Subgroups — C₁₉×#21772 #18027731

Order 4864.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#537	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#537	—	2	4	no	—
21	C₁₉×#537	C₄	1	8	yes	complemented
22	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#121	—	2	1	no	—
26	C₂×C₁₉×#121	—	2	1	no	—
27	C₂×C₁₉×#121	—	2	1	no	—
28	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₉	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×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
41	C₁₉×#408	—	2	4	no	—
42	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×#391	—	2	1	no	—
47	C₁₉×#390	—	2	1	no	—
48	C₁₉×#386	—	2	1	no	—
49	C₁₉×#386	—	2	1	no	—
50	C₁₉×#380	C₂²	1	1	yes	characteristic
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₁₉×#380	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	C₂×#41×C₁₉	—	2	2	no	—
63	C₂×#41×C₁₉	—	4	1	no	—
64	C₂×#41×C₁₉	—	4	1	no	—
65	C₂×#41×C₁₉	—	4	1	no	—
66	C₂×#41×C₁₉	—	4	1	no	—
67	C₂×#41×C₁₉	—	4	1	no	—
68	C₂×#41×C₁₉	—	4	1	no	—
69	C₂×#41×C₁₉	—	4	1	no	—
70	C₂×#41×C₁₉	—	4	1	no	—
71	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
72	C₂×#41×C₁₉	C₂×C₄	1	4	yes	complemented
73	C₂×#41×C₁₉	D₄	1	4	yes	—
74	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
75	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₉	—	2	1	no	—
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	—	2	1	no	—
84	C₂³×C₄×C₁₉	—	2	1	no	—
85	C₂³×C₄×C₁₉	—	2	1	no	—
86	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₁₉	—	2	2	no	—
90	C₂×M₁₆×C₁₉	—	4	1	no	—
91	C₂×M₁₆×C₁₉	—	4	1	no	—
92	C₂²×C₈×C₁₉	—	2	2	no	—
93	C₂²×C₈×C₁₉	—	4	1	no	—
94	C₂²×C₈×C₁₉	—	4	1	no	—
95	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×C₂²⋊Q₈	—	2	8	no	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	2	no	—
102	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
103	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
104	C₁₉×#121	—	2	8	no	—
105	C₁₉×#121	—	2	8	no	—
106	C₁₉×#121	—	2	8	no	—
107	C₁₉×#121	—	2	2	no	—
108	C₁₉×#121	—	2	2	no	—
109	C₁₉×#121	C₂×C₄	1	4	yes	—
110	C₁₉×#121	C₂×C₄	1	4	yes	complemented
111	C₁₉×#117	—	4	1	no	—
112	C₁₉×#117	—	4	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
136	C₂×C₄²×C₁₉	—	2	1	no	—
137	C₁₉×#103	—	4	1	no	—
138	C₁₉×#103	—	4	1	no	—
139	C₁₉×#103	—	4	1	no	—
140	C₁₉×#103	—	4	1	no	—
141	C₁₉×#102	—	4	1	no	—
142	C₁₉×#102	—	4	1	no	—
143	C₁₉×#102	—	4	1	no	—
144	C₁₉×#102	—	4	1	no	—
145	C₁₉×C₂²⋊C₈	—	2	2	no	—
146	C₁₉×C₂²⋊C₈	—	2	2	no	—
147	C₁₉×C₂²⋊C₈	—	2	2	no	—
148	C₁₉×C₂²⋊C₈	—	2	2	no	—
149	C₁₉×#95	—	2	1	no	—
150	C₁₉×#95	—	2	1	no	—
151	C₁₉×#95	—	2	1	no	—
152	C₁₉×#95	—	2	1	no	—
153	C₂⁴×C₁₉	—	2	1	no	—
154	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
157	#41×C₁₉	—	4	4	no	—
158	#41×C₁₉	—	4	4	no	—
159	#41×C₁₉	—	4	4	no	—
160	#41×C₁₉	—	4	4	no	—
161	#41×C₁₉	—	4	4	no	—
162	#41×C₁₉	—	4	4	no	—
163	#41×C₁₉	—	4	4	no	—
164	#41×C₁₉	—	4	4	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	1	no	—
169	C₂×Q₈×C₁₉	—	2	1	no	—
170	C₂×Q₈×C₁₉	—	4	1	no	—
171	C₂×Q₈×C₁₉	—	4	1	no	—
