Subgroups — C₁₉×#18250 #18024209

Order 4864.

932 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2636	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1617	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1615	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1614	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1600	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1599	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1597	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1596	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1518	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1512	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1473	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	—	2	1	no	—
17	C₁₉×#563	—	2	1	no	—
18	C₁₉×#556	—	2	1	no	—
19	C₁₉×#554	—	2	1	no	—
20	C₁₉×#552	—	2	1	no	—
21	C₁₉×#552	—	2	1	no	—
22	C₁₉×#551	—	2	1	no	—
23	C₁₉×#551	—	2	1	no	—
24	C₁₉×#544	C₂²	1	1	yes	characteristic
25	C₁₉×#543	C₂²	1	1	yes	characteristic
26	C₁₉×#542	—	2	1	no	—
27	C₁₉×#541	—	2	1	no	—
28	C₁₉×#541	—	2	1	no	—
29	C₁₉×#539	—	2	1	no	—
30	C₁₉×#539	C₂²	1	1	yes	characteristic
31	C₁₉×#538	C₂²	1	1	yes	characteristic
32	C₁₉×#533	C₂²	1	1	yes	characteristic
33	C₁₉×#529	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#126	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#484	C₂²	1	1	yes	characteristic
37	C₁₉×#484	C₂²	1	1	yes	characteristic
38	C₁₉×#484	C₂²	1	1	yes	characteristic
39	C₁₉×#481	C₂²	1	1	yes	characteristic
40	C₁₉×#478	—	2	1	no	—
41	C₁₉×#474	—	2	1	no	—
42	C₁₉×#463	—	2	1	no	—
43	C₁₉×#461	—	2	1	no	—
44	C₁₉×#450	C₂²	1	1	yes	characteristic
45	C₁₉×#450	C₂²	1	1	yes	characteristic
46	C₁₉×#450	C₂²	1	1	yes	characteristic
47	C₁₉×#447	C₂²	1	1	yes	characteristic
48	C₁₉×#440	—	2	1	no	—
49	C₁₉×#440	—	2	1	no	—
50	C₄×SD₁₆×C₁₉	—	2	1	no	—
51	C₄×D₈×C₁₉	—	2	1	no	—
52	C₁₉×#432	C₂²	1	1	yes	characteristic
53	C₁₉×#431	C₂²	1	1	yes	characteristic
54	C₁₉×#400	C₂²	1	1	yes	characteristic
55	C₁₉×#399	C₂²	1	1	yes	characteristic
56	C₁₉×#396	—	2	1	no	—
57	C₁₉×#394	—	2	1	no	—
58	C₁₉×#394	C₂²	1	1	yes	characteristic
59	C₁₉×#392	C₂²	1	1	yes	characteristic
60	C₁₉×#386	—	2	1	no	—
61	C₁₉×#385	—	2	1	no	—
62	C₁₉×#382	C₂²	1	1	yes	characteristic
63	C₁₉×#328	C₂²	1	1	yes	characteristic
64	C₁₉×#328	C₂²	1	1	yes	characteristic
65	C₁₉×#328	C₂²	1	1	yes	characteristic
66	C₁₉×#328	C₂²	1	1	yes	characteristic
67	C₁₉×#328	C₂²	1	1	yes	characteristic
68	C₁₉×#328	C₂²	1	1	yes	characteristic
69	C₁₉×#327	C₂²	1	1	yes	characteristic
70	C₁₉×#327	C₂²	1	1	yes	characteristic
71	C₁₉×#324	C₂²	1	1	yes	characteristic
72	C₁₉×#324	C₂²	1	1	yes	characteristic
