Subgroups — C₁₉×#21347 #18027306

Order 4864.

666 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2295	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1940	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1916	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1916	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1746	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1726	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#391	C₄	1	1	yes	characteristic
32	C₁₉×#391	C₄	1	1	yes	characteristic
33	C₁₉×#389	C₄	1	1	yes	characteristic
34	C₁₉×#389	C₄	1	1	yes	characteristic
35	C₁₉×#387	C₄	1	1	yes	characteristic
36	C₁₉×#387	C₄	1	1	yes	characteristic
37	C₁₉×#387	C₄	1	1	yes	characteristic
38	C₁₉×#387	C₄	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#376	C₂²	1	1	yes	characteristic
43	C₁₉×#376	C₂²	1	1	yes	characteristic
44	C₄³×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#336	C₂²	1	1	yes	characteristic
46	C₁₉×#336	C₂²	1	1	yes	characteristic
47	C₁₉×#336	C₂²	1	1	yes	characteristic
48	C₁₉×#336	C₂²	1	1	yes	characteristic
49	C₁₉×#336	C₂²	1	1	yes	characteristic
50	C₁₉×#336	C₂²	1	1	yes	characteristic
51	C₁₉×#336	C₂²	1	1	yes	characteristic
52	C₁₉×#336	C₂²	1	1	yes	characteristic
53	C₁₉×#336	C₂²	1	1	yes	characteristic
54	C₁₉×#336	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×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	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×C₄⋊C₈	—	2	2	no	—
92	C₁₉×C₄⋊C₈	—	2	2	no	—
93	C₁₉×C₄⋊C₈	—	2	2	no	—
94	C₁₉×C₄⋊C₈	—	2	2	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×#97	—	2	2	no	—
97	C₁₉×#97	—	2	2	no	—
98	C₁₉×#97	—	2	2	no	—
99	C₁₉×#97	—	2	2	no	—
100	C₄×C₈×C₁₉	—	2	2	no	—
101	C₄×C₈×C₁₉	—	2	2	no	—
102	C₄×C₈×C₁₉	—	2	2	no	—
103	C₄×C₈×C₁₉	Q₈	1	4	yes	complemented
104	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
157	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
158	C₂×C₈×C₁₉	#41	1	2	yes	—
159	C₂×C₈×C₁₉	#41	1	2	yes	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	2	1	no	—
173	C₄²×C₁₉	—	2	1	no	—
174	C₄²×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	1	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	2	1	no	—
178	C₄²×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	4	1	no	—
182	C₄²×C₁₉	—	4	1	no	—
183	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
184	C₄²×C₁₉	#41	1	2	yes	—
185	C₄²×C₁₉	#41	1	2	yes	—
186	C₄²×C₁₉	#41	1	2	yes	—
187	#21347	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
189	Q₈×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	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	#117	1	2	yes	—
227	C₂×C₄×C₁₉	#117	1	2	yes	—
228	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
229	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
230	C₂×C₄×C₁₉	#131	1	2	yes	—
231	C₂×C₄×C₁₉	#131	1	2	yes	—
232	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₈×C₁₉	—	2	2	no	—
239	C₈×C₁₉	—	2	2	no	—
240	C₈×C₁₉	—	2	2	no	—
241	C₈×C₁₉	—	2	2	no	—
242	C₈×C₁₉	—	4	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	#2295	C₂×C₁₉	1	1	yes	characteristic
247	#1985	C₂×C₁₉	1	1	yes	characteristic
248	#1984	C₂×C₁₉	1	1	yes	characteristic
249	#1940	C₂×C₁₉	1	1	yes	characteristic
250	#1939	C₂×C₁₉	1	1	yes	characteristic
251	#1917	C₂×C₁₉	1	1	yes	characteristic
252	#1917	C₂×C₁₉	1	1	yes	characteristic
253	#1916	C₂×C₁₉	1	1	yes	characteristic
254	#1916	C₂×C₁₉	1	1	yes	characteristic
255	#1768	C₂×C₁₉	1	1	yes	characteristic
256	#1768	C₂×C₁₉	1	1	yes	characteristic
257	#1767	C₂×C₁₉	1	1	yes	characteristic
258	#1746	C₂×C₁₉	1	1	yes	characteristic
259	#1744	C₂×C₁₉	1	1	yes	characteristic
260	#1726	C₂×C₁₉	1	1	yes	characteristic
261	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
265	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
266	C₂²×C₁₉	#568	1	1	yes	characteristic
267	C₂²×C₁₉	#568	1	1	yes	characteristic
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	2	2	no	—
271	C₄×C₁₉	—	2	2	no	—
272	C₄×C₁₉	—	2	2	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	#529	1	1	yes	characteristic
283	C₄×C₁₉	#529	1	1	yes	characteristic
284	C₄×C₁₉	#533	1	1	yes	characteristic
285	C₄×C₁₉	#533	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
301	#391	C₄×C₁₉	1	1	yes	characteristic
302	#391	C₄×C₁₉	1	1	yes	characteristic
303	#389	C₄×C₁₉	1	1	yes	characteristic
304	#389	C₄×C₁₉	1	1	yes	characteristic
305	#387	C₄×C₁₉	1	1	yes	characteristic
306	#387	C₄×C₁₉	1	1	yes	characteristic
307	#387	C₄×C₁₉	1	1	yes	characteristic
