Subgroups — C₁₉×#21569 #18027528

Order 4864.

852 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2395	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1924	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1917	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1771	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1753	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#435	—	2	4	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#405	—	2	4	no	—
25	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#97	C₂²	1	2	yes	—
27	C₂×C₁₉×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#400	C₄	1	1	yes	characteristic
30	C₁₉×#399	C₄	1	1	yes	characteristic
31	C₁₉×#398	C₄	1	1	yes	characteristic
32	C₁₉×#397	C₄	1	2	yes	—
33	C₁₉×#397	C₄	1	1	yes	characteristic
34	C₁₉×#394	C₄	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₁₉×#336	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂²×C₈×C₁₉	—	2	4	no	—
51	C₂²×C₈×C₁₉	D₄	1	4	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	2	4	no	—
78	C₁₉×C₂²⋊C₈	—	2	2	no	—
79	C₁₉×C₂²⋊C₈	—	2	2	no	—
80	C₁₉×C₂²⋊C₈	—	2	2	no	—
81	C₁₉×C₂²⋊C₈	—	2	4	no	—
82	C₁₉×#97	—	2	4	no	—
83	C₁₉×#97	—	2	2	no	—
84	C₁₉×#97	—	2	4	no	—
85	C₄×C₈×C₁₉	—	2	4	no	—
86	C₁₉×#95	C₂×C₄	1	2	yes	—
87	C₁₉×#95	C₂×C₄	1	2	yes	—
88	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
89	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₉×#95	C₂×C₄	1	2	yes	—
91	C₁₉×#95	C₂×C₄	1	2	yes	—
92	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	#41	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₁₉	—	2	8	no	—
115	M₁₆×C₁₉	—	4	4	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	8	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	1	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₉	#41	1	4	yes	—
130	C₂×C₈×C₁₉	#41	1	4	yes	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	4	2	no	—
135	C₄⋊C₄×C₁₉	—	4	2	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	4	2	no	—
140	C₂²⋊C₄×C₁₉	—	4	2	no	—
141	C₂²⋊C₄×C₁₉	—	4	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	1	no	—
144	C₄²×C₁₉	—	2	2	no	—
145	C₄²×C₁₉	—	2	1	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	2	no	—
148	#21569	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	2	1	no	—
153	C₂³×C₁₉	—	2	1	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	C₄×D₄	1	2	yes	—
159	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
160	D₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	4	1	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₉	—	2	2	no	—
193	C₈×C₁₉	—	2	4	no	—
194	C₈×C₁₉	—	4	1	no	—
195	C₈×C₁₉	—	4	1	no	—
196	C₈×C₁₉	—	4	2	no	—
197	C₈×C₁₉	#123	1	4	yes	—
198	C₂×#435	C₂×C₁₉	1	1	yes	characteristic
199	C₂×#405	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#2395	C₂×C₁₉	1	1	yes	characteristic
201	#1924	C₂×C₁₉	1	2	yes	complemented
202	#1917	C₂×C₁₉	1	2	yes	complemented
203	#1870	C₂×C₁₉	1	1	yes	characteristic
204	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#1818	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#1771	C₂×C₁₉	1	2	yes	complemented
207	#1753	C₂×C₁₉	1	2	yes	complemented
208	#1752	C₂×C₁₉	1	1	yes	characteristic, complemented
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	1	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	1	no	—
219	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₁₉	C₄×#41	1	2	yes	—
221	C₂²×C₁₉	#568	1	1	yes	characteristic
222	C₂²×C₁₉	#568	1	1	yes	characteristic
223	C₂²×C₁₉	#568	1	2	yes	—
224	C₄×C₁₉	—	2	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	1	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	—	4	2	no	—
229	C₄×C₁₉	—	4	2	no	—
230	C₄×C₁₉	—	4	2	no	—
231	C₄×C₁₉	—	4	1	no	—
232	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
233	C₄×C₁₉	#525	1	1	yes	characteristic
234	C₄×C₁₉	#529	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