73	C₁₉×#323	C₂²	1	1	yes	characteristic
74	C₁₉×#323	C₂²	1	1	yes	characteristic
75	C₂²×D₄×C₁₉	—	2	1	no	—
76	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	—	2	1	no	—
78	C₂×SD₁₆×C₁₉	—	2	1	no	—
79	C₂×SD₁₆×C₁₉	—	2	1	no	—
80	C₂×SD₁₆×C₁₉	—	2	1	no	—
81	C₂×D₈×C₁₉	—	2	1	no	—
82	C₁₉×C₄⋊Q₈	—	2	1	no	—
83	C₁₉×C₄⋊Q₈	—	2	1	no	—
84	C₁₉×C₄⋊Q₈	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
86	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
87	C₁₉×#126	—	2	1	no	—
88	C₁₉×#126	—	2	1	no	—
89	C₁₉×#126	—	2	1	no	—
90	C₁₉×#126	—	2	1	no	—
91	C₁₉×#126	—	2	1	no	—
92	C₁₉×#126	—	2	1	no	—
93	C₁₉×#126	—	2	1	no	—
94	C₁₉×#126	—	2	1	no	—
95	C₁₉×#126	—	2	1	no	—
96	C₁₉×#126	—	2	1	no	—
97	C₁₉×#126	—	2	1	no	—
98	C₁₉×#126	—	2	1	no	—
99	C₁₉×#126	—	2	1	no	—
100	C₁₉×#125	—	2	1	no	—
101	C₁₉×#125	—	2	1	no	—
102	C₁₉×#125	—	2	1	no	—
103	C₁₉×#125	—	2	1	no	—
104	C₁₉×#125	—	2	1	no	—
105	C₁₉×#125	—	2	1	no	—
106	C₁₉×#125	—	2	1	no	—
107	C₁₉×#125	—	2	1	no	—
108	C₁₉×#125	—	2	1	no	—
109	C₁₉×#125	D₄	1	1	yes	characteristic, complemented
110	C₁₉×#124	—	2	1	no	—
111	C₁₉×#124	—	2	1	no	—
112	C₁₉×#124	—	2	1	no	—
113	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
114	C₁₉×#123	—	2	1	no	—
115	C₁₉×#123	—	2	1	no	—
116	C₁₉×#123	—	2	1	no	—
117	C₁₉×#123	—	2	1	no	—
118	C₁₉×#123	—	2	1	no	—
119	C₁₉×#123	—	2	1	no	—
120	C₁₉×#123	—	2	1	no	—
121	C₁₉×#123	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	—	2	1	no	—
123	C₁₉×C₂²⋊Q₈	—	2	1	no	—
124	C₁₉×C₂²⋊Q₈	—	2	1	no	—
125	C₁₉×C₂²⋊Q₈	—	2	1	no	—
126	C₁₉×C₂²⋊Q₈	—	2	1	no	—
127	C₁₉×C₂²⋊Q₈	—	2	1	no	—
128	C₁₉×C₂²⋊Q₈	—	2	1	no	—
129	C₁₉×C₂²⋊Q₈	—	2	1	no	—
130	C₁₉×C₂²⋊Q₈	—	2	1	no	—
131	C₁₉×C₂²⋊Q₈	—	2	1	no	—
132	C₁₉×C₂²⋊Q₈	—	2	1	no	—
133	C₁₉×C₂²⋊Q₈	—	2	1	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	—	2	1	no	—
136	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₉×#121	—	2	1	no	—
140	C₁₉×#121	C₂³	1	1	yes	characteristic
141	C₁₉×#120	—	2	1	no	—
142	C₄×Q₈×C₁₉	—	2	1	no	—
143	C₄×Q₈×C₁₉	—	2	1	no	—
144	C₄×Q₈×C₁₉	—	2	1	no	—
145	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
146	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
147	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
148	C₄×D₄×C₁₉	—	2	1	no	—
149	C₄×D₄×C₁₉	—	2	1	no	—
150	C₄×D₄×C₁₉	—	2	1	no	—
151	C₄×D₄×C₁₉	—	2	1	no	—
152	C₄×D₄×C₁₉	—	2	1	no	—
153	C₄×D₄×C₁₉	—	2	1	no	—
154	C₄×D₄×C₁₉	—	2	1	no	—
155	C₄×D₄×C₁₉	—	2	1	no	—
156	C₄×D₄×C₁₉	—	2	1	no	—
157	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
158	C₁₉×#117	—	2	1	no	—
159	C₁₉×#117	—	2	1	no	—
160	C₁₉×#117	—	2	1	no	—
161	C₁₉×#117	—	2	1	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	—	2	1	no	—
