Subgroups — C₁₉×#22426 #18028385

Order 4864.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×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×#548	—	2	4	no	—
21	C₁₉×#548	C₄	1	8	yes	complemented
22	C₂×C₁₉×#124	—	2	1	no	—
23	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	—	2	1	no	—
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₉	—	2	1	no	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
33	C₁₉×#435	—	2	4	no	—
34	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₁₉×#419	—	2	4	no	—
36	C₁₉×#416	—	2	4	no	—
37	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
52	C₁₉×#390	—	2	1	no	—
53	C₁₉×#388	—	2	1	no	—
54	C₁₉×#388	—	2	1	no	—
55	C₁₉×#384	C₂²	1	1	yes	characteristic
56	C₁₉×#380	C₂²	1	1	yes	characteristic
57	C₁₉×#380	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₁₉×#340	C₂²	1	1	yes	characteristic
63	C₁₉×#340	C₂²	1	1	yes	characteristic
64	C₂×#41×C₁₉	—	2	2	no	—
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	—	4	1	no	—
68	C₂×#41×C₁₉	—	4	1	no	—
69	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
70	C₂²×Q₈×C₁₉	—	2	1	no	—
71	C₂²×Q₈×C₁₉	—	2	2	no	—
72	C₂²×Q₈×C₁₉	—	2	2	no	—
73	C₂²×Q₈×C₁₉	—	2	2	no	—
74	C₂²×Q₈×C₁₉	—	4	1	no	—
75	C₂²×Q₈×C₁₉	—	4	1	no	—
76	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
77	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₁₉	—	2	2	no	—
88	C₂×M₁₆×C₁₉	—	2	2	no	—
89	C₂×M₁₆×C₁₉	—	4	1	no	—
90	C₂²×C₈×C₁₉	—	2	2	no	—
91	C₂²×C₈×C₁₉	—	2	2	no	—
92	C₂²×C₈×C₁₉	—	4	1	no	—
93	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₁₉×#124	—	2	8	no	—
98	C₁₉×#124	—	2	2	no	—
99	C₁₉×#124	C₂×C₄	1	4	yes	—
100	C₁₉×C₂²⋊Q₈	—	2	2	no	—
101	C₁₉×C₂²⋊Q₈	—	2	8	no	—
102	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
103	C₁₉×#121	—	2	8	no	—
104	C₁₉×#121	—	2	2	no	—
105	C₁₉×#121	C₂×C₄	1	4	yes	—
106	C₄×Q₈×C₁₉	—	2	2	no	—
107	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
108	C₄×D₄×C₁₉	—	2	8	no	—
109	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
110	C₄×D₄×C₁₉	D₄	1	4	yes	—
111	C₁₉×#117	—	2	2	no	—
112	C₁₉×#117	—	2	2	no	—
113	C₁₉×#117	—	4	1	no	—
114	C₁₉×#117	—	4	1	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	—	2	1	no	—
119	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
135	C₂×C₄²×C₁₉	—	2	1	no	—
136	C₂×C₄²×C₁₉	—	2	1	no	—
137	C₂×C₄²×C₁₉	—	2	1	no	—
138	C₂×C₄²×C₁₉	—	2	1	no	—
139	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
140	C₁₉×C₄⋊C₈	—	2	2	no	—
141	C₁₉×#103	—	2	2	no	—
142	C₁₉×#103	—	2	2	no	—
143	C₁₉×#103	—	2	2	no	—
144	C₁₉×#103	—	2	2	no	—
145	C₁₉×#103	—	2	2	no	—
146	C₁₉×#103	—	4	1	no	—
147	C₁₉×#103	—	4	1	no	—
148	C₁₉×#103	D₄	1	4	yes	complemented
149	C₁₉×#102	—	2	2	no	—
150	C₁₉×#102	—	2	2	no	—
151	C₁₉×#102	—	4	1	no	—
152	C₁₉×#102	—	4	1	no	—
153	C₁₉×C₂²⋊C₈	—	2	2	no	—
154	C₁₉×C₂²⋊C₈	—	2	2	no	—
155	C₁₉×#97	—	2	2	no	—
156	C₁₉×#95	—	2	1	no	—
157	C₁₉×#95	—	2	1	no	—
158	C₁₉×#95	—	2	1	no	—
159	C₂⁴×C₁₉	—	2	1	no	—
160	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
162	#41×C₁₉	—	2	8	no	—
163	#41×C₁₉	—	4	4	no	—
164	#41×C₁₉	—	4	4	no	—
165	#41×C₁₉	—	4	4	no	—
166	C₂×Q₈×C₁₉	—	2	4	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	—	2	1	no	—
171	C₂×Q₈×C₁₉	—	2	8	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	—	2	1	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	4	2	no	—
177	C₂×Q₈×C₁₉	—	4	2	no	—
178	C₂×Q₈×C₁₉	—	4	4	no	—
179	C₂×Q₈×C₁₉	—	4	4	no	—
180	C₂×Q₈×C₁₉	—	4	4	no	—
181	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
182	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