172	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
173	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
174	C₂×D₄×C₁₉	—	2	4	no	—
175	C₂×D₄×C₁₉	—	2	4	no	—
176	C₂×D₄×C₁₉	—	2	4	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	4	1	no	—
183	C₂×D₄×C₁₉	—	4	1	no	—
184	C₂×D₄×C₁₉	—	4	1	no	—
185	C₂×D₄×C₁₉	—	4	1	no	—
186	C₂×D₄×C₁₉	—	4	1	no	—
187	C₂×D₄×C₁₉	—	4	1	no	—
188	C₂×D₄×C₁₉	—	4	2	no	—
189	C₂×D₄×C₁₉	—	4	2	no	—
190	C₂×D₄×C₁₉	—	8	1	no	—
191	C₂×D₄×C₁₉	—	8	1	no	—
192	C₂×D₄×C₁₉	—	8	1	no	—
193	C₂×D₄×C₁₉	—	8	1	no	—
194	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
195	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
196	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
197	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
210	C₂²×C₄×C₁₉	—	2	1	no	—
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	2	1	no	—
213	C₂²×C₄×C₁₉	—	2	4	no	—
214	C₂²×C₄×C₁₉	—	2	4	no	—
215	C₂²×C₄×C₁₉	—	2	1	no	—
216	C₂²×C₄×C₁₉	—	2	1	no	—
217	C₂²×C₄×C₁₉	—	2	1	no	—
218	C₂²×C₄×C₁₉	—	2	1	no	—
219	C₂²×C₄×C₁₉	—	4	2	no	—
220	C₂²×C₄×C₁₉	—	4	2	no	—
221	C₂²×C₄×C₁₉	—	4	2	no	—
222	C₂²×C₄×C₁₉	—	8	1	no	—
223	C₂²×C₄×C₁₉	—	8	1	no	—
224	C₂²×C₄×C₁₉	—	8	1	no	—
225	C₂²×C₄×C₁₉	—	8	1	no	—
226	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
228	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
229	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
236	M₁₆×C₁₉	—	4	4	no	—
237	C₂×C₈×C₁₉	—	2	1	no	—
238	C₂×C₈×C₁₉	—	2	1	no	—
239	C₂×C₈×C₁₉	—	2	1	no	—
240	C₂×C₈×C₁₉	—	2	1	no	—
241	C₂×C₈×C₁₉	—	2	1	no	—
242	C₂×C₈×C₁₉	—	2	1	no	—
243	C₂×C₈×C₁₉	—	2	1	no	—
244	C₂×C₈×C₁₉	—	2	1	no	—
245	C₂×C₈×C₁₉	—	2	1	no	—
246	C₂×C₈×C₁₉	—	2	1	no	—
247	C₂×C₈×C₁₉	—	2	1	no	—
248	C₂×C₈×C₁₉	—	2	1	no	—
249	C₂×C₈×C₁₉	—	4	4	no	—
250	C₄⋊C₄×C₁₉	—	2	4	no	—
251	C₄⋊C₄×C₁₉	—	2	4	no	—
252	C₄⋊C₄×C₁₉	—	2	4	no	—
253	C₄⋊C₄×C₁₉	—	2	1	no	—
254	C₄⋊C₄×C₁₉	—	2	1	no	—
255	C₄⋊C₄×C₁₉	—	2	1	no	—
256	C₄⋊C₄×C₁₉	—	2	1	no	—
257	C₄⋊C₄×C₁₉	—	2	1	no	—
258	C₄⋊C₄×C₁₉	—	2	1	no	—
259	C₄⋊C₄×C₁₉	—	2	1	no	—
260	C₄⋊C₄×C₁₉	—	2	1	no	—
261	C₄⋊C₄×C₁₉	—	2	1	no	—
262	C₄⋊C₄×C₁₉	—	2	1	no	—
263	C₄⋊C₄×C₁₉	—	4	2	no	—
264	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
265	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
266	C₂²⋊C₄×C₁₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₉	—	4	2	no	—
271	C₂²⋊C₄×C₁₉	—	8	1	no	—
272	C₂²⋊C₄×C₁₉	—	8	1	no	—
273	C₂²⋊C₄×C₁₉	—	8	1	no	—
274	C₂²⋊C₄×C₁₉	—	8	1	no	—
275	C₄²×C₁₉	—	4	2	no	—
276	#21772	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂³×C₁₉	—	2	1	no	—
278	C₂³×C₁₉	—	2	1	no	—
279	C₂³×C₁₉	—	2	1	no	—
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	1	no	—
282	C₂³×C₁₉	—	2	1	no	—
283	C₂³×C₁₉	—	2	1	no	—
284	C₂³×C₁₉	—	2	1	no	—
285	C₂³×C₁₉	—	2	1	no	—
286	C₂³×C₁₉	—	2	1	no	—
287	C₂³×C₁₉	—	2	1	no	—
288	C₂³×C₁₉	—	2	1	no	—
289	C₂³×C₁₉	—	2	1	no	—
290	C₂³×C₁₉	—	2	1	no	—
291	C₂³×C₁₉	—	2	1	no	—
292	C₂³×C₁₉	—	2	1	no	—
293	C₂³×C₁₉	—	2	1	no	—
294	C₂³×C₁₉	—	2	1	no	—
295	C₂³×C₁₉	—	2	2	no	—
296	C₂³×C₁₉	—	4	1	no	—
297	C₂³×C₁₉	—	4	1	no	—
298	C₂³×C₁₉	—	4	1	no	—