164	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
172	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
181	C₁₉×#107	—	2	1	no	—
182	C₁₉×#107	—	2	1	no	—
183	C₁₉×#107	—	2	1	no	—
184	C₁₉×#106	—	2	1	no	—
185	C₁₉×C₄⋊C₈	—	2	1	no	—
186	C₁₉×C₄⋊C₈	—	2	1	no	—
187	C₁₉×#103	—	2	1	no	—
188	C₁₉×#103	—	2	1	no	—
189	C₁₉×#103	—	2	1	no	—
190	C₁₉×#102	—	2	1	no	—
191	C₁₉×#102	—	2	1	no	—
192	C₁₉×#102	—	2	1	no	—
193	C₁₉×#102	—	2	1	no	—
194	C₁₉×#102	—	2	1	no	—
195	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
196	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
197	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
198	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
199	C₁₉×#97	—	2	1	no	—
200	C₄×C₈×C₁₉	—	2	1	no	—
201	C₁₉×#95	—	2	1	no	—
202	C₁₉×#95	—	2	1	no	—
203	C₁₉×#95	—	2	1	no	—
204	C₁₉×#95	C₂³	1	1	yes	characteristic
205	C₁₉×#95	C₂³	1	1	yes	characteristic
206	C₂⁴×C₁₉	—	2	1	no	—
207	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₉	—	2	1	no	—
209	C₂×Q₈×C₁₉	—	2	1	no	—
210	C₂×Q₈×C₁₉	—	2	1	no	—
211	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₁₉	—	2	1	no	—
215	C₂×D₄×C₁₉	—	2	1	no	—
216	C₂×D₄×C₁₉	—	2	1	no	—
217	C₂×D₄×C₁₉	—	2	1	no	—
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	4	2	no	—
220	C₂×D₄×C₁₉	—	4	2	no	—
221	C₂×D₄×C₁₉	—	8	1	no	—
222	C₂×D₄×C₁₉	—	8	1	no	—
223	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	—	2	1	no	—
225	C₂²×C₄×C₁₉	—	2	1	no	—
226	C₂²×C₄×C₁₉	—	2	1	no	—
227	C₂²×C₄×C₁₉	—	2	1	no	—
228	C₂²×C₄×C₁₉	—	2	1	no	—
229	C₂²×C₄×C₁₉	—	2	1	no	—
230	C₂²×C₄×C₁₉	—	2	1	no	—
231	C₂²×C₄×C₁₉	—	2	1	no	—
232	C₂²×C₄×C₁₉	—	4	1	no	—
233	C₂²×C₄×C₁₉	—	4	1	no	—
234	C₂²×C₄×C₁₉	—	8	1	no	—
235	C₂²×C₄×C₁₉	—	8	1	no	—
236	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	SD₁₆×C₁₉	—	4	2	no	—
243	SD₁₆×C₁₉	—	4	2	no	—
244	SD₁₆×C₁₉	—	4	2	no	—
245	D₈×C₁₉	—	4	2	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	—	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	—	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	—	2	1	no	—
264	C₄⋊C₄×C₁₉	—	2	1	no	—
265	C₄⋊C₄×C₁₉	—	2	1	no	—
266	C₄⋊C₄×C₁₉	—	2	1	no	—
267	C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	no	—
273	C₄⋊C₄×C₁₉	—	2	1	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	1	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	2	1	no	—
281	C₄⋊C₄×C₁₉	—	8	1	no	—
282	C₄⋊C₄×C₁₉	—	8	1	no	—
283	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
284	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
285	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
286	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂²⋊C₄×C₁₉	—	2	1	no	—
288	C₂²⋊C₄×C₁₉	—	2	1	no	—
