Subgroups — C₁₉×#18435 #18024394

Order 4864.

922 conjugacy classes of subgroups.

The subgroup lattice has 906 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×#3215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3211	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2662	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1606	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1605	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1603	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1602	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×#1509	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1503	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×C₁₉×#124	C₂²	1	1	yes	characteristic
36	C₁₉×#497	—	2	1	no	—
37	C₁₉×#495	—	2	1	no	—
38	C₁₉×#489	—	2	1	no	—
39	C₁₉×#488	—	2	1	no	—
40	C₁₉×#464	—	2	1	no	—
41	C₁₉×#464	—	2	1	no	—
42	C₁₉×#464	—	2	1	no	—
43	C₁₉×#463	—	2	1	no	—
44	C₁₉×#451	C₂²	1	1	yes	characteristic
45	C₁₉×#451	C₂²	1	1	yes	characteristic
46	C₁₉×#451	C₂²	1	1	yes	characteristic
47	C₁₉×#450	C₂²	1	1	yes	characteristic
48	C₁₉×#450	C₂²	1	1	yes	characteristic
49	C₁₉×#450	C₂²	1	1	yes	characteristic
50	C₁₉×#448	C₂²	1	1	yes	characteristic
51	C₁₉×#447	C₂²	1	1	yes	characteristic
52	C₁₉×#432	C₂²	1	1	yes	characteristic
53	C₁₉×#431	C₂²	1	1	yes	characteristic
54	C₁₉×#396	—	2	1	no	—
55	C₁₉×#395	C₂²	1	1	yes	characteristic
56	C₁₉×#394	—	2	1	no	—
57	C₁₉×#394	C₂²	1	1	yes	characteristic
58	C₁₉×#393	C₂²	1	1	yes	characteristic
59	C₁₉×#392	C₂²	1	1	yes	characteristic
60	C₁₉×#390	—	2	1	no	—
61	C₁₉×#388	—	2	1	no	—
62	C₄×C₄⋊C₄×C₁₉	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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₉	—	2	1	no	—
77	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×Q₁₆×C₁₉	—	2	1	no	—
79	C₂×Q₁₆×C₁₉	—	2	1	no	—
80	C₂×Q₁₆×C₁₉	—	2	1	no	—
81	C₂×SD₁₆×C₁₉	—	2	1	no	—
82	C₂×SD₁₆×C₁₉	—	2	1	no	—
83	C₂×SD₁₆×C₁₉	—	2	1	no	—
84	C₂×SD₁₆×C₁₉	—	2	1	no	—
85	C₂×D₈×C₁₉	—	2	1	no	—
86	C₁₉×C₄⋊Q₈	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	—	2	1	no	—
88	C₁₉×C₄⋊Q₈	—	2	1	no	—
89	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
90	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
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×#126	—	2	1	no	—
101	C₁₉×#126	—	2	1	no	—
102	C₁₉×#126	—	2	1	no	—
103	C₁₉×#126	—	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	—	2	1	no	—
110	C₁₉×#125	—	2	1	no	—
111	C₁₉×#125	—	2	1	no	—
112	C₁₉×#125	—	2	1	no	—
113	C₁₉×#125	D₄	1	1	yes	characteristic, complemented
114	C₁₉×#124	—	2	1	no	—
115	C₁₉×#124	—	2	1	no	—
116	C₁₉×#124	—	2	1	no	—
117	C₁₉×#124	—	2	1	no	—
118	C₁₉×#124	—	2	1	no	—
119	C₁₉×#124	—	2	1	no	—
120	C₁₉×#124	—	2	1	no	—
121	C₁₉×#124	D₄	1	1	yes	characteristic, complemented
122	C₁₉×#123	—	2	1	no	—
123	C₁₉×#123	—	2	1	no	—
124	C₁₉×#123	—	2	1	no	—
125	C₁₉×#123	—	2	1	no	—
126	C₁₉×#123	—	2	1	no	—
127	C₁₉×#123	—	2	1	no	—
128	C₁₉×#123	—	2	1	no	—
129	C₁₉×#123	—	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	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	—	2	1	no	—
139	C₁₉×C₂²⋊Q₈	—	2	1	no	—
140	C₁₉×C₂²⋊Q₈	—	2	1	no	—
141	C₁₉×C₂²⋊Q₈	—	2	1	no	—
142	C₁₉×C₂²⋊Q₈	—	2	1	no	—