299	C₂³×C₁₉	—	4	1	no	—
300	C₂³×C₁₉	—	4	1	no	—
301	C₂³×C₁₉	—	4	1	no	—
302	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₁₉	—	2	2	no	—
307	Q₈×C₁₉	—	2	2	no	—
308	Q₈×C₁₉	—	4	4	no	—
309	Q₈×C₁₉	—	4	1	no	—
310	Q₈×C₁₉	—	4	1	no	—
311	D₄×C₁₉	—	2	2	no	—
312	D₄×C₁₉	—	2	2	no	—
313	D₄×C₁₉	—	4	4	no	—
314	D₄×C₁₉	—	4	4	no	—
315	D₄×C₁₉	—	4	4	no	—
316	D₄×C₁₉	—	4	8	no	—
317	D₄×C₁₉	—	4	1	no	—
318	D₄×C₁₉	—	4	1	no	—
319	D₄×C₁₉	—	8	4	no	—
320	D₄×C₁₉	—	8	4	no	—
321	C₂×C₄×C₁₉	—	2	1	no	—
322	C₂×C₄×C₁₉	—	2	1	no	—
323	C₂×C₄×C₁₉	—	2	1	no	—
324	C₂×C₄×C₁₉	—	2	1	no	—
325	C₂×C₄×C₁₉	—	2	1	no	—
326	C₂×C₄×C₁₉	—	2	1	no	—
327	C₂×C₄×C₁₉	—	2	2	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	2	no	—
330	C₂×C₄×C₁₉	—	2	2	no	—
331	C₂×C₄×C₁₉	—	2	2	no	—
332	C₂×C₄×C₁₉	—	2	2	no	—
333	C₂×C₄×C₁₉	—	2	2	no	—
334	C₂×C₄×C₁₉	—	2	2	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	2	no	—
338	C₂×C₄×C₁₉	—	2	2	no	—
339	C₂×C₄×C₁₉	—	2	2	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	4	8	no	—
343	C₂×C₄×C₁₉	—	4	1	no	—
344	C₂×C₄×C₁₉	—	4	1	no	—
345	C₂×C₄×C₁₉	—	4	1	no	—
346	C₂×C₄×C₁₉	—	4	1	no	—
347	C₂×C₄×C₁₉	—	4	1	no	—
348	C₂×C₄×C₁₉	—	4	1	no	—
349	C₂×C₄×C₁₉	—	4	1	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	—	4	1	no	—
359	C₂×C₄×C₁₉	—	4	1	no	—
360	C₂×C₄×C₁₉	—	4	1	no	—
361	C₂×C₄×C₁₉	—	8	4	no	—
362	C₂×C₄×C₁₉	—	8	4	no	—
363	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
364	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
365	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
372	C₈×C₁₉	—	4	1	no	—
373	C₈×C₁₉	—	4	1	no	—
374	C₈×C₁₉	—	4	1	no	—
375	C₈×C₁₉	—	4	1	no	—
376	C₂×#537	C₂×C₁₉	1	1	yes	characteristic
377	C₂×#408	C₂×C₁₉	1	1	yes	characteristic, complemented
378	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
379	#1895	C₂×C₁₉	1	1	yes	characteristic, complemented
380	#1894	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
384	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
386	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
388	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
391	C₂²×C₁₉	—	2	2	no	—
392	C₂²×C₁₉	—	2	2	no	—
393	C₂²×C₁₉	—	2	2	no	—
394	C₂²×C₁₉	—	2	2	no	—
395	C₂²×C₁₉	—	2	2	no	—
396	C₂²×C₁₉	—	2	2	no	—
397	C₂²×C₁₉	—	2	2	no	—
398	C₂²×C₁₉	—	2	2	no	—
399	C₂²×C₁₉	—	2	2	no	—
400	C₂²×C₁₉	—	4	1	no	—
401	C₂²×C₁₉	—	4	1	no	—
402	C₂²×C₁₉	—	4	1	no	—
403	C₂²×C₁₉	—	4	1	no	—
404	C₂²×C₁₉	—	4	1	no	—
405	C₂²×C₁₉	—	4	1	no	—
406	C₂²×C₁₉	—	4	1	no	—
407	C₂²×C₁₉	—	4	1	no	—
408	C₂²×C₁₉	—	4	1	no	—
409	C₂²×C₁₉	—	4	1	no	—
410	C₂²×C₁₉	—	4	1	no	—
411	C₂²×C₁₉	—	4	1	no	—
412	C₂²×C₁₉	—	4	2	no	—
413	C₂²×C₁₉	—	4	2	no	—
414	C₂²×C₁₉	—	4	2	no	—
415	C₂²×C₁₉	—	8	1	no	—
416	C₂²×C₁₉	—	8	1	no	—
417	C₂²×C₁₉	—	8	1	no	—
418	C₂²×C₁₉	—	8	1	no	—
419	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×C₁₉	#534	1	1	yes	characteristic
421	C₂²×C₁₉	#534	1	1	yes	characteristic
422	C₂²×C₁₉	#576	1	1	yes	characteristic
423	C₂²×C₁₉	#577	1	1	yes	characteristic
424	C₂²×C₁₉	#577	1	1	yes	characteristic
425	C₂²×C₁₉	#578	1	1	yes	characteristic
426	C₄×C₁₉	—	2	2	no	—