289	C₂²⋊C₄×C₁₉	—	2	1	no	—
290	C₂²⋊C₄×C₁₉	—	2	1	no	—
291	C₂²⋊C₄×C₁₉	—	2	1	no	—
292	C₂²⋊C₄×C₁₉	—	2	1	no	—
293	C₂²⋊C₄×C₁₉	—	2	1	no	—
294	C₂²⋊C₄×C₁₉	—	2	1	no	—
295	C₂²⋊C₄×C₁₉	—	2	1	no	—
296	C₂²⋊C₄×C₁₉	—	2	1	no	—
297	C₂²⋊C₄×C₁₉	—	2	1	no	—
298	C₂²⋊C₄×C₁₉	—	2	1	no	—
299	C₂²⋊C₄×C₁₉	—	2	1	no	—
300	C₂²⋊C₄×C₁₉	—	2	1	no	—
301	C₂²⋊C₄×C₁₉	—	2	1	no	—
302	C₂²⋊C₄×C₁₉	—	2	1	no	—
303	C₂²⋊C₄×C₁₉	—	2	1	no	—
304	C₂²⋊C₄×C₁₉	—	2	1	no	—
305	C₂²⋊C₄×C₁₉	—	2	1	no	—
306	C₂²⋊C₄×C₁₉	—	2	1	no	—
307	C₂²⋊C₄×C₁₉	—	2	1	no	—
308	C₂²⋊C₄×C₁₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₉	—	4	1	no	—
310	C₂²⋊C₄×C₁₉	—	4	1	no	—
311	C₂²⋊C₄×C₁₉	—	8	1	no	—
312	C₂²⋊C₄×C₁₉	—	8	1	no	—
313	C₂²⋊C₄×C₁₉	—	8	1	no	—
314	C₄²×C₁₉	—	2	1	no	—
315	C₄²×C₁₉	—	2	1	no	—
316	C₄²×C₁₉	—	2	1	no	—
317	C₄²×C₁₉	—	2	1	no	—
318	C₄²×C₁₉	—	2	1	no	—
319	C₄²×C₁₉	—	2	1	no	—
320	C₄²×C₁₉	—	2	1	no	—
321	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
325	#18250	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂³×C₁₉	—	2	2	no	—
327	C₂³×C₁₉	—	2	1	no	—
328	C₂³×C₁₉	—	2	1	no	—
329	C₂³×C₁₉	—	2	1	no	—
330	C₂³×C₁₉	—	2	1	no	—
331	C₂³×C₁₉	—	4	1	no	—
332	C₂³×C₁₉	—	4	1	no	—
333	C₂³×C₁₉	—	4	1	no	—
334	C₂³×C₁₉	—	4	1	no	—
335	C₂³×C₁₉	—	4	1	no	—
336	C₂³×C₁₉	—	4	1	no	—
337	C₂³×C₁₉	—	4	1	no	—
338	C₂³×C₁₉	—	4	1	no	—
339	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₁₉	—	4	1	no	—
341	Q₈×C₁₉	—	4	1	no	—
342	Q₈×C₁₉	—	4	1	no	—
343	Q₈×C₁₉	—	8	1	no	—
344	Q₈×C₁₉	—	8	1	no	—
345	Q₈×C₁₉	—	8	1	no	—
346	D₄×C₁₉	—	2	2	no	—
347	D₄×C₁₉	—	2	2	no	—
348	D₄×C₁₉	—	4	1	no	—
349	D₄×C₁₉	—	4	1	no	—
350	D₄×C₁₉	—	4	1	no	—
351	D₄×C₁₉	—	4	1	no	—
352	D₄×C₁₉	—	4	1	no	—
353	D₄×C₁₉	—	8	1	no	—
354	D₄×C₁₉	—	8	1	no	—
355	D₄×C₁₉	—	8	4	no	—
356	C₂×C₄×C₁₉	—	2	1	no	—
357	C₂×C₄×C₁₉	—	2	1	no	—
358	C₂×C₄×C₁₉	—	2	1	no	—
359	C₂×C₄×C₁₉	—	2	1	no	—
360	C₂×C₄×C₁₉	—	2	1	no	—
361	C₂×C₄×C₁₉	—	2	1	no	—
362	C₂×C₄×C₁₉	—	2	1	no	—
363	C₂×C₄×C₁₉	—	2	1	no	—
364	C₂×C₄×C₁₉	—	2	1	no	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	2	1	no	—
367	C₂×C₄×C₁₉	—	2	1	no	—
368	C₂×C₄×C₁₉	—	2	1	no	—
369	C₂×C₄×C₁₉	—	2	1	no	—
370	C₂×C₄×C₁₉	—	4	1	no	—
371	C₂×C₄×C₁₉	—	4	1	no	—
372	C₂×C₄×C₁₉	—	4	1	no	—
373	C₂×C₄×C₁₉	—	4	1	no	—
374	C₂×C₄×C₁₉	—	4	1	no	—
375	C₂×C₄×C₁₉	—	4	1	no	—
376	C₂×C₄×C₁₉	—	4	1	no	—
377	C₂×C₄×C₁₉	—	4	1	no	—
378	C₂×C₄×C₁₉	—	4	1	no	—
379	C₂×C₄×C₁₉	—	4	1	no	—
380	C₂×C₄×C₁₉	—	4	1	no	—
381	C₂×C₄×C₁₉	—	4	1	no	—
382	C₂×C₄×C₁₉	—	4	1	no	—
383	C₂×C₄×C₁₉	—	8	1	no	—
384	C₂×C₄×C₁₉	—	8	2	no	—
385	C₂×C₄×C₁₉	—	8	2	no	—
386	C₂×C₄×C₁₉	—	8	1	no	—
387	C₂×C₄×C₁₉	—	8	1	no	—
388	C₂×C₄×C₁₉	—	8	1	no	—
389	C₂×C₄×C₁₉	—	8	1	no	—
390	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