183	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₁₉	#41	1	2	yes	—
185	C₂×D₄×C₁₉	—	2	4	no	—
186	C₂×D₄×C₁₉	—	2	4	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	2	1	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	4	1	no	—
193	C₂×D₄×C₁₉	—	4	1	no	—
194	C₂×D₄×C₁₉	—	4	2	no	—
195	C₂×D₄×C₁₉	—	4	2	no	—
196	C₂×D₄×C₁₉	—	4	2	no	—
197	C₂×D₄×C₁₉	—	4	2	no	—
198	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
199	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
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	4	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	1	no	—
215	C₂²×C₄×C₁₉	—	2	1	no	—
216	C₂²×C₄×C₁₉	—	2	1	no	—
217	C₂²×C₄×C₁₉	—	4	2	no	—
218	C₂²×C₄×C₁₉	—	4	2	no	—
219	C₂²×C₄×C₁₉	—	4	2	no	—
220	C₂²×C₄×C₁₉	—	4	2	no	—
221	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
222	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
223	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
230	M₁₆×C₁₉	—	4	4	no	—
231	C₂×C₈×C₁₉	—	2	1	no	—
232	C₂×C₈×C₁₉	—	2	1	no	—
233	C₂×C₈×C₁₉	—	2	1	no	—
234	C₂×C₈×C₁₉	—	2	1	no	—
235	C₂×C₈×C₁₉	—	2	1	no	—
236	C₂×C₈×C₁₉	—	2	1	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	—	4	4	no	—
243	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
244	C₄⋊C₄×C₁₉	—	2	4	no	—
245	C₄⋊C₄×C₁₉	—	2	4	no	—
246	C₄⋊C₄×C₁₉	—	2	1	no	—
247	C₄⋊C₄×C₁₉	—	2	1	no	—
248	C₄⋊C₄×C₁₉	—	2	1	no	—
249	C₄⋊C₄×C₁₉	—	2	1	no	—
250	C₄⋊C₄×C₁₉	—	2	1	no	—
251	C₄⋊C₄×C₁₉	—	2	1	no	—
252	C₄⋊C₄×C₁₉	—	2	1	no	—
253	C₄⋊C₄×C₁₉	—	2	1	no	—
254	C₄⋊C₄×C₁₉	—	4	2	no	—
255	C₄⋊C₄×C₁₉	—	8	1	no	—
256	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
257	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
258	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
259	C₂²⋊C₄×C₁₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₉	—	4	2	no	—
264	C₂²⋊C₄×C₁₉	—	4	2	no	—
265	C₂²⋊C₄×C₁₉	—	8	1	no	—
266	C₂²⋊C₄×C₁₉	—	8	1	no	—
267	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
268	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
269	C₄²×C₁₉	—	2	4	no	—
270	C₄²×C₁₉	—	4	2	no	—
271	C₄²×C₁₉	—	4	2	no	—
272	C₄²×C₁₉	—	4	2	no	—
273	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
274	C₄²×C₁₉	C₂×D₄	1	2	yes	—
275	#22426	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₁₉	—	2	1	no	—
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	2	no	—
289	C₂³×C₁₉	—	4	1	no	—
290	C₂³×C₁₉	—	4	1	no	—
291	C₂³×C₁₉	—	4	1	no	—
292	C₂³×C₁₉	—	4	1	no	—
293	C₂³×C₁₉	—	4	1	no	—
294	C₂³×C₁₉	—	4	1	no	—
295	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₁₉	—	2	2	no	—
299	Q₈×C₁₉	—	2	2	no	—
300	Q₈×C₁₉	—	2	2	no	—
301	Q₈×C₁₉	—	2	2	no	—
302	Q₈×C₁₉	—	2	2	no	—
303	Q₈×C₁₉	—	4	8	no	—
304	Q₈×C₁₉	—	4	1	no	—
305	Q₈×C₁₉	—	4	1	no	—
306	Q₈×C₁₉	C₄×D₄	1	4	yes	—
307	D₄×C₁₉	—	2	2	no	—
308	D₄×C₁₉	—	2	2	no	—
309	D₄×C₁₉	—	4	4	no	—
310	D₄×C₁₉	—	4	8	no	—
311	D₄×C₁₉	—	4	8	no	—
312	D₄×C₁₉	—	4	1	no	—
313	D₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	2	no	—
318	C₂×C₄×C₁₉	—	2	1	no	—
319	C₂×C₄×C₁₉	—	2	1	no	—
320	C₂×C₄×C₁₉	—	2	2	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	2	no	—
326	C₂×C₄×C₁₉	—	2	2	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	—	4	8	no	—
337	C₂×C₄×C₁₉	—	4	8	no	—
338	C₂×C₄×C₁₉	—	4	1	no	—
339	C₂×C₄×C₁₉	—	4	1	no	—
340	C₂×C₄×C₁₉	—	4	1	no	—
341	C₂×C₄×C₁₉	—	4	1	no	—
342	C₂×C₄×C₁₉	—	4	1	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	C₂×C₂²⋊C₄	1	2	yes	—
354	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
355	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
