	no	—
211	C₄⋊C₄×C₁₉	—	2	1	no	—
212	C₄⋊C₄×C₁₉	—	2	1	no	—
213	C₄⋊C₄×C₁₉	—	2	1	no	—
214	C₄⋊C₄×C₁₉	—	2	1	no	—
215	C₄⋊C₄×C₁₉	—	2	1	no	—
216	C₄⋊C₄×C₁₉	—	2	1	no	—
217	C₄⋊C₄×C₁₉	—	2	1	no	—
218	C₄⋊C₄×C₁₉	—	2	1	no	—
219	C₄⋊C₄×C₁₉	—	4	2	no	—
220	C₄⋊C₄×C₁₉	—	4	2	no	—
221	C₄⋊C₄×C₁₉	—	4	2	no	—
222	C₄⋊C₄×C₁₉	—	4	2	no	—
223	C₄⋊C₄×C₁₉	—	8	1	no	—
224	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
225	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
226	C₂²⋊C₄×C₁₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	4	2	no	—
229	C₂²⋊C₄×C₁₉	Q₁₆	1	4	yes	complemented
230	C₄²×C₁₉	—	2	1	no	—
231	C₄²×C₁₉	—	2	1	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	—	2	1	no	—
234	C₄²×C₁₉	—	4	2	no	—
235	C₄²×C₁₉	—	4	2	no	—
236	C₄²×C₁₉	—	4	2	no	—
237	C₄²×C₁₉	—	8	1	no	—
238	#22871	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₉	—	2	1	no	—
240	C₂³×C₁₉	—	2	1	no	—
241	C₂³×C₁₉	—	2	1	no	—
242	C₂³×C₁₉	—	2	1	no	—
243	C₂³×C₁₉	C₄×D₄	1	2	yes	—
244	C₂³×C₁₉	C₂×Q₁₆	1	2	yes	—
245	C₂³×C₁₉	#135	1	2	yes	—
246	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₁₉	—	2	2	no	—
248	Q₈×C₁₉	—	2	2	no	—
249	Q₈×C₁₉	—	2	2	no	—
250	Q₈×C₁₉	—	2	2	no	—
251	Q₈×C₁₉	—	2	2	no	—
252	Q₈×C₁₉	—	2	2	no	—
253	Q₈×C₁₉	—	2	2	no	—
254	Q₈×C₁₉	—	4	8	no	—
255	Q₈×C₁₉	—	4	1	no	—
256	Q₈×C₁₉	—	4	1	no	—
257	Q₈×C₁₉	—	4	1	no	—
258	Q₈×C₁₉	—	4	1	no	—
259	Q₈×C₁₉	C₄×D₄	1	4	yes	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	1	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	1	no	—
283	C₂×C₄×C₁₉	—	4	8	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	4	1	no	—
294	C₂×C₄×C₁₉	—	4	1	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	1	no	—
298	C₂×C₄×C₁₉	—	4	1	no	—
299	C₂×C₄×C₁₉	—	4	1	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	8	4	no	—
302	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
303	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
304	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
305	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₈×C₁₉	—	2	2	no	—
312	C₈×C₁₉	—	2	2	no	—
313	C₈×C₁₉	—	2	2	no	—
314	C₈×C₁₉	—	4	1	no	—
315	C₂×#451	C₂×C₁₉	1	1	yes	characteristic
316	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
317	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic
318	#2360	C₂×C₁₉	1	1	yes	characteristic
319	Q₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
320	#1969	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#1892	C₂×C₁₉	1	1	yes	characteristic
324	#1878	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#1878	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#1852	C₂×C₁₉	1	1	yes	characteristic
328	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
329	C₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
330	C₂²×C₁₉	—	2	2	no	—
331	C₂²×C₁₉	—	2	2	no	—
332	C₂²×C₁₉	—	2	2	no	—
333	C₂²×C₁₉	—	2	2	no	—
334	C₂²×C₁₉	—	2	2	no	—
335	C₂²×C₁₉	—	2	2	no	—
336	C₂²×C₁₉	C₄×Q₁₆	1	4	yes	complemented
337	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
338	C₂²×C₁₉	D₄²	1	1	yes	characteristic
339	C₂²×C₁₉	#546	1	1	yes	characteristic
340	C₂²×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
341	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
342	C₂²×C₁₉	#577	1	1	yes	characteristic
343	C₂²×C₁₉	#578	1	1	yes	characteristic
344	C₄×C₁₉	—	2	2	no	—
345	C₄×C₁₉	—	2	4	no	—
346	C₄×C₁₉	—	2	2	no	—
347	C₄×C₁₉	—	2	2	no	—
348	C₄×C₁₉	—	4	2	no	—
349	C₄×C₁₉	—	4	2	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	4	1	no	—
352	C₄×C₁₉	—	4	2	no	—
353	C₄×C₁₉	—	4	1	no	—
354	C₄×C₁₉	—	8	1	no	—
355	C₄×C₁₉	—	8	1	no	—
356	C₄×C₁₉	—	8	1	no	—
357	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
358	C₄×C₁₉	#518	1	1	yes	characteristic
359	C₄×C₁₉	#546	1	1	yes	characteristic
360	C₄×C₁₉	#551	1	1	yes	characteristic