391	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
392	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
393	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
394	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
396	C₈×C₁₉	—	4	1	no	—
397	C₈×C₁₉	—	4	1	no	—
398	C₈×C₁₉	—	4	1	no	—
399	C₈×C₁₉	—	4	1	no	—
400	#3564	C₂×C₁₉	1	1	yes	characteristic, complemented
401	#3110	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#3105	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#2636	C₂×C₁₉	1	1	yes	characteristic, complemented
404	#1618	C₂×C₁₉	1	1	yes	characteristic, complemented
405	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
406	#1615	C₂×C₁₉	1	1	yes	characteristic, complemented
407	#1614	C₂×C₁₉	1	1	yes	characteristic, complemented
408	#1600	C₂×C₁₉	1	1	yes	characteristic
409	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
410	#1597	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#1596	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#1518	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#1512	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#1473	C₂×C₁₉	1	1	yes	characteristic, complemented
415	C₂²×C₁₉	—	2	1	no	—
416	C₂²×C₁₉	—	2	1	no	—
417	C₂²×C₁₉	—	4	2	no	—
418	C₂²×C₁₉	—	4	2	no	—
419	C₂²×C₁₉	—	4	1	no	—
420	C₂²×C₁₉	—	4	1	no	—
421	C₂²×C₁₉	—	4	1	no	—
422	C₂²×C₁₉	—	4	1	no	—
423	C₂²×C₁₉	—	4	1	no	—
424	C₂²×C₁₉	—	4	1	no	—
425	C₂²×C₁₉	—	4	2	no	—
426	C₂²×C₁₉	—	8	1	no	—
427	C₂²×C₁₉	—	8	1	no	—
428	C₂²×C₁₉	—	8	1	no	—
429	C₂²×C₁₉	—	8	1	no	—
430	C₂²×C₁₉	—	8	1	no	—
431	C₂²×C₁₉	—	8	1	no	—
432	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
433	C₂²×C₁₉	#577	1	1	yes	characteristic
434	C₂²×C₁₉	#578	1	1	yes	characteristic
435	C₄×C₁₉	—	2	1	no	—
436	C₄×C₁₉	—	2	1	no	—
437	C₄×C₁₉	—	2	1	no	—
438	C₄×C₁₉	—	2	1	no	—
439	C₄×C₁₉	—	2	1	no	—
440	C₄×C₁₉	—	2	1	no	—
441	C₄×C₁₉	—	4	1	no	—
442	C₄×C₁₉	—	4	1	no	—
443	C₄×C₁₉	—	4	1	no	—
444	C₄×C₁₉	—	4	1	no	—
445	C₄×C₁₉	—	4	1	no	—
446	C₄×C₁₉	—	4	1	no	—
447	C₄×C₁₉	—	4	1	no	—
448	C₄×C₁₉	—	4	1	no	—
449	C₄×C₁₉	—	4	1	no	—
450	C₄×C₁₉	—	4	1	no	—
451	C₄×C₁₉	—	8	1	no	—
452	C₄×C₁₉	—	8	1	no	—
453	C₄×C₁₉	—	8	1	no	—
454	#563	—	2	1	no	—
455	#563	—	2	1	no	—
456	#556	—	2	1	no	—
457	#554	—	2	1	no	—
458	#552	—	2	1	no	—
459	#552	—	2	1	no	—
460	#551	—	2	1	no	—
461	#551	—	2	1	no	—
462	#544	C₂²×C₁₉	1	1	yes	characteristic
463	#543	C₂²×C₁₉	1	1	yes	characteristic
464	#542	—	2	1	no	—
465	#541	—	2	1	no	—
466	#541	—	2	1	no	—
467	#539	—	2	1	no	—
468	#539	C₂²×C₁₉	1	1	yes	characteristic
469	#538	C₂²×C₁₉	1	1	yes	characteristic
470	#533	C₂²×C₁₉	1	1	yes	characteristic
471	#529	C₂²×C₁₉	1	1	yes	characteristic
