Subgroups — C₁₉×#22527 #18028486

Order 4864.

990 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1993	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1763	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	C₁₉×#557	—	2	4	no	—
17	C₁₉×#557	C₄	1	8	yes	complemented
18	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#125	—	2	1	no	—
21	C₂×C₁₉×#125	—	2	1	no	—
22	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#446	—	2	4	no	—
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#391	—	2	1	no	—
41	C₁₉×#387	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#384	C₂²	1	1	yes	characteristic
44	C₁₉×#382	C₂²	1	1	yes	characteristic
45	C₁₉×#382	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₁₉	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×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	—	2	1	no	—
63	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	—	2	8	no	—
70	C₁₉×C₄⋊Q₈	—	2	2	no	—
71	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
72	C₁₉×#125	—	2	8	no	—
73	C₁₉×#125	—	2	8	no	—
74	C₁₉×#125	—	2	2	no	—
75	C₁₉×#125	—	2	2	no	—
76	C₁₉×#125	C₂×C₄	1	4	yes	—
77	C₁₉×#125	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₁₉	—	2	8	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
83	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
84	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
86	C₄×Q₈×C₁₉	D₄	1	4	yes	—
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	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊C₈	—	2	2	no	—
117	C₁₉×C₄⋊C₈	—	2	2	no	—
118	C₁₉×C₄⋊C₈	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	—	2	2	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	Q₈	1	4	yes	complemented
123	C₁₉×#97	—	2	2	no	—
124	C₁₉×#97	—	2	2	no	—
125	C₄×C₈×C₁₉	—	2	2	no	—
126	C₁₉×#95	—	2	1	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	C₂×Q₈×C₁₉	—	2	4	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	4	2	no	—
140	C₂×Q₈×C₁₉	—	4	2	no	—
141	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
142	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
144	C₂×Q₈×C₁₉	#41	1	2	yes	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
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	C₂×Q₈	1	2	yes	—
172	C₄⋊C₄×C₁₉	—	2	4	no	—
173	C₄⋊C₄×C₁₉	—	2	4	no	—
174	C₄⋊C₄×C₁₉	—	2	4	no	—
175	C₄⋊C₄×C₁₉	—	2	4	no	—
176	C₄⋊C₄×C₁₉	—	2	4	no	—
177	C₄⋊C₄×C₁₉	—	2	4	no	—
178	C₄⋊C₄×C₁₉	—	2	4	no	—
179	C₄⋊C₄×C₁₉	—	2	4	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	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	4	2	no	—
191	C₄⋊C₄×C₁₉	—	8	1	no	—
192	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
193	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
194	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
195	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
196	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
198	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
199	C₄²×C₁₉	—	2	4	no	—
200	C₄²×C₁₉	—	2	4	no	—
201	C₄²×C₁₉	—	2	4	no	—
202	C₄²×C₁₉	—	4	2	no	—
203	C₄²×C₁₉	—	8	1	no	—
204	C₄²×C₁₉	—	8	1	no	—
205	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
206	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
207	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
208	C₄²×C₁₉	C₂×D₄	1	2	yes	—
209	C₄²×C₁₉	C₂×D₄	1	2	yes	—
210	C₄²×C₁₉	C₂×D₄	1	2	yes	—
211	#22527	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₉	—	2	2	no	—
214	Q₈×C₁₉	—	2	2	no	—
215	Q₈×C₁₉	—	2	2	no	—
216	Q₈×C₁₉	—	4	4	no	—
217	Q₈×C₁₉	—	4	8	no	—
218	Q₈×C₁₉	C₄×Q₈	1	4	yes	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	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	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	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	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	4	1	no	—
269	C₈×C₁₉	—	4	1	no	—
270	C₈×C₁₉	—	4	1	no	—
271	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
272	C₂×#446	C₂×C₁₉	1	1	yes	characteristic
273	#2355	C₂×C₁₉	1	1	yes	characteristic
274	#1993	C₂×C₁₉	1	1	yes	characteristic
275	#1992	C₂×C₁₉	1	1	yes	characteristic
276	#1991	C₂×C₁₉	1	1	yes	characteristic
277	#1989	C₂×C₁₉	1	1	yes	characteristic
278	#1989	C₂×C₁₉	1	1	yes	characteristic
279	#1987	C₂×C₁₉	1	1	yes	characteristic
280	#1805	C₂×C₁₉	1	1	yes	characteristic
281	#1805	C₂×C₁₉	1	1	yes	characteristic
282	#1803	C₂×C₁₉	1	1	yes	characteristic
283	#1763	C₂×C₁₉	1	1	yes	characteristic
284	#1763	C₂×C₁₉	1	1	yes	characteristic
285	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
286	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₁₉	#548	1	1	yes	characteristic
288	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
289	C₂²×C₁₉	#575	1	1	yes	characteristic
290	C₂²×C₁₉	#575	1	1	yes	characteristic
291	C₂²×C₁₉	#577	1	1	yes	characteristic
292	C₂²×C₁₉	#578	1	1	yes	characteristic
293	C₄×C₁₉	—	2	4	no	—
294	C₄×C₁₉	—	2	2	no	—
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	2	no	—
304	C₄×C₁₉	—	8	1	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
308	C₄×C₁₉	#519	1	1	yes	characteristic
309	C₄×C₁₉	#548	1	1	yes	characteristic
310	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
311	#557	—	2	4	no	—
312	#557	C₄×C₁₉	1	8	yes	complemented
313	C₂×C₄⋊Q₈	—	2	1	no	—
314	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#125	—	2	1	no	—
316	C₂×#125	—	2	1	no	—
317	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₄×Q₈	—	2	1	no	—
320	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
324	#446	—	2	4	no	—
325	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
331	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