427	C₄×C₁₉	—	2	2	no	—
428	C₄×C₁₉	—	2	2	no	—
429	C₄×C₁₉	—	4	2	no	—
430	C₄×C₁₉	—	4	2	no	—
431	C₄×C₁₉	—	4	2	no	—
432	C₄×C₁₉	—	8	1	no	—
433	C₄×C₁₉	—	8	1	no	—
434	C₄×C₁₉	—	8	1	no	—
435	C₄×C₁₉	—	8	1	no	—
436	C₄×C₁₉	#518	1	1	yes	characteristic
437	C₄×C₁₉	#518	1	1	yes	characteristic
438	C₄×C₁₉	#534	1	1	yes	characteristic
439	C₄×C₁₉	#534	1	1	yes	characteristic
440	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
441	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
442	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
443	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
444	#537	—	2	4	no	—
445	#537	C₄×C₁₉	1	8	yes	complemented
446	C₂×C₂²⋊Q₈	—	2	1	no	—
447	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
449	C₂×#121	—	2	1	no	—
450	C₂×#121	—	2	1	no	—
451	C₂×#121	—	2	1	no	—
452	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
454	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
455	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
463	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
465	#408	—	2	4	no	—
466	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
470	#391	—	2	1	no	—
471	#390	—	2	1	no	—
472	#386	—	2	1	no	—
473	#386	—	2	1	no	—
474	#380	C₂²×C₁₉	1	1	yes	characteristic
475	#380	C₂²×C₁₉	1	1	yes	characteristic
476	#380	C₂²×C₁₉	1	1	yes	characteristic
477	#380	C₂²×C₁₉	1	1	yes	characteristic
478	#340	C₂²×C₁₉	1	1	yes	characteristic
479	#340	C₂²×C₁₉	1	1	yes	characteristic
480	#340	C₂²×C₁₉	1	1	yes	characteristic
481	#340	C₂²×C₁₉	1	1	yes	characteristic
482	#340	C₂²×C₁₉	1	1	yes	characteristic
483	#340	C₂²×C₁₉	1	1	yes	characteristic
484	#340	C₂²×C₁₉	1	1	yes	characteristic
485	#340	C₂²×C₁₉	1	1	yes	characteristic
486	C₂×C₁₉	—	4	2	no	—
487	C₂×C₁₉	—	4	2	no	—
488	C₂×C₁₉	—	4	2	no	—
489	C₂×C₁₉	—	8	2	no	—
490	C₂×C₁₉	#2308	1	1	yes	characteristic
491	C₂×C₁₉	#2897	1	1	yes	characteristic
492	C₂×C₁₉	#2898	1	1	yes	characteristic
493	C₂×C₁₉	#3198	1	1	yes	characteristic
494	C₂×C₁₉	#3201	1	1	yes	characteristic
495	C₂×C₁₉	#3203	1	1	yes	characteristic
496	C₂×C₁₉	#3204	1	1	yes	characteristic
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	4	1	no	—
499	C₂×#41	—	4	1	no	—
500	C₂×#41	—	4	1	no	—
501	C₂×#41	—	4	1	no	—
502	C₂×#41	—	4	1	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂×#41	—	4	1	no	—
506	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
507	C₂×#41	C₂×C₄×C₁₉	1	4	yes	complemented
508	C₂×#41	D₄×C₁₉	1	4	yes	—
509	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
510	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
515	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
516	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
524	C₂×M₁₆	—	2	2	no	—
525	C₂×M₁₆	—	4	1	no	—
526	C₂×M₁₆	—	4	1	no	—
527	C₂²×C₈	—	2	2	no	—
528	C₂²×C₈	—	4	1	no	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
534	C₂²⋊Q₈	—	2	8	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
538	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
539	#121	—	2	8	no	—
540	#121	—	2	8	no	—