472	C₂×#126	C₂²×C₁₉	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
474	#484	C₂²×C₁₉	1	1	yes	characteristic
475	#484	C₂²×C₁₉	1	1	yes	characteristic
476	#484	C₂²×C₁₉	1	1	yes	characteristic
477	#481	C₂²×C₁₉	1	1	yes	characteristic
478	#478	—	2	1	no	—
479	#474	—	2	1	no	—
480	#463	—	2	1	no	—
481	#461	—	2	1	no	—
482	#450	C₂²×C₁₉	1	1	yes	characteristic
483	#450	C₂²×C₁₉	1	1	yes	characteristic
484	#450	C₂²×C₁₉	1	1	yes	characteristic
485	#447	C₂²×C₁₉	1	1	yes	characteristic
486	#440	—	2	1	no	—
487	#440	—	2	1	no	—
488	C₄×SD₁₆	—	2	1	no	—
489	C₄×D₈	—	2	1	no	—
490	#432	C₂²×C₁₉	1	1	yes	characteristic
491	#431	C₂²×C₁₉	1	1	yes	characteristic
492	#400	C₂²×C₁₉	1	1	yes	characteristic
493	#399	C₂²×C₁₉	1	1	yes	characteristic
494	#396	—	2	1	no	—
495	#394	—	2	1	no	—
496	#394	C₂²×C₁₉	1	1	yes	characteristic
497	#392	C₂²×C₁₉	1	1	yes	characteristic
498	#386	—	2	1	no	—
499	#385	—	2	1	no	—
500	#382	C₂²×C₁₉	1	1	yes	characteristic
501	#328	C₂²×C₁₉	1	1	yes	characteristic
502	#328	C₂²×C₁₉	1	1	yes	characteristic
503	#328	C₂²×C₁₉	1	1	yes	characteristic
504	#328	C₂²×C₁₉	1	1	yes	characteristic
505	#328	C₂²×C₁₉	1	1	yes	characteristic
506	#328	C₂²×C₁₉	1	1	yes	characteristic
507	#327	C₂²×C₁₉	1	1	yes	characteristic
508	#327	C₂²×C₁₉	1	1	yes	characteristic
509	#324	C₂²×C₁₉	1	1	yes	characteristic
510	#324	C₂²×C₁₉	1	1	yes	characteristic
511	#323	C₂²×C₁₉	1	1	yes	characteristic
512	#323	C₂²×C₁₉	1	1	yes	characteristic
513	C₂×C₁₉	—	2	1	no	—
514	C₂×C₁₉	—	2	1	no	—
515	C₂×C₁₉	—	8	1	no	—
516	C₂×C₁₉	—	8	1	no	—
517	C₂×C₁₉	—	8	2	no	—
518	C₂×C₁₉	#3013	1	1	yes	characteristic
519	C₂×C₁₉	#3021	1	1	yes	characteristic
520	C₂×C₁₉	#3025	1	1	yes	characteristic
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
523	C₂³×C₄	—	2	1	no	—
524	C₂×SD₁₆	—	2	1	no	—
525	C₂×SD₁₆	—	2	1	no	—
526	C₂×SD₁₆	—	2	1	no	—
527	C₂×D₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
532	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
533	#126	—	2	1	no	—
534	#126	—	2	1	no	—
535	#126	—	2	1	no	—
536	#126	—	2	1	no	—
537	#126	—	2	1	no	—
538	#126	—	2	1	no	—
539	#126	—	2	1	no	—
540	#126	—	2	1	no	—
541	#126	—	2	1	no	—
542	#126	—	2	1	no	—
543	#126	—	2	1	no	—
544	#126	—	2	1	no	—
545	#126	—	2	1	no	—
546	#125	—	2	1	no	—
547	#125	—	2	1	no	—
548	#125	—	2	1	no	—
549	#125	—	2	1	no	—
550	#125	—	2	1	no	—
551	#125	—	2	1	no	—
552	#125	—	2	1	no	—
553	#125	—	2	1	no	—
554	#125	—	2	1	no	—
555	#125	D₄×C₁₉	1	1	yes	characteristic, complemented
556	#124	—	2	1	no	—
557	#124	—	2	1	no	—
558	#124	—	2	1	no	—
559	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
560	#123	—	2	1	no	—
561	#123	—	2	1	no	—
562	#123	—	2	1	no	—