357	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
358	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₁₉	—	2	2	no	—
364	C₈×C₁₉	—	4	1	no	—
365	C₈×C₁₉	—	4	1	no	—
366	C₈×C₁₉	—	4	1	no	—
367	C₂×#548	C₂×C₁₉	1	1	yes	characteristic
368	C₂×#435	C₂×C₁₉	1	1	yes	characteristic, complemented
369	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
370	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
371	#2354	C₂×C₁₉	1	1	yes	characteristic, complemented
372	#1983	C₂×C₁₉	1	1	yes	characteristic, complemented
373	#1959	C₂×C₁₉	1	1	yes	characteristic, complemented
374	#1895	C₂×C₁₉	1	1	yes	characteristic, complemented
375	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
377	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
378	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
379	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
380	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#1763	C₂×C₁₉	1	1	yes	characteristic, complemented
382	C₂²×C₁₉	—	2	2	no	—
383	C₂²×C₁₉	—	2	2	no	—
384	C₂²×C₁₉	—	2	2	no	—
385	C₂²×C₁₉	—	2	2	no	—
386	C₂²×C₁₉	—	2	2	no	—
387	C₂²×C₁₉	—	2	2	no	—
388	C₂²×C₁₉	—	4	1	no	—
389	C₂²×C₁₉	—	4	1	no	—
390	C₂²×C₁₉	—	4	1	no	—
391	C₂²×C₁₉	—	4	1	no	—
392	C₂²×C₁₉	—	4	1	no	—
393	C₂²×C₁₉	—	4	1	no	—
394	C₂²×C₁₉	—	4	1	no	—
395	C₂²×C₁₉	—	4	1	no	—
396	C₂²×C₁₉	—	4	2	no	—
397	C₂²×C₁₉	—	4	2	no	—
398	C₂²×C₁₉	—	4	2	no	—
399	C₂²×C₁₉	—	8	1	no	—
400	C₂²×C₁₉	—	8	1	no	—
401	C₂²×C₁₉	—	8	1	no	—
402	C₂²×C₁₉	—	8	1	no	—
403	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
404	C₂²×C₁₉	D₄²	1	1	yes	characteristic
405	C₂²×C₁₉	#546	1	1	yes	characteristic
406	C₂²×C₁₉	#575	1	1	yes	characteristic
407	C₂²×C₁₉	#575	1	1	yes	characteristic
408	C₂²×C₁₉	#577	1	1	yes	characteristic
409	C₂²×C₁₉	#578	1	1	yes	characteristic
410	C₄×C₁₉	—	2	2	no	—
411	C₄×C₁₉	—	2	2	no	—
412	C₄×C₁₉	—	2	4	no	—
413	C₄×C₁₉	—	2	2	no	—
414	C₄×C₁₉	—	2	2	no	—
415	C₄×C₁₉	—	4	2	no	—
416	C₄×C₁₉	—	4	2	no	—
417	C₄×C₁₉	—	4	2	no	—
418	C₄×C₁₉	—	8	1	no	—
419	C₄×C₁₉	—	8	1	no	—
420	C₄×C₁₉	—	8	1	no	—
421	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
422	C₄×C₁₉	#518	1	1	yes	characteristic
423	C₄×C₁₉	D₄²	1	1	yes	characteristic
424	C₄×C₁₉	#546	1	1	yes	characteristic
425	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
426	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
427	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
428	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
429	#548	—	2	4	no	—
430	#548	C₄×C₁₉	1	8	yes	complemented
431	C₂×#124	—	2	1	no	—
432	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×C₂²⋊Q₈	—	2	1	no	—
434	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
435	C₂×#121	—	2	1	no	—
436	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
438	C₂×C₄×D₄	—	2	1	no	—
439	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
441	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
442	#435	—	2	4	no	—
443	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
444	#419	—	2	4	no	—
445	#416	—	2	4	no	—
446	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
447	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
449	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
450	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
451	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
454	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
455	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
461	#390	—	2	1	no	—
462	#388	—	2	1	no	—
463	#388	—	2	1	no	—
