Subgroups — C₁₉×#22679 #18028638

Order 4864.

906 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1944	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1941	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×#1863	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1847	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₁₉	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	C₂×C₄×Q₈×C₁₉	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	C₁₉×#441	—	2	4	no	—
24	C₁₉×#441	C₄	1	8	yes	complemented
25	C₄×Q₁₆×C₁₉	—	2	4	no	—
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#389	—	2	1	no	—
42	C₁₉×#389	—	2	1	no	—
43	C₁₉×#389	—	2	1	no	—
44	C₁₉×#389	—	2	1	no	—
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#389	C₂²	1	1	yes	characteristic
47	C₁₉×#389	C₂²	1	1	yes	characteristic
48	C₁₉×#389	C₂²	1	1	yes	characteristic
49	C₁₉×#384	—	2	1	no	—
50	C₁₉×#384	C₂²	1	1	yes	characteristic
51	C₁₉×#382	—	2	1	no	—
52	C₁₉×#382	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₄×C₄⋊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	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
65	C₂×Q₁₆×C₁₉	D₄	1	4	yes	—
66	C₂×Q₁₆×C₁₉	Q₈	1	4	yes	—
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	4	1	no	—
78	C₄×Q₈×C₁₉	—	4	1	no	—
79	C₄×Q₈×C₁₉	—	4	1	no	—
80	C₄×Q₈×C₁₉	—	4	1	no	—
81	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
82	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	—	2	1	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#107	—	2	2	no	—
113	C₁₉×#107	—	4	1	no	—
114	C₁₉×#106	—	2	2	no	—
115	C₁₉×#106	—	4	1	no	—
116	C₁₉×#106	C₂×C₄	1	4	yes	—
117	C₁₉×C₄⋊C₈	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	C₂×C₄	1	4	yes	—
123	C₁₉×#103	C₂×C₄	1	4	yes	—
124	C₁₉×#97	—	2	2	no	—
125	C₁₉×#97	C₂×C₄	1	4	yes	—
126	C₄×C₈×C₁₉	—	2	2	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	D₄	1	1	yes	characteristic
134	C₁₉×#95	D₄	1	1	yes	characteristic
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
142	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
146	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
162	Q₁₆×C₁₉	C₄⋊C₄	1	16	yes	complemented
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	1	no	—
168	C₂×C₈×C₁₉	—	2	1	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	4	1	no	—
189	C₄⋊C₄×C₁₉	—	4	2	no	—
190	C₄⋊C₄×C₁₉	—	4	2	no	—
191	C₄⋊C₄×C₁₉	—	4	2	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	—	4	2	no	—
194	C₄⋊C₄×C₁₉	—	4	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	—	8	1	no	—
197	C₄⋊C₄×C₁₉	—	8	1	no	—
198	C₄⋊C₄×C₁₉	—	8	1	no	—
199	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
200	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
201	C₄²×C₁₉	—	2	4	no	—
202	C₄²×C₁₉	—	2	4	no	—
203	C₄²×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	4	2	no	—
208	C₄²×C₁₉	—	4	2	no	—
209	C₄²×C₁₉	—	4	2	no	—
210	C₄²×C₁₉	—	4	2	no	—
211	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
212	C₄²×C₁₉	#41	1	2	yes	—
213	#22679	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₉	—	2	2	no	—
216	Q₈×C₁₉	—	2	2	no	—
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	—	2	2	no	—
219	Q₈×C₁₉	—	2	2	no	—
220	Q₈×C₁₉	—	2	2	no	—
221	Q₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
222	Q₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	4	1	no	—
258	C₂×C₄×C₁₉	—	4	1	no	—
259	C₂×C₄×C₁₉	—	4	1	no	—
260	C₂×C₄×C₁₉	—	4	1	no	—
261	C₂×C₄×C₁₉	—	4	1	no	—
262	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
263	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
264	C₂×C₄×C₁₉	#137	1	2	yes	—
265	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
270	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
271	C₈×C₁₉	—	2	2	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₈×C₁₉	—	4	1	no	—
274	C₈×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
275	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
276	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
277	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
278	#2351	C₂×C₁₉	1	1	yes	characteristic
279	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
280	#1944	C₂×C₁₉	1	1	yes	characteristic
281	#1941	C₂×C₁₉	1	1	yes	characteristic
282	#1865	C₂×C₁₉	1	1	yes	characteristic
283	#1865	C₂×C₁₉	1	1	yes	characteristic
284	#1863	C₂×C₁₉	1	1	yes	characteristic
285	#1863	C₂×C₁₉	1	1	yes	characteristic
286	#1847	C₂×C₁₉	1	1	yes	characteristic
287	#1805	C₂×C₁₉	1	1	yes	characteristic
288	#1803	C₂×C₁₉	1	1	yes	characteristic
289	#1771	C₂×C₁₉	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₁₉	D₄²	1	1	yes	characteristic
292	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
293	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
294	C₂²×C₁₉	#575	1	1	yes	characteristic
295	C₂²×C₁₉	#577	1	1	yes	characteristic
296	C₂²×C₁₉	#578	1	1	yes	characteristic
297	C₄×C₁₉	—	2	4	no	—
298	C₄×C₁₉	—	2	4	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	2	no	—
301	C₄×C₁₉	—	2	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	—	8	1	no	—
311	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
312	C₄×C₁₉	#520	1	1	yes	characteristic
313	C₄×C₁₉	#547	1	1	yes	characteristic