563	#123	—	2	1	no	—
564	#123	—	2	1	no	—
565	#123	—	2	1	no	—
566	#123	—	2	1	no	—
567	#123	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
583	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
584	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
585	#121	—	2	1	no	—
586	#121	C₂³×C₁₉	1	1	yes	characteristic
587	#120	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
592	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
593	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
604	#117	—	2	1	no	—
605	#117	—	2	1	no	—
606	#117	—	2	1	no	—
607	#117	—	2	1	no	—
608	#117	—	2	1	no	—
609	#117	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
627	#107	—	2	1	no	—
628	#107	—	2	1	no	—
629	#107	—	2	1	no	—
630	#106	—	2	1	no	—
631	C₄⋊C₈	—	2	1	no	—
632	C₄⋊C₈	—	2	1	no	—
633	#103	—	2	1	no	—
634	#103	—	2	1	no	—
635	#103	—	2	1	no	—
636	#102	—	2	1	no	—
637	#102	—	2	1	no	—
638	#102	—	2	1	no	—
639	#102	—	2	1	no	—
640	#102	—	2	1	no	—
641	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
642	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
643	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
644	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
645	#97	—	2	1	no	—
646	C₄×C₈	—	2	1	no	—
647	#95	—	2	1	no	—
648	#95	—	2	1	no	—
649	#95	—	2	1	no	—
650	#95	C₂³×C₁₉	1	1	yes	characteristic
651	#95	C₂³×C₁₉	1	1	yes	characteristic
652	C₁₉	#18250	1	1	yes	characteristic, direct product factor, Sylow
653	C₂⁴	—	2	1	no	—
654	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
659	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
660	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	8	1	no	—
669	C₂×D₄	—	8	1	no	—
670	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	8	1	no	—
682	C₂²×C₄	—	8	1	no	—
683	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
689	SD₁₆	—	4	2	no	—
690	SD₁₆	—	4	2	no	—
691	SD₁₆	—	4	2	no	—
692	D₈	—	4	2	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	8	1	no	—
729	C₄⋊C₄	—	8	1	no	—
730	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	—	8	1	no	—
759	C₂²⋊C₄	—	8	1	no	—
760	C₂²⋊C₄	—	8	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
772	C₂³	—	2	2	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
786	Q₈	—	4	1	no	—
787	Q₈	—	4	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	8	1	no	—
790	Q₈	—	8	1	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	4	1	no	—
795	D₄	—	4	1	no	—
796	D₄	—	4	1	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	1	no	—
799	D₄	—	8	1	no	—
800	D₄	—	8	1	no	—
801	D₄	—	8	4	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	—	8	1	no	—