464	#384	C₂²×C₁₉	1	1	yes	characteristic
465	#380	C₂²×C₁₉	1	1	yes	characteristic
466	#380	C₂²×C₁₉	1	1	yes	characteristic
467	C₄×C₄⋊C₄	—	2	1	no	—
468	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
469	#340	C₂²×C₁₉	1	1	yes	characteristic
470	#340	C₂²×C₁₉	1	1	yes	characteristic
471	#340	C₂²×C₁₉	1	1	yes	characteristic
472	#340	C₂²×C₁₉	1	1	yes	characteristic
473	C₂×C₁₉	—	4	2	no	—
474	C₂×C₁₉	—	4	2	no	—
475	C₂×C₁₉	—	8	2	no	—
476	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
477	C₂×C₁₉	#2896	1	1	yes	characteristic
478	C₂×C₁₉	#2898	1	1	yes	characteristic
479	C₂×C₁₉	#3269	1	1	yes	characteristic
480	C₂×C₁₉	#3271	1	1	yes	characteristic
481	C₂×C₁₉	#3313	1	1	yes	characteristic
482	C₂×C₁₉	#3321	1	1	yes	characteristic
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	2	2	no	—
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	4	1	no	—
487	C₂×#41	—	4	1	no	—
488	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	2	no	—
491	C₂²×Q₈	—	2	2	no	—
492	C₂²×Q₈	—	2	2	no	—
493	C₂²×Q₈	—	4	1	no	—
494	C₂²×Q₈	—	4	1	no	—
495	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
496	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
506	C₂×M₁₆	—	2	2	no	—
507	C₂×M₁₆	—	2	2	no	—
508	C₂×M₁₆	—	4	1	no	—
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	2	2	no	—
511	C₂²×C₈	—	4	1	no	—
512	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
516	#124	—	2	8	no	—
517	#124	—	2	2	no	—
518	#124	C₂×C₄×C₁₉	1	4	yes	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	8	no	—
521	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
522	#121	—	2	8	no	—
523	#121	—	2	2	no	—
524	#121	C₂×C₄×C₁₉	1	4	yes	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
529	C₄×D₄	D₄×C₁₉	1	4	yes	—
530	#117	—	2	2	no	—
531	#117	—	2	2	no	—
532	#117	—	4	1	no	—
533	#117	—	4	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
554	C₂×C₄²	—	2	1	no	—
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
559	C₄⋊C₈	—	2	2	no	—
560	#103	—	2	2	no	—
561	#103	—	2	2	no	—
562	#103	—	2	2	no	—
563	#103	—	2	2	no	—
564	#103	—	2	2	no	—
565	#103	—	4	1	no	—
566	#103	—	4	1	no	—
567	#103	D₄×C₁₉	1	4	yes	complemented
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	—	4	1	no	—
571	#102	—	4	1	no	—
572	C₂²⋊C₈	—	2	2	no	—
573	C₂²⋊C₈	—	2	2	no	—
574	#97	—	2	2	no	—
575	#95	—	2	1	no	—
576	#95	—	2	1	no	—
577	#95	—	2	1	no	—
578	C₁₉	#22426	1	1	yes	characteristic, direct product factor, Sylow
579	C₂⁴	—	2	1	no	—
580	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
582	#41	—	2	8	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	4	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	8	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	4	2	no	—
597	C₂×Q₈	—	4	2	no	—
598	C₂×Q₈	—	4	4	no	—
599	C₂×Q₈	—	4	4	no	—
600	C₂×Q₈	—	4	4	no	—
601	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
602	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
603	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
604	C₂×Q₈	#41×C₁₉	1	2	yes	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	4	1	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
619	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
642	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
643	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
648	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
650	M₁₆	—	4	4	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	4	4	no	—
663	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	8	1	no	—