314	C₄×C₁₉	#554	1	1	yes	characteristic
315	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
322	#441	—	2	4	no	—
323	#441	C₄×C₁₉	1	8	yes	complemented
324	C₄×Q₁₆	—	2	4	no	—
325	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
340	#389	—	2	1	no	—
341	#389	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	—	2	1	no	—
344	#389	C₂²×C₁₉	1	1	yes	characteristic
345	#389	C₂²×C₁₉	1	1	yes	characteristic
346	#389	C₂²×C₁₉	1	1	yes	characteristic
347	#389	C₂²×C₁₉	1	1	yes	characteristic
348	#384	—	2	1	no	—
349	#384	C₂²×C₁₉	1	1	yes	characteristic
350	#382	—	2	1	no	—
351	#382	C₂²×C₁₉	1	1	yes	characteristic
352	C₄×C₄⋊C₄	—	2	1	no	—
353	C₄×C₄⋊C₄	—	2	1	no	—
354	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
355	#340	C₂²×C₁₉	1	1	yes	characteristic
356	#340	C₂²×C₁₉	1	1	yes	characteristic
357	#340	C₂²×C₁₉	1	1	yes	characteristic
358	#340	C₂²×C₁₉	1	1	yes	characteristic
359	#336	C₂²×C₁₉	1	1	yes	characteristic
360	#336	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×C₁₉	D₄×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
363	C₂×C₁₉	#2947	1	1	yes	characteristic
364	C₂×C₁₉	#3270	1	1	yes	characteristic
365	C₂×C₁₉	#3271	1	1	yes	characteristic
366	C₂×C₁₉	#3387	1	1	yes	characteristic
367	C₂×C₁₉	#3390	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
371	C₂×Q₁₆	D₄×C₁₉	1	4	yes	—
372	C₂×Q₁₆	Q₈×C₁₉	1	4	yes	—
373	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	4	1	no	—
384	C₄×Q₈	—	4	1	no	—
385	C₄×Q₈	—	4	1	no	—
386	C₄×Q₈	—	4	1	no	—
387	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
388	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
418	#107	—	2	2	no	—
419	#107	—	4	1	no	—
420	#106	—	2	2	no	—
421	#106	—	4	1	no	—
422	#106	C₂×C₄×C₁₉	1	4	yes	—
423	C₄⋊C₈	—	2	2	no	—
424	#103	—	2	2	no	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	C₂×C₄×C₁₉	1	4	yes	—
429	#103	C₂×C₄×C₁₉	1	4	yes	—
430	#97	—	2	2	no	—
431	#97	C₂×C₄×C₁₉	1	4	yes	—
432	C₄×C₈	—	2	2	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	D₄×C₁₉	1	1	yes	characteristic
440	#95	D₄×C₁₉	1	1	yes	characteristic
441	C₁₉	#22679	1	1	yes	characteristic, direct product factor, Sylow
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
449	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
450	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
451	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
452	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
453	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
469	Q₁₆	C₄⋊C₄×C₁₉	1	16	yes	complemented
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
479	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
480	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
481	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	8	1	no	—
504	C₄⋊C₄	—	8	1	no	—
505	C₄⋊C₄	—	8	1	no	—
506	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
508	C₄²	—	2	4	no	—
509	C₄²	—	2	4	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	4	2	no	—
515	C₄²	—	4	2	no	—
516	C₄²	—	4	2	no	—
517	C₄²	—	4	2	no	—
518	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
519	C₄²	#41×C₁₉	1	2	yes	—
520	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	2	2	no	—
526	Q₈	—	2	2	no	—
527	Q₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
528	Q₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
569	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
570	C₂×C₄	C₁₉×#137	1	2	yes	—
571	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
573	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
575	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
577	C₈	—	2	2	no	—
578	C₈	—	4	1	no	—
579	C₈	—	4	1	no	—
580	C₈	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
581	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
582	C₂²	D₄²×C₁₉	1	1	yes	characteristic
583	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
584	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
585	C₂²	C₁₉×#575	1	1	yes	characteristic
586	C₂²	C₁₉×#577	1	1	yes	characteristic
587	C₂²	C₁₉×#578	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	4	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
603	C₄	C₁₉×#520	1	1	yes	characteristic
604	C₄	C₁₉×#547	1	1	yes	characteristic
605	C₄	C₁₉×#554	1	1	yes	characteristic
606	C₂	D₄×C₄⋊C₄×C₁₉	1	1	yes	characteristic
607	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
608	C₂	C₁₉×#2947	1	1	yes	characteristic
609	C₂	C₁₉×#3270	1	1	yes	characteristic
610	C₂	C₁₉×#3271	1	1	yes	characteristic
611	C₂	C₁₉×#3387	1	1	yes	characteristic
612	C₂	C₁₉×#3390	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 ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
24. C₁₉×#441	C₄	semidirect
162. Q₁₆×C₁₉	C₄⋊C₄	semidirect
213. #22679	C₁₉	direct (N × H)
323. #441	C₄×C₁₉	semidirect
441. C₁₉	#22679	direct (N × H)
469. Q₁₆	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
C₂×C₁₉×#441	2
C₂×C₄×Q₁₆×C₁₉	2
C₁₉×#2351	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#1944	2
C₁₉×#1941	2
C₁₉×#1865	2
C₁₉×#1863	2
C₁₉×#1847	2
C₁₉×#1805	2
C₁₉×#1803	2
C₁₉×#1771	2
#22679	19

Subgroups — C19×#22679 #18028638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22679 #18028638