361	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
362	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
363	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
364	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
370	#451	C₄×C₁₉	1	8	yes	complemented
371	C₄×Q₁₆	—	2	4	no	—
372	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#103	—	2	4	no	—
375	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
386	#391	—	2	1	no	—
387	#391	—	2	1	no	—
388	#391	C₂²×C₁₉	1	1	yes	characteristic
389	#391	C₂²×C₁₉	1	1	yes	characteristic
390	#391	C₂²×C₁₉	1	1	yes	characteristic
391	#389	—	2	1	no	—
392	#389	C₂²×C₁₉	1	1	yes	characteristic
393	#387	—	2	1	no	—
394	#385	—	2	1	no	—
395	#380	—	2	1	no	—
396	#380	C₂²×C₁₉	1	1	yes	characteristic
397	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
398	C₄×C₂²⋊C₄	—	2	1	no	—
399	C₄×C₂²⋊C₄	—	2	1	no	—
400	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
401	#340	C₂²×C₁₉	1	1	yes	characteristic
402	#340	C₂²×C₁₉	1	1	yes	characteristic
403	#340	C₂²×C₁₉	1	1	yes	characteristic
404	#340	C₂²×C₁₉	1	1	yes	characteristic
405	#336	C₂²×C₁₉	1	1	yes	characteristic
406	#336	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₁₉	—	2	4	no	—
408	C₂×C₁₉	#2358	1	1	yes	characteristic
409	C₂×C₁₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
410	C₂×C₁₉	#2947	1	1	yes	characteristic
411	C₂×C₁₉	#3282	1	1	yes	characteristic
412	C₂×C₁₉	D₄×Q₁₆	1	1	yes	characteristic
413	C₂×C₁₉	#3299	1	1	yes	characteristic
414	C₂×C₁₉	#3300	1	1	yes	characteristic
415	C₂²×Q₈	—	2	1	no	—
416	C₂²×Q₈	—	2	2	no	—
417	C₂²×Q₈	—	2	2	no	—
418	C₂²×Q₈	—	2	2	no	—
419	C₂²×Q₈	—	4	1	no	—
420	C₂²×Q₈	—	4	1	no	—
421	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
422	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
423	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₂³×C₄	—	2	1	no	—
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
428	C₂×Q₁₆	—	2	2	no	—
429	C₂×Q₁₆	—	2	2	no	—
430	C₂×Q₁₆	—	4	1	no	—
431	C₂×Q₁₆	—	4	1	no	—
432	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
433	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
434	C₂²×C₈	—	2	2	no	—
435	C₂²×C₈	—	2	2	no	—
436	C₂²×C₈	—	4	1	no	—
437	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	—	2	2	no	—
446	C₄×Q₈	—	4	1	no	—
447	C₄×Q₈	—	4	1	no	—
448	C₄×Q₈	—	4	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	2	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	4	1	no	—
457	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	2	1	no	—
470	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
472	#107	—	2	2	no	—
473	#107	—	4	1	no	—
474	#103	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	—	2	2	no	—
477	#103	—	2	2	no	—
478	#103	—	4	1	no	—
479	#103	C₂×C₄×C₁₉	1	4	yes	complemented
480	#103	C₂×C₄×C₁₉	1	4	yes	complemented
481	#103	D₄×C₁₉	1	4	yes	—
482	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
483	C₄×C₈	—	2	2	no	—
484	C₄×C₈	—	4	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	D₄×C₁₉	1	1	yes	characteristic
495	#95	D₄×C₁₉	1	1	yes	characteristic
496	C₁₉	#22871	1	1	yes	characteristic, direct product factor, Sylow
497	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	8	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂×Q₈	—	4	2	no	—
515	C₂×Q₈	—	4	4	no	—
516	C₂×Q₈	—	4	4	no	—
517	C₂×Q₈	—	4	4	no	—
518	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
519	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
520	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
521	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
522	C₂×Q₈	#41×C₁₉	1	2	yes	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
542	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
