Subgroups — C₁₉×#23110 #18029069

Order 4864.

806 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#462	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2356	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1971	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1927	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1878	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1771	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	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	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	C₁₉×#462	C₄	1	8	yes	complemented
23	C₂×C₁₉×#107	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×#103	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×#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×#97	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#391	C₂²	1	1	yes	characteristic
40	C₁₉×#391	C₂²	1	1	yes	characteristic
41	C₁₉×#389	—	2	1	no	—
42	C₁₉×#387	—	2	1	no	—
43	C₁₉×#387	—	2	1	no	—
44	C₁₉×#387	—	2	1	no	—
45	C₁₉×#387	—	2	1	no	—
46	C₁₉×#383	—	2	1	no	—
47	C₁₉×#382	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₁₉×#376	—	2	1	no	—
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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₁₉	—	4	1	no	—
64	C₂×Q₁₆×C₁₉	—	4	1	no	—
65	C₂×Q₁₆×C₁₉	—	4	1	no	—
66	C₂×Q₁₆×C₁₉	—	4	1	no	—
67	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
68	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	—	2	2	no	—
74	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	4	1	no	—
79	C₄×Q₈×C₁₉	—	4	1	no	—
80	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
98	C₂×C₄²×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	4	1	no	—
103	C₁₉×#106	—	4	1	no	—
104	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	—	2	2	no	—
107	C₁₉×#103	—	2	2	no	—
108	C₁₉×#103	—	2	2	no	—
109	C₁₉×#103	—	4	1	no	—
110	C₁₉×#103	—	4	1	no	—
111	C₁₉×#103	C₂×C₄	1	4	yes	—
112	C₁₉×#103	C₂×C₄	1	4	yes	—
113	C₁₉×#97	—	2	2	no	—
114	C₁₉×#97	—	4	1	no	—
115	C₄×C₈×C₁₉	—	4	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	—	2	1	no	—
122	C₁₉×#95	—	2	1	no	—
123	C₁₉×#95	—	2	1	no	—
124	C₁₉×#95	—	2	1	no	—
125	C₁₉×#95	—	2	1	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	D₄	1	1	yes	characteristic
130	C₁₉×#95	D₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	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	—	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	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
147	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
148	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	Q₁₆×C₁₉	—	4	4	no	—
165	Q₁₆×C₁₉	—	4	4	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	—	2	1	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₁₉	#41	1	2	yes	—
178	C₄⋊C₄×C₁₉	—	2	4	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
191	C₄⋊C₄×C₁₉	—	4	2	no	—
192	C₄⋊C₄×C₁₉	—	4	2	no	—
193	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
194	C₄⋊C₄×C₁₉	#41	1	2	yes	—
195	C₄²×C₁₉	—	2	4	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	2	1	no	—
199	C₄²×C₁₉	—	2	1	no	—
200	C₄²×C₁₉	—	4	2	no	—
201	C₄²×C₁₉	—	4	2	no	—
202	C₄²×C₁₉	—	4	2	no	—
203	C₄²×C₁₉	—	4	2	no	—
204	C₄²×C₁₉	—	4	2	no	—
205	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
206	C₄²×C₁₉	#41	1	2	yes	—
207	#23110	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₁₉	—	2	2	no	—
210	Q₈×C₁₉	—	2	2	no	—
211	Q₈×C₁₉	—	2	2	no	—
212	Q₈×C₁₉	—	2	2	no	—
213	Q₈×C₁₉	—	2	2	no	—
214	Q₈×C₁₉	—	2	2	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	2	1	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	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	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	1	no	—
236	C₂×C₄×C₁₉	—	2	1	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	—	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	—	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	C₄×D₄	1	2	yes	—
261	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
262	C₂×C₄×C₁₉	#137	1	2	yes	—
263	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
268	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
269	C₈×C₁₉	—	2	2	no	—
270	C₈×C₁₉	—	2	2	no	—
271	C₈×C₁₉	—	2	2	no	—
272	C₈×C₁₉	—	4	1	no	—
273	C₂×#462	C₂×C₁₉	1	1	yes	characteristic
274	#2365	C₂×C₁₉	1	1	yes	characteristic
275	#2356	C₂×C₁₉	1	1	yes	characteristic
276	#1971	C₂×C₁₉	1	1	yes	characteristic
277	#1969	C₂×C₁₉	1	1	yes	characteristic
278	#1960	C₂×C₁₉	1	1	yes	characteristic
279	#1949	C₂×C₁₉	1	1	yes	characteristic
280	#1928	C₂×C₁₉	1	1	yes	characteristic
281	#1927	C₂×C₁₉	1	1	yes	characteristic
282	#1878	C₂×C₁₉	1	1	yes	characteristic
283	#1878	C₂×C₁₉	1	1	yes	characteristic
284	#1771	C₂×C₁₉	1	1	yes	characteristic
285	#1763	C₂×C₁₉	1	1	yes	characteristic
286	#1763	C₂×C₁₉	1	1	yes	characteristic
287	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
288	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂²×C₁₉	#546	1	1	yes	characteristic
290	C₂²×C₁₉	#550	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
292	C₂²×C₁₉	#575	1	1	yes	characteristic
293	C₂²×C₁₉	#578	1	1	yes	characteristic
294	C₂²×C₁₉	#578	1	1	yes	characteristic