676	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
677	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	8	1	no	—
686	C₂²⋊C₄	—	8	1	no	—
687	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
688	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
689	C₄²	—	2	4	no	—
690	C₄²	—	4	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
694	C₄²	C₂×D₄×C₁₉	1	2	yes	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
715	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
716	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	8	no	—
723	Q₈	—	4	1	no	—
724	Q₈	—	4	1	no	—
725	Q₈	C₄×D₄×C₁₉	1	4	yes	—
726	D₄	—	2	2	no	—
727	D₄	—	2	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
773	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
774	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
775	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
776	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
779	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
780	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
781	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
782	C₈	—	2	2	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
808	C₂²	D₄²×C₁₉	1	1	yes	characteristic
809	C₂²	C₁₉×#546	1	1	yes	characteristic
810	C₂²	C₁₉×#575	1	1	yes	characteristic
811	C₂²	C₁₉×#575	1	1	yes	characteristic
812	C₂²	C₁₉×#577	1	1	yes	characteristic
813	C₂²	C₁₉×#578	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	4	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	8	1	no	—
823	C₄	—	8	1	no	—
824	C₄	—	8	1	no	—
825	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
826	C₄	C₁₉×#518	1	1	yes	characteristic
827	C₄	D₄²×C₁₉	1	1	yes	characteristic
828	C₄	C₁₉×#546	1	1	yes	characteristic
829	C₂	—	4	2	no	—
830	C₂	—	4	2	no	—
831	C₂	—	8	2	no	—
832	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
833	C₂	C₁₉×#2896	1	1	yes	characteristic
834	C₂	C₁₉×#2898	1	1	yes	characteristic
835	C₂	C₁₉×#3269	1	1	yes	characteristic
836	C₂	C₁₉×#3271	1	1	yes	characteristic
837	C₂	C₁₉×#3313	1	1	yes	characteristic
838	C₂	C₁₉×#3321	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×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#435	C₂	semidirect
3. C₂×C₁₉×#419	C₂	semidirect
4. C₂×C₁₉×#416	C₂	semidirect
5. C₁₉×#2354	C₂	semidirect
6. C₁₉×#1983	C₂	semidirect
7. C₁₉×#1959	C₂	semidirect
8. C₁₉×#1895	C₂	semidirect
9. C₁₉×#1892	C₂	semidirect
10. C₁₉×#1875	C₂	semidirect
11. C₁₉×#1873	C₂	semidirect
12. C₁₉×#1803	C₂	semidirect
13. C₁₉×#1788	C₂	semidirect
14. C₁₉×#1787	C₂	semidirect
15. C₁₉×#1763	C₂	semidirect
21. C₁₉×#548	C₄	semidirect
148. C₁₉×#103	D₄	semidirect
275. #22426	C₁₉	direct (N × H)
368. C₂×#435	C₂×C₁₉	semidirect
369. C₂×#419	C₂×C₁₉	semidirect
370. C₂×#416	C₂×C₁₉	semidirect
371. #2354	C₂×C₁₉	semidirect
372. #1983	C₂×C₁₉	semidirect
373. #1959	C₂×C₁₉	semidirect
374. #1895	C₂×C₁₉	semidirect
375. #1892	C₂×C₁₉	semidirect
376. #1875	C₂×C₁₉	semidirect
377. #1873	C₂×C₁₉	semidirect
378. #1803	C₂×C₁₉	semidirect
379. #1788	C₂×C₁₉	semidirect
380. #1787	C₂×C₁₉	semidirect
381. #1763	C₂×C₁₉	semidirect
430. #548	C₄×C₁₉	semidirect
567. #103	D₄×C₁₉	semidirect
578. C₁₉	#22426	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×#548	2
C₂×C₁₉×#435	2
C₂×C₁₉×#419	2
C₂×C₁₉×#416	2
C₁₉×#2354	2
C₁₉×#1983	2
C₁₉×#1959	2
C₁₉×#1895	2
C₁₉×#1892	2
C₁₉×#1875	2
C₁₉×#1873	2
C₁₉×#1803	2
C₁₉×#1788	2
C₁₉×#1787	2
C₁₉×#1763	2
#22426	19

Subgroups — C19×#22426 #18028385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22426 #18028385