541	#121	—	2	8	no	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#121	C₂×C₄×C₁₉	1	4	yes	—
545	#121	C₂×C₄×C₁₉	1	4	yes	complemented
546	#117	—	4	1	no	—
547	#117	—	4	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	4	1	no	—
554	C₂×C₄⋊C₄	—	4	1	no	—
555	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
556	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₄²	—	2	1	no	—
572	#103	—	4	1	no	—
573	#103	—	4	1	no	—
574	#103	—	4	1	no	—
575	#103	—	4	1	no	—
576	#102	—	4	1	no	—
577	#102	—	4	1	no	—
578	#102	—	4	1	no	—
579	#102	—	4	1	no	—
580	C₂²⋊C₈	—	2	2	no	—
581	C₂²⋊C₈	—	2	2	no	—
582	C₂²⋊C₈	—	2	2	no	—
583	C₂²⋊C₈	—	2	2	no	—
584	#95	—	2	1	no	—
585	#95	—	2	1	no	—
586	#95	—	2	1	no	—
587	#95	—	2	1	no	—
588	C₁₉	#21772	1	1	yes	characteristic, direct product factor, Sylow
589	C₂⁴	—	2	1	no	—
590	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
591	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
592	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
593	#41	—	4	4	no	—
594	#41	—	4	4	no	—
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	4	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	4	1	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
609	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	4	1	no	—
619	C₂×D₄	—	4	1	no	—
620	C₂×D₄	—	4	1	no	—
621	C₂×D₄	—	4	1	no	—
622	C₂×D₄	—	4	1	no	—
623	C₂×D₄	—	4	1	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	8	1	no	—
627	C₂×D₄	—	8	1	no	—
628	C₂×D₄	—	8	1	no	—
629	C₂×D₄	—	8	1	no	—
630	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
631	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
632	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
633	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	8	1	no	—
659	C₂²×C₄	—	8	1	no	—
660	C₂²×C₄	—	8	1	no	—
661	C₂²×C₄	—	8	1	no	—
662	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
663	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
664	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
665	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
672	M₁₆	—	4	4	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	4	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
701	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	8	1	no	—
708	C₂²⋊C₄	—	8	1	no	—
709	C₂²⋊C₄	—	8	1	no	—
710	C₂²⋊C₄	—	8	1	no	—
711	C₄²	—	4	2	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	1	no	—
736	C₂³	—	4	1	no	—
737	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
738	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
739	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
740	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
741	Q₈	—	2	2	no	—
742	Q₈	—	2	2	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	1	no	—
745	Q₈	—	4	1	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	4	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	8	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	8	4	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
799	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