237	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
239	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
240	#435	—	2	4	no	—
241	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
247	#405	—	2	4	no	—
248	C₂×#97	C₂²×C₁₉	1	2	yes	—
249	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#97	C₂²×C₁₉	1	2	yes	—
251	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
252	#400	C₄×C₁₉	1	1	yes	characteristic
253	#399	C₄×C₁₉	1	1	yes	characteristic
254	#398	C₄×C₁₉	1	1	yes	characteristic
255	#397	C₄×C₁₉	1	2	yes	—
256	#397	C₄×C₁₉	1	1	yes	characteristic
257	#394	C₄×C₁₉	1	2	yes	—
258	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
261	#336	C₂²×C₁₉	1	2	yes	—
262	#336	C₂²×C₁₉	1	2	yes	—
263	#336	C₂²×C₁₉	1	2	yes	—
264	#336	C₂²×C₁₉	1	2	yes	—
265	#336	C₂²×C₁₉	1	2	yes	—
266	C₂×C₁₉	—	4	2	no	—
267	C₂×C₁₉	—	8	1	no	—
268	C₂×C₁₉	C₄×#123	1	1	yes	characteristic
269	C₂×C₁₉	#2930	1	1	yes	characteristic
270	C₂×C₁₉	#2932	1	1	yes	characteristic
271	C₂×C₁₉	#2967	1	2	yes	—
272	C₂×C₁₉	#2967	1	2	yes	—
273	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂²×C₈	—	2	4	no	—
281	C₂²×C₈	D₄×C₁₉	1	4	yes	—
282	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
284	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	4	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	4	no	—
312	#97	—	2	4	no	—
313	#97	—	2	2	no	—
314	#97	—	2	4	no	—
315	C₄×C₈	—	2	4	no	—
316	#95	C₂×C₄×C₁₉	1	2	yes	—
317	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
318	#95	C₂×C₄×C₁₉	1	2	yes	—
319	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
320	#95	C₂×C₄×C₁₉	1	2	yes	—
321	#95	C₂×C₄×C₁₉	1	2	yes	—
322	C₁₉	#21569	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
324	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
343	C₂²×C₄	#41×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	M₁₆	—	2	8	no	—
346	M₁₆	—	4	4	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	8	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
360	C₂×C₈	#41×C₁₉	1	4	yes	—
361	C₂×C₈	#41×C₁₉	1	4	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₄×D₄×C₁₉	1	2	yes	—
389	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
390	D₄	—	4	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
420	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
421	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	2	4	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	C₁₉×#123	1	4	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
439	C₂²	C₄×#41×C₁₉	1	2	yes	—
440	C₂²	C₁₉×#568	1	1	yes	characteristic
441	C₂²	C₁₉×#568	1	1	yes	characteristic
442	C₂²	C₁₉×#568	1	2	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
452	C₄	C₁₉×#525	1	1	yes	characteristic
453	C₄	C₁₉×#529	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	8	1	no	—
456	C₂	C₄×C₁₉×#123	1	1	yes	characteristic
457	C₂	C₁₉×#2930	1	1	yes	characteristic
458	C₂	C₁₉×#2932	1	1	yes	characteristic
459	C₂	C₁₉×#2967	1	2	yes	—
460	C₂	C₁₉×#2967	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂²×D₄×C₁₉	C₂×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
2. C₂×C₁₉×#405	C₂	semidirect
4. C₁₉×#1924	C₂	semidirect
5. C₁₉×#1917	C₂	semidirect
7. C₁₉×#1851	C₂	semidirect
8. C₁₉×#1818	C₂	semidirect
9. C₁₉×#1771	C₂	semidirect
10. C₁₉×#1753	C₂	semidirect
11. C₁₉×#1752	C₂	semidirect
148. #21569	C₁₉	direct (N × H)
199. C₂×#405	C₂×C₁₉	semidirect
201. #1924	C₂×C₁₉	semidirect
202. #1917	C₂×C₁₉	semidirect
204. #1851	C₂×C₁₉	semidirect
205. #1818	C₂×C₁₉	semidirect
206. #1771	C₂×C₁₉	semidirect
207. #1753	C₂×C₁₉	semidirect
208. #1752	C₂×C₁₉	semidirect
322. C₁₉	#21569	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×#435	2
C₂×C₁₉×#405	2
C₁₉×#2395	2
C₁₉×#1924	2
C₁₉×#1917	2
C₁₉×#1870	2
C₁₉×#1851	2
C₁₉×#1818	2
C₁₉×#1771	2
C₁₉×#1753	2
C₁₉×#1752	2
#21569	19

Subgroups — C19×#21569 #18027528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21569 #18027528