833	C₂×C₄	—	8	1	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	—	8	1	no	—
836	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
837	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
838	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
839	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
842	C₈	—	4	1	no	—
843	C₈	—	4	1	no	—
844	C₈	—	4	1	no	—
845	C₈	—	4	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	8	1	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
864	C₂²	C₁₉×#577	1	1	yes	characteristic
865	C₂²	C₁₉×#578	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	8	1	no	—
883	C₄	—	8	1	no	—
884	C₄	—	8	1	no	—
885	C₂	—	2	1	no	—
886	C₂	—	2	1	no	—
887	C₂	—	8	2	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	1	no	—
890	C₂	C₁₉×#3013	1	1	yes	characteristic
891	C₂	C₁₉×#3021	1	1	yes	characteristic
892	C₂	C₁₉×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#1600	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3564	C₂	semidirect
2. C₁₉×#3110	C₂	semidirect
3. C₁₉×#3105	C₂	semidirect
4. C₁₉×#2636	C₂	semidirect
5. C₁₉×#1618	C₂	semidirect
6. C₁₉×#1617	C₂	semidirect
7. C₁₉×#1615	C₂	semidirect
8. C₁₉×#1614	C₂	semidirect
10. C₁₉×#1599	C₂	semidirect
11. C₁₉×#1597	C₂	semidirect
12. C₁₉×#1596	C₂	semidirect
13. C₁₉×#1518	C₂	semidirect
14. C₁₉×#1512	C₂	semidirect
15. C₁₉×#1473	C₂	semidirect
85. C₁₉×C₄⋊Q₈	D₄	semidirect
86. C₁₉×C₄⋊Q₈	D₄	semidirect
109. C₁₉×#125	D₄	semidirect
113. C₁₉×#124	D₄	semidirect
145. C₄×Q₈×C₁₉	D₄	semidirect
146. C₄×Q₈×C₁₉	D₄	semidirect
147. C₄×Q₈×C₁₉	D₄	semidirect
157. C₄×D₄×C₁₉	D₄	semidirect
325. #18250	C₁₉	direct (N × H)
400. #3564	C₂×C₁₉	semidirect
401. #3110	C₂×C₁₉	semidirect
402. #3105	C₂×C₁₉	semidirect
403. #2636	C₂×C₁₉	semidirect
404. #1618	C₂×C₁₉	semidirect
405. #1617	C₂×C₁₉	semidirect
406. #1615	C₂×C₁₉	semidirect
407. #1614	C₂×C₁₉	semidirect
409. #1599	C₂×C₁₉	semidirect
410. #1597	C₂×C₁₉	semidirect
411. #1596	C₂×C₁₉	semidirect
412. #1518	C₂×C₁₉	semidirect
413. #1512	C₂×C₁₉	semidirect
414. #1473	C₂×C₁₉	semidirect
531. C₄⋊Q₈	D₄×C₁₉	semidirect
532. C₄⋊Q₈	D₄×C₁₉	semidirect
555. #125	D₄×C₁₉	semidirect
559. #124	D₄×C₁₉	semidirect
591. C₄×Q₈	D₄×C₁₉	semidirect
592. C₄×Q₈	D₄×C₁₉	semidirect
593. C₄×Q₈	D₄×C₁₉	semidirect
603. C₄×D₄	D₄×C₁₉	semidirect
652. C₁₉	#18250	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×#3564	2
C₁₉×#3110	2
C₁₉×#3105	2
C₁₉×#2636	2
C₁₉×#1618	2
C₁₉×#1617	2
C₁₉×#1615	2
C₁₉×#1614	2
C₁₉×#1600	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1596	2
C₁₉×#1518	2
C₁₉×#1512	2
C₁₉×#1473	2
#18250	19

Subgroups — C19×#18250 #18024209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18250 #18024209