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	4	2	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
310	C₄×C₁₉	#518	1	1	yes	characteristic
311	C₄×C₁₉	#553	1	1	yes	characteristic
312	C₄×C₁₉	#555	1	1	yes	characteristic
313	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
314	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	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	#462	C₄×C₁₉	1	8	yes	complemented
320	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#103	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×#97	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
334	#391	C₂²×C₁₉	1	1	yes	characteristic
335	#391	C₂²×C₁₉	1	1	yes	characteristic
336	#391	C₂²×C₁₉	1	1	yes	characteristic
337	#391	C₂²×C₁₉	1	1	yes	characteristic
338	#389	—	2	1	no	—
339	#387	—	2	1	no	—
340	#387	—	2	1	no	—
341	#387	—	2	1	no	—
342	#387	—	2	1	no	—
343	#383	—	2	1	no	—
344	#382	C₂²×C₁₉	1	1	yes	characteristic
345	C₄×C₄⋊C₄	—	2	1	no	—
346	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
350	#376	—	2	1	no	—
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	#336	C₂²×C₁₉	1	1	yes	characteristic
356	#336	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₁₉	#2363	1	1	yes	characteristic
358	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
359	C₂×C₁₉	#2950	1	1	yes	characteristic
360	C₂×C₁₉	#3312	1	1	yes	characteristic
361	C₂×C₁₉	#3315	1	1	yes	characteristic
362	C₂×C₁₉	#3398	1	1	yes	characteristic
363	C₂×C₁₉	#3402	1	1	yes	characteristic
364	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×Q₁₆	—	4	1	no	—
368	C₂×Q₁₆	—	4	1	no	—
369	C₂×Q₁₆	—	4	1	no	—
370	C₂×Q₁₆	—	4	1	no	—
371	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
372	C₂×Q₁₆	C₂×C₄×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	C₂×C₄×C₁₉	1	4	yes	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	4	1	no	—
383	C₄×Q₈	—	4	1	no	—
384	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	#107	—	4	1	no	—
407	#106	—	4	1	no	—
408	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	#103	—	2	2	no	—
413	#103	—	4	1	no	—
414	#103	—	4	1	no	—
415	#103	C₂×C₄×C₁₉	1	4	yes	—
416	#103	C₂×C₄×C₁₉	1	4	yes	—
417	#97	—	2	2	no	—
418	#97	—	4	1	no	—
419	C₄×C₈	—	4	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	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	D₄×C₁₉	1	1	yes	characteristic
434	#95	D₄×C₁₉	1	1	yes	characteristic
435	C₁₉	#23110	1	1	yes	characteristic, direct product factor, Sylow
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
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	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
452	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
453	C₂×Q₈	C₂²×C₄×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	—	4	4	no	—
470	Q₁₆	—	4	4	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	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
481	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
482	C₂×C₈	#41×C₁₉	1	2	yes	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	2	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	C₂²×C₄×C₁₉	1	2	yes	—
499	C₄⋊C₄	#41×C₁₉	1	2	yes	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
511	C₄²	#41×C₁₉	1	2	yes	—
512	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	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	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	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	—	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	C₄×D₄×C₁₉	1	2	yes	—
565	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
566	C₂×C₄	C₁₉×#137	1	2	yes	—
567	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
572	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
573	C₈	—	2	2	no	—
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	4	1	no	—
577	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
578	C₂²	C₁₉×#546	1	1	yes	characteristic
579	C₂²	C₁₉×#550	1	1	yes	characteristic
580	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
581	C₂²	C₁₉×#575	1	1	yes	characteristic
582	C₂²	C₁₉×#578	1	1	yes	characteristic
583	C₂²	C₁₉×#578	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	1	no	—
598	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
599	C₄	C₁₉×#518	1	1	yes	characteristic
600	C₄	C₁₉×#553	1	1	yes	characteristic
601	C₄	C₁₉×#555	1	1	yes	characteristic
602	C₂	C₁₉×#2363	1	1	yes	characteristic
603	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
604	C₂	C₁₉×#2950	1	1	yes	characteristic
605	C₂	C₁₉×#3312	1	1	yes	characteristic
606	C₂	C₁₉×#3315	1	1	yes	characteristic
607	C₂	C₁₉×#3398	1	1	yes	characteristic
608	C₂	C₁₉×#3402	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
22. C₁₉×#462	C₄	semidirect
207. #23110	C₁₉	direct (N × H)
319. #462	C₄×C₁₉	semidirect
435. C₁₉	#23110	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×#462	2
C₁₉×#2365	2
C₁₉×#2356	2
C₁₉×#1971	2
C₁₉×#1969	2
C₁₉×#1960	2
C₁₉×#1949	2
C₁₉×#1928	2
C₁₉×#1927	2
C₁₉×#1878	2
C₁₉×#1771	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#23110	19

Subgroups — C19×#23110 #18029069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23110 #18029069