547	C₂²×C₄	#41×C₁₉	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
549	Q₁₆	—	2	8	no	—
550	Q₁₆	—	4	4	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	4	4	no	—
561	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
562	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
563	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	8	1	no	—
578	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
579	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	Q₁₆×C₁₉	1	4	yes	complemented
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	4	2	no	—
589	C₄²	—	4	2	no	—
590	C₄²	—	4	2	no	—
591	C₄²	—	8	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	C₄×D₄×C₁₉	1	2	yes	—
597	C₂³	C₂×Q₁₆×C₁₉	1	2	yes	—
598	C₂³	C₁₉×#135	1	2	yes	—
599	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	2	2	no	—
603	Q₈	—	2	2	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	2	2	no	—
607	Q₈	—	4	8	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	Q₈	—	4	1	no	—
612	Q₈	C₄×D₄×C₁₉	1	4	yes	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	8	4	no	—
655	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
656	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
657	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
660	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
661	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
662	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
664	C₈	—	2	2	no	—
665	C₈	—	2	2	no	—
666	C₈	—	2	2	no	—
667	C₈	—	4	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	C₄×Q₁₆×C₁₉	1	4	yes	complemented
675	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
676	C₂²	D₄²×C₁₉	1	1	yes	characteristic
677	C₂²	C₁₉×#546	1	1	yes	characteristic
678	C₂²	C₂²×Q₁₆×C₁₉	1	1	yes	characteristic
679	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
680	C₂²	C₁₉×#577	1	1	yes	characteristic
681	C₂²	C₁₉×#578	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
696	C₄	C₁₉×#518	1	1	yes	characteristic
697	C₄	C₁₉×#546	1	1	yes	characteristic
698	C₄	C₁₉×#551	1	1	yes	characteristic
699	C₂	—	2	4	no	—
700	C₂	C₁₉×#2358	1	1	yes	characteristic
701	C₂	C₂×C₄×Q₁₆×C₁₉	1	1	yes	characteristic
702	C₂	C₁₉×#2947	1	1	yes	characteristic
703	C₂	C₁₉×#3282	1	1	yes	characteristic
704	C₂	D₄×Q₁₆×C₁₉	1	1	yes	characteristic
705	C₂	C₁₉×#3299	1	1	yes	characteristic
706	C₂	C₁₉×#3300	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₁₉	C₂	semidirect
6. C₁₉×#1969	C₂	semidirect
7. C₁₉×#1933	C₂	semidirect
8. C₁₉×#1928	C₂	semidirect
10. C₁₉×#1878	C₂	semidirect
11. C₁₉×#1878	C₂	semidirect
12. C₁₉×#1863	C₂	semidirect
14. C₄×C₁₉×#103	C₂	semidirect
25. C₁₉×#451	C₄	semidirect
79. C₂×Q₁₆×C₁₉	C₂×C₄	semidirect
80. C₂×Q₁₆×C₁₉	C₂×C₄	semidirect
126. C₁₉×#103	C₂×C₄	semidirect
127. C₁₉×#103	C₂×C₄	semidirect
229. C₂²⋊C₄×C₁₉	Q₁₆	semidirect
238. #22871	C₁₉	direct (N × H)
316. C₂×C₄×Q₁₆	C₂×C₁₉	semidirect
320. #1969	C₂×C₁₉	semidirect
321. #1933	C₂×C₁₉	semidirect
322. #1928	C₂×C₁₉	semidirect
324. #1878	C₂×C₁₉	semidirect
325. #1878	C₂×C₁₉	semidirect
326. #1863	C₂×C₁₉	semidirect
328. C₄×#103	C₂×C₁₉	semidirect
336. C₂²×C₁₉	C₄×Q₁₆	semidirect
370. #451	C₄×C₁₉	semidirect
432. C₂×Q₁₆	C₂×C₄×C₁₉	semidirect
433. C₂×Q₁₆	C₂×C₄×C₁₉	semidirect
479. #103	C₂×C₄×C₁₉	semidirect
480. #103	C₂×C₄×C₁₉	semidirect
496. C₁₉	#22871	direct (N × H)
583. C₂²⋊C₄	Q₁₆×C₁₉	semidirect
674. C₂²	C₄×Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#451	2
C₂×C₄×Q₁₆×C₁₉	2
C₂²×C₁₉×#103	2
C₁₉×#2360	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#1969	2
C₁₉×#1933	2
C₁₉×#1928	2
C₁₉×#1892	2
C₁₉×#1878	2
C₁₉×#1863	2
C₁₉×#1852	2
C₄×C₁₉×#103	2
C₈×C₂²⋊C₄×C₁₉	2
#22871	19

Subgroups — C19×#22871 #18028830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22871 #18028830