Subgroups — C₁₉×#21516 #18027475

Order 4864.

932 conjugacy classes of subgroups.

The subgroup lattice has 626 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	C₂×C₁₉×#441	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2327	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2276	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1981	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×#1805	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	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	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#462	C₄	1	8	yes	complemented
25	C₁₉×#441	—	2	4	no	—
26	C₄×Q₁₆×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₄⋊C₈	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×#103	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×#391	C₂²	1	1	yes	characteristic
42	C₁₉×#391	C₂²	1	1	yes	characteristic
43	C₁₉×#387	—	2	1	no	—
44	C₁₉×#387	—	2	1	no	—
45	C₁₉×#387	—	2	1	no	—
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#382	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#376	—	2	1	no	—
55	C₁₉×#376	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	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₁₉	—	2	2	no	—
66	C₂×Q₁₆×C₁₉	—	2	2	no	—
67	C₂×Q₁₆×C₁₉	—	2	2	no	—
68	C₂×Q₁₆×C₁₉	—	2	2	no	—
69	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
70	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	—	2	2	no	—
76	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	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	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#107	—	2	2	no	—
111	C₁₉×#106	—	2	2	no	—
112	C₁₉×C₄⋊C₈	—	2	2	no	—
113	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
114	C₁₉×#103	—	2	2	no	—
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#103	—	2	2	no	—
118	C₁₉×#103	—	2	2	no	—
119	C₁₉×#103	—	2	2	no	—
120	C₁₉×#103	C₂×C₄	1	4	yes	—
121	C₁₉×#103	C₂×C₄	1	4	yes	—
122	C₁₉×#97	—	2	2	no	—
123	C₄×C₈×C₁₉	—	2	2	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	—	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	C₁₉×#95	D₄	1	1	yes	characteristic
136	C₁₉×#95	D₄	1	1	yes	characteristic
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	—	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	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
152	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
153	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
154	C₂×Q₈×C₁₉	#41	1	2	yes	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₁₉	—	2	8	no	—
171	Q₁₆×C₁₉	—	2	8	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	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	1	no	—
178	C₂×C₈×C₁₉	—	2	1	no	—
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
184	C₄⋊C₄×C₁₉	—	2	4	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	—	2	4	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	2	no	—
197	C₄⋊C₄×C₁₉	—	4	2	no	—
198	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
199	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₁₉	#41	1	2	yes	—
201	C₄²×C₁₉	—	2	4	no	—
202	C₄²×C₁₉	—	2	4	no	—
203	C₄²×C₁₉	—	2	4	no	—
204	C₄²×C₁₉	—	2	1	no	—
205	C₄²×C₁₉	—	2	1	no	—
206	C₄²×C₁₉	—	4	2	no	—
207	C₄²×C₁₉	—	4	2	no	—
208	C₄²×C₁₉	—	8	1	no	—
209	C₄²×C₁₉	—	8	1	no	—
210	C₄²×C₁₉	—	8	1	no	—
211	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
212	C₄²×C₁₉	C₂×D₄	1	2	yes	—
213	C₄²×C₁₉	#41	1	2	yes	—
214	C₄²×C₁₉	#41	1	2	yes	—
215	#21516	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
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	—	2	2	no	—
222	Q₈×C₁₉	—	2	2	no	—
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	4	1	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	C₄×D₄	1	4	yes	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	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	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	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
268	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
269	C₂×C₄×C₁₉	#121	1	2	yes	—
270	C₂×C₄×C₁₉	#121	1	2	yes	—
271	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
277	C₈×C₁₉	—	2	2	no	—
278	C₈×C₁₉	—	2	2	no	—
279	C₈×C₁₉	—	4	1	no	—
280	C₈×C₁₉	—	4	1	no	—
281	C₂×#462	C₂×C₁₉	1	1	yes	characteristic
282	C₂×#441	C₂×C₁₉	1	1	yes	characteristic
283	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
284	#2327	C₂×C₁₉	1	1	yes	characteristic
285	#2276	C₂×C₁₉	1	1	yes	characteristic
286	#1981	C₂×C₁₉	1	1	yes	characteristic
287	#1949	C₂×C₁₉	1	1	yes	characteristic
288	#1928	C₂×C₁₉	1	1	yes	characteristic
289	#1927	C₂×C₁₉	1	1	yes	characteristic
290	#1878	C₂×C₁₉	1	1	yes	characteristic
291	#1878	C₂×C₁₉	1	1	yes	characteristic
292	#1805	C₂×C₁₉	1	1	yes	characteristic
293	#1768	C₂×C₁₉	1	1	yes	characteristic
294	#1763	C₂×C₁₉	1	1	yes	characteristic
295	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
297	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
298	C₂²×C₁₉	#525	1	1	yes	characteristic
299	C₂²×C₁₉	#577	1	1	yes	characteristic
300	C₂²×C₁₉	#578	1	1	yes	characteristic
301	C₂²×C₁₉	#578	1	1	yes	characteristic
302	C₂²×C₁₉	#578	1	1	yes	characteristic
303	C₄×C₁₉	—	2	2	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	2	no	—
307	C₄×C₁₉	—	2	4	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	4	1	no	—
311	C₄×C₁₉	—	4	2	no	—
312	C₄×C₁₉	—	4	2	no	—
313	C₄×C₁₉	—	4	2	no	—