800	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
801	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
803	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
804	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
806	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
807	C₈	—	4	1	no	—
808	C₈	—	4	1	no	—
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	8	1	no	—
836	C₂²	—	8	1	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
840	C₂²	C₁₉×#534	1	1	yes	characteristic
841	C₂²	C₁₉×#534	1	1	yes	characteristic
842	C₂²	C₁₉×#576	1	1	yes	characteristic
843	C₂²	C₁₉×#577	1	1	yes	characteristic
844	C₂²	C₁₉×#577	1	1	yes	characteristic
845	C₂²	C₁₉×#578	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	8	1	no	—
853	C₄	—	8	1	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	C₁₉×#518	1	1	yes	characteristic
857	C₄	C₁₉×#518	1	1	yes	characteristic
858	C₄	C₁₉×#534	1	1	yes	characteristic
859	C₄	C₁₉×#534	1	1	yes	characteristic
860	C₂	—	4	2	no	—
861	C₂	—	4	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₁₉×#2308	1	1	yes	characteristic
865	C₂	C₁₉×#2897	1	1	yes	characteristic
866	C₂	C₁₉×#2898	1	1	yes	characteristic
867	C₂	C₁₉×#3198	1	1	yes	characteristic
868	C₂	C₁₉×#3201	1	1	yes	characteristic
869	C₂	C₁₉×#3203	1	1	yes	characteristic
870	C₂	C₁₉×#3204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#408	C₂	semidirect
3. C₁₉×#2311	C₂	semidirect
4. C₁₉×#1895	C₂	semidirect
5. C₁₉×#1894	C₂	semidirect
6. C₁₉×#1893	C₂	semidirect
7. C₁₉×#1892	C₂	semidirect
8. C₁₉×#1875	C₂	semidirect
9. C₁₉×#1874	C₂	semidirect
10. C₁₉×#1873	C₂	semidirect
11. C₁₉×#1872	C₂	semidirect
12. C₁₉×#1824	C₂	semidirect
13. C₁₉×#1823	C₂	semidirect
14. C₁₉×#1788	C₂	semidirect
15. C₁₉×#1788	C₂	semidirect
21. C₁₉×#537	C₄	semidirect
72. C₂×#41×C₁₉	C₂×C₄	semidirect
103. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
110. C₁₉×#121	C₂×C₄	semidirect
120. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
276. #21772	C₁₉	direct (N × H)
377. C₂×#408	C₂×C₁₉	semidirect
378. #2311	C₂×C₁₉	semidirect
379. #1895	C₂×C₁₉	semidirect
380. #1894	C₂×C₁₉	semidirect
381. #1893	C₂×C₁₉	semidirect
382. #1892	C₂×C₁₉	semidirect
383. #1875	C₂×C₁₉	semidirect
384. #1874	C₂×C₁₉	semidirect
385. #1873	C₂×C₁₉	semidirect
386. #1872	C₂×C₁₉	semidirect
387. #1824	C₂×C₁₉	semidirect
388. #1823	C₂×C₁₉	semidirect
389. #1788	C₂×C₁₉	semidirect
390. #1788	C₂×C₁₉	semidirect
445. #537	C₄×C₁₉	semidirect
507. C₂×#41	C₂×C₄×C₁₉	semidirect
538. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
545. #121	C₂×C₄×C₁₉	semidirect
555. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
588. C₁₉	#21772	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×#537	2
C₂×C₁₉×#408	2
C₁₉×#2311	2
C₁₉×#1895	2
C₁₉×#1894	2
C₁₉×#1893	2
C₁₉×#1892	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1873	2
C₁₉×#1872	2
C₁₉×#1824	2
C₁₉×#1823	2
C₁₉×#1788	2
#21772	19

Subgroups — C19×#21772 #18027731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21772 #18027731