308	#387	C₄×C₁₉	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	#376	C₂²×C₁₉	1	1	yes	characteristic
313	#376	C₂²×C₁₉	1	1	yes	characteristic
314	C₄³	C₂²×C₁₉	1	1	yes	characteristic
315	#336	C₂²×C₁₉	1	1	yes	characteristic
316	#336	C₂²×C₁₉	1	1	yes	characteristic
317	#336	C₂²×C₁₉	1	1	yes	characteristic
318	#336	C₂²×C₁₉	1	1	yes	characteristic
319	#336	C₂²×C₁₉	1	1	yes	characteristic
320	#336	C₂²×C₁₉	1	1	yes	characteristic
321	#336	C₂²×C₁₉	1	1	yes	characteristic
322	#336	C₂²×C₁₉	1	1	yes	characteristic
323	#336	C₂²×C₁₉	1	1	yes	characteristic
324	#336	C₂²×C₁₉	1	1	yes	characteristic
325	#336	C₂²×C₁₉	1	1	yes	characteristic
326	#336	C₂²×C₁₉	1	1	yes	characteristic
327	#336	C₂²×C₁₉	1	1	yes	characteristic
328	#336	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₁₉	#2295	1	1	yes	characteristic
330	C₂×C₁₉	#2924	1	1	yes	characteristic
331	C₂×C₁₉	#2925	1	1	yes	characteristic
332	C₂×C₁₉	#2960	1	1	yes	characteristic
333	C₂×C₁₉	#2961	1	1	yes	characteristic
334	C₂×C₁₉	#2968	1	1	yes	characteristic
335	C₂×C₁₉	#2969	1	1	yes	characteristic
336	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
356	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
358	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₄⋊C₈	—	2	2	no	—
373	#97	—	2	2	no	—
374	#97	—	2	2	no	—
375	#97	—	2	2	no	—
376	#97	—	2	2	no	—
377	C₄×C₈	—	2	2	no	—
378	C₄×C₈	—	2	2	no	—
379	C₄×C₈	—	2	2	no	—
380	C₄×C₈	Q₈×C₁₉	1	4	yes	complemented
381	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
382	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
383	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
384	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
385	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
386	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
387	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
388	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
389	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
390	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
391	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
392	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
393	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
394	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
395	C₁₉	#21347	1	1	yes	characteristic, direct product factor, Sylow
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
435	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
436	C₂×C₈	#41×C₁₉	1	2	yes	—
437	C₂×C₈	#41×C₁₉	1	2	yes	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	4	1	no	—
460	C₄²	—	4	1	no	—
461	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
462	C₄²	#41×C₁₉	1	2	yes	—
463	C₄²	#41×C₁₉	1	2	yes	—
464	C₄²	#41×C₁₉	1	2	yes	—
465	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
466	Q₈	—	4	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	C₁₉×#117	1	2	yes	—
504	C₂×C₄	C₁₉×#117	1	2	yes	—
505	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
506	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
507	C₂×C₄	C₁₉×#131	1	2	yes	—
508	C₂×C₄	C₁₉×#131	1	2	yes	—
509	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	2	no	—
518	C₈	—	2	2	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
524	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
525	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
526	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
527	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
528	C₂²	C₁₉×#568	1	1	yes	characteristic
529	C₂²	C₁₉×#568	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	C₁₉×#529	1	1	yes	characteristic
545	C₄	C₁₉×#529	1	1	yes	characteristic
546	C₄	C₁₉×#533	1	1	yes	characteristic
547	C₄	C₁₉×#533	1	1	yes	characteristic
548	C₂	C₁₉×#2295	1	1	yes	characteristic
549	C₂	C₁₉×#2924	1	1	yes	characteristic
550	C₂	C₁₉×#2925	1	1	yes	characteristic
551	C₂	C₁₉×#2960	1	1	yes	characteristic
552	C₂	C₁₉×#2961	1	1	yes	characteristic
553	C₂	C₁₉×#2968	1	1	yes	characteristic
554	C₂	C₁₉×#2969	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
103. C₄×C₈×C₁₉	Q₈	semidirect
187. #21347	C₁₉	direct (N × H)
380. C₄×C₈	Q₈×C₁₉	semidirect
395. C₁₉	#21347	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2295	2
C₁₉×#1985	2
C₁₉×#1984	2
C₁₉×#1940	2
C₁₉×#1939	2
C₁₉×#1917	2
C₁₉×#1916	2
C₁₉×#1768	2
C₁₉×#1767	2
C₁₉×#1746	2
C₁₉×#1744	2
C₁₉×#1726	2
#21347	19

Subgroups — C19×#21347 #18027306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21347 #18027306