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	8	1	no	—
316	C₄×C₁₉	—	8	1	no	—
317	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
319	C₄×C₁₉	#529	1	1	yes	characteristic
320	C₄×C₁₉	#532	1	1	yes	characteristic
321	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
322	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	#462	C₄×C₁₉	1	8	yes	complemented
330	#441	—	2	4	no	—
331	C₄×Q₁₆	—	2	4	no	—
332	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
346	#391	C₂²×C₁₉	1	1	yes	characteristic
347	#391	C₂²×C₁₉	1	1	yes	characteristic
348	#387	—	2	1	no	—
349	#387	—	2	1	no	—
350	#387	—	2	1	no	—
351	#387	—	2	1	no	—
352	#382	C₂²×C₁₉	1	1	yes	characteristic
353	C₄×C₄⋊C₄	—	2	1	no	—
354	C₄×C₄⋊C₄	—	2	1	no	—
355	C₄×C₄⋊C₄	—	2	1	no	—
356	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
357	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
359	#376	—	2	1	no	—
360	#376	C₂²×C₁₉	1	1	yes	characteristic
361	#340	C₂²×C₁₉	1	1	yes	characteristic
362	#340	C₂²×C₁₉	1	1	yes	characteristic
363	#340	C₂²×C₁₉	1	1	yes	characteristic
364	#340	C₂²×C₁₉	1	1	yes	characteristic
365	#336	C₂²×C₁₉	1	1	yes	characteristic
366	#336	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₁₉	C₄×#121	1	1	yes	characteristic
368	C₂×C₁₉	#2947	1	1	yes	characteristic
369	C₂×C₁₉	#2950	1	1	yes	characteristic
370	C₂×C₁₉	#3044	1	1	yes	characteristic
371	C₂×C₁₉	#3046	1	1	yes	characteristic
372	C₂×C₁₉	#3120	1	1	yes	characteristic
373	C₂×C₁₉	#3127	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
377	C₂×Q₁₆	—	2	2	no	—
378	C₂×Q₁₆	—	2	2	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	—	2	2	no	—
381	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
382	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
383	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
387	C₄⋊Q₈	—	2	2	no	—
388	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
398	C₄×Q₈	D₄×C₁₉	1	4	yes	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
422	#107	—	2	2	no	—
423	#106	—	2	2	no	—
424	C₄⋊C₈	—	2	2	no	—
425	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	C₂×C₄×C₁₉	1	4	yes	—
433	#103	C₂×C₄×C₁₉	1	4	yes	—
434	#97	—	2	2	no	—
435	C₄×C₈	—	2	2	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	D₄×C₁₉	1	1	yes	characteristic
446	#95	D₄×C₁₉	1	1	yes	characteristic
447	#95	D₄×C₁₉	1	1	yes	characteristic
448	#95	D₄×C₁₉	1	1	yes	characteristic
449	C₁₉	#21516	1	1	yes	characteristic, direct product factor, Sylow
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
464	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
465	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
466	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
467	C₂×Q₈	#41×C₁₉	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
483	Q₁₆	—	2	8	no	—
484	Q₁₆	—	2	8	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
496	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
513	C₄⋊C₄	#41×C₁₉	1	2	yes	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	8	1	no	—
522	C₄²	—	8	1	no	—
523	C₄²	—	8	1	no	—
524	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
525	C₄²	C₂×D₄×C₁₉	1	2	yes	—
526	C₄²	#41×C₁₉	1	2	yes	—
527	C₄²	#41×C₁₉	1	2	yes	—
528	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	C₄×D₄×C₁₉	1	4	yes	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	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	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	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	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
580	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
581	C₂×C₄	C₁₉×#121	1	2	yes	—
582	C₂×C₄	C₁₉×#121	1	2	yes	—
583	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
585	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
586	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
587	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
588	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
589	C₈	—	2	2	no	—
590	C₈	—	2	2	no	—
591	C₈	—	4	1	no	—
592	C₈	—	4	1	no	—
593	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
594	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
595	C₂²	C₁₉×#525	1	1	yes	characteristic
596	C₂²	C₁₉×#577	1	1	yes	characteristic
597	C₂²	C₁₉×#578	1	1	yes	characteristic
598	C₂²	C₁₉×#578	1	1	yes	characteristic
599	C₂²	C₁₉×#578	1	1	yes	characteristic
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	4	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
615	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
616	C₄	C₁₉×#529	1	1	yes	characteristic
617	C₄	C₁₉×#532	1	1	yes	characteristic
618	C₂	C₄×C₁₉×#121	1	1	yes	characteristic
619	C₂	C₁₉×#2947	1	1	yes	characteristic
620	C₂	C₁₉×#2950	1	1	yes	characteristic
621	C₂	C₁₉×#3044	1	1	yes	characteristic
622	C₂	C₁₉×#3046	1	1	yes	characteristic
623	C₂	C₁₉×#3120	1	1	yes	characteristic
624	C₂	C₁₉×#3127	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
24. C₁₉×#462	C₄	semidirect
215. #21516	C₁₉	direct (N × H)
329. #462	C₄×C₁₉	semidirect
449. C₁₉	#21516	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
C₂×C₁₉×#441	2
C₂×C₄×Q₁₆×C₁₉	2
C₁₉×#2327	2
C₁₉×#2276	2
C₁₉×#1981	2
C₁₉×#1949	2
C₁₉×#1928	2
C₁₉×#1927	2
C₁₉×#1878	2
C₁₉×#1805	2
C₁₉×#1768	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#21516	19

Subgroups — C19×#21516 #18027475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21516 #18027475