335	#391	—	2	1	no	—
336	#387	—	2	1	no	—
337	#387	—	2	1	no	—
338	#384	C₂²×C₁₉	1	1	yes	characteristic
339	#382	C₂²×C₁₉	1	1	yes	characteristic
340	#382	C₂²×C₁₉	1	1	yes	characteristic
341	C₄×C₄⋊C₄	—	2	1	no	—
342	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
345	#340	C₂²×C₁₉	1	1	yes	characteristic
346	#340	C₂²×C₁₉	1	1	yes	characteristic
347	#340	C₂²×C₁₉	1	1	yes	characteristic
348	#340	C₂²×C₁₉	1	1	yes	characteristic
349	#340	C₂²×C₁₉	1	1	yes	characteristic
350	#340	C₂²×C₁₉	1	1	yes	characteristic
351	#340	C₂²×C₁₉	1	1	yes	characteristic
352	#340	C₂²×C₁₉	1	1	yes	characteristic
353	#340	C₂²×C₁₉	1	1	yes	characteristic
354	#340	C₂²×C₁₉	1	1	yes	characteristic
355	#340	C₂²×C₁₉	1	1	yes	characteristic
356	#340	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₁₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×C₁₉	#2896	1	1	yes	characteristic
359	C₂×C₁₉	#2898	1	1	yes	characteristic
360	C₂×C₁₉	#3371	1	1	yes	characteristic
361	C₂×C₁₉	#3377	1	1	yes	characteristic
362	C₂×C₁₉	#3388	1	1	yes	characteristic
363	C₂×C₁₉	#3390	1	1	yes	characteristic
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	8	no	—
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
374	#125	—	2	8	no	—
375	#125	—	2	8	no	—
376	#125	—	2	2	no	—
377	#125	—	2	2	no	—
378	#125	C₂×C₄×C₁₉	1	4	yes	—
379	#125	C₂×C₄×C₁₉	1	4	yes	—
380	C₄×Q₈	—	2	8	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
385	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
386	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
387	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
388	C₄×Q₈	D₄×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	D₄×C₁₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×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	C₄⋊C₈	—	2	2	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#103	Q₈×C₁₉	1	4	yes	complemented
425	#97	—	2	2	no	—
426	#97	—	2	2	no	—
427	C₄×C₈	—	2	2	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	C₁₉	#22527	1	1	yes	characteristic, direct product factor, Sylow
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	4	1	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	—	4	2	no	—
443	C₂×Q₈	—	4	2	no	—
444	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
445	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
446	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
447	C₂×Q₈	#41×C₁₉	1	2	yes	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
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	C₂×Q₈×C₁₉	1	2	yes	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	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	—	4	2	no	—
494	C₄⋊C₄	—	8	1	no	—
495	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
496	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
497	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
498	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
499	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
500	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
501	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	4	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	8	1	no	—
507	C₄²	—	8	1	no	—
508	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
509	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
510	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
511	C₄²	C₂×D₄×C₁₉	1	2	yes	—
512	C₄²	C₂×D₄×C₁₉	1	2	yes	—
513	C₄²	C₂×D₄×C₁₉	1	2	yes	—
514	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	Q₈	—	2	2	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	4	4	no	—
519	Q₈	—	4	8	no	—
520	Q₈	C₄×Q₈×C₁₉	1	4	yes	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	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	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
558	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
559	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
560	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
561	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
562	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
563	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
567	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
568	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
574	C₂²	C₁₉×#548	1	1	yes	characteristic
575	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
576	C₂²	C₁₉×#575	1	1	yes	characteristic
577	C₂²	C₁₉×#575	1	1	yes	characteristic
578	C₂²	C₁₉×#577	1	1	yes	characteristic
579	C₂²	C₁₉×#578	1	1	yes	characteristic
580	C₄	—	2	4	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
595	C₄	C₁₉×#519	1	1	yes	characteristic
596	C₄	C₁₉×#548	1	1	yes	characteristic
597	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
598	C₂	Q₈×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
599	C₂	C₁₉×#2896	1	1	yes	characteristic
600	C₂	C₁₉×#2898	1	1	yes	characteristic
601	C₂	C₁₉×#3371	1	1	yes	characteristic
602	C₂	C₁₉×#3377	1	1	yes	characteristic
603	C₂	C₁₉×#3388	1	1	yes	characteristic
604	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 ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₁₉×#557	C₄	semidirect
122. C₁₉×#103	Q₈	semidirect
211. #22527	C₁₉	direct (N × H)
312. #557	C₄×C₁₉	semidirect
424. #103	Q₈×C₁₉	semidirect
435. C₁₉	#22527	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×#557	2
C₂×C₁₉×#446	2
C₁₉×#2355	2
C₁₉×#1993	2
C₁₉×#1992	2
C₁₉×#1991	2
C₁₉×#1989	2
C₁₉×#1987	2
C₁₉×#1805	2
C₁₉×#1803	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#22527	19

Subgroups — C19×#22527 #18028486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22527 #18028486