143	C₁₉×C₂²⋊Q₈	—	2	1	no	—
144	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
145	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
146	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	C₂³	1	1	yes	characteristic
149	C₁₉×#120	—	2	1	no	—
150	C₄×Q₈×C₁₉	—	2	1	no	—
151	C₄×Q₈×C₁₉	—	2	1	no	—
152	C₄×Q₈×C₁₉	—	2	1	no	—
153	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
154	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
155	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic, complemented
156	C₄×D₄×C₁₉	—	2	1	no	—
157	C₄×D₄×C₁₉	—	2	1	no	—
158	C₄×D₄×C₁₉	—	2	1	no	—
159	C₄×D₄×C₁₉	—	2	1	no	—
160	C₄×D₄×C₁₉	—	2	1	no	—
161	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	—	2	1	no	—
164	C₁₉×#117	—	2	1	no	—
165	C₁₉×#117	—	2	1	no	—
166	C₁₉×#117	—	2	1	no	—
167	C₁₉×#117	—	2	1	no	—
168	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₉	—	2	1	no	—
185	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
186	C₁₉×C₄⋊C₈	—	2	1	no	—
187	C₁₉×C₄⋊C₈	—	2	1	no	—
188	C₁₉×#103	—	2	1	no	—
189	C₁₉×#103	—	2	1	no	—
190	C₁₉×#103	—	2	1	no	—
191	C₁₉×#103	—	2	1	no	—
192	C₁₉×#102	—	2	1	no	—
193	C₁₉×#102	—	2	1	no	—
194	C₁₉×#102	—	2	1	no	—
195	C₁₉×#102	—	2	1	no	—
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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₉×#97	—	2	1	no	—
201	C₄×C₈×C₁₉	—	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	—	2	1	no	—
212	C₂×Q₈×C₁₉	—	2	1	no	—
213	C₂×Q₈×C₁₉	—	8	1	no	—
214	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₁₉	—	2	1	no	—
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	2	1	no	—
220	C₂×D₄×C₁₉	—	2	1	no	—
221	C₂×D₄×C₁₉	—	2	1	no	—
222	C₂×D₄×C₁₉	—	4	2	no	—
223	C₂×D₄×C₁₉	—	8	1	no	—
224	C₂×D₄×C₁₉	—	8	1	no	—
225	C₂×D₄×C₁₉	—	8	1	no	—
226	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
233	C₂²×C₄×C₁₉	—	2	1	no	—
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
241	Q₁₆×C₁₉	—	8	1	no	—
242	Q₁₆×C₁₉	—	8	1	no	—
243	Q₁₆×C₁₉	—	8	1	no	—
244	SD₁₆×C₁₉	—	8	1	no	—
245	SD₁₆×C₁₉	—	8	1	no	—
246	SD₁₆×C₁₉	—	8	1	no	—
247	SD₁₆×C₁₉	—	8	1	no	—
248	D₈×C₁₉	—	8	1	no	—
249	C₂×C₈×C₁₉	—	2	1	no	—
250	C₂×C₈×C₁₉	—	2	1	no	—
251	C₂×C₈×C₁₉	—	2	1	no	—
252	C₂×C₈×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	—	2	1	no	—
282	C₄⋊C₄×C₁₉	—	4	2	no	—
283	C₄⋊C₄×C₁₉	—	8	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
309	C₂²⋊C₄×C₁₉	—	4	2	no	—
310	C₂²⋊C₄×C₁₉	—	4	1	no	—
311	C₂²⋊C₄×C₁₉	—	4	1	no	—
312	C₂²⋊C₄×C₁₉	—	4	1	no	—
313	C₂²⋊C₄×C₁₉	—	4	1	no	—
314	C₂²⋊C₄×C₁₉	—	8	1	no	—
315	C₂²⋊C₄×C₁₉	—	8	1	no	—
316	C₂²⋊C₄×C₁₉	—	8	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	—	2	1	no	—
322	C₄²×C₁₉	—	2	1	no	—
323	C₄²×C₁₉	—	2	1	no	—
324	C₄²×C₁₉	—	8	1	no	—
325	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
329	#18435	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂³×C₁₉	—	2	1	no	—
331	C₂³×C₁₉	—	2	1	no	—
332	C₂³×C₁₉	—	2	1	no	—
333	C₂³×C₁₉	—	2	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	—	4	1	no	—
340	C₂³×C₁₉	—	4	1	no	—
341	C₂³×C₁₉	—	4	1	no	—
342	C₂³×C₁₉	—	4	1	no	—
343	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₁₉	—	4	1	no	—
345	Q₈×C₁₉	—	4	1	no	—
346	Q₈×C₁₉	—	4	1	no	—
347	Q₈×C₁₉	—	4	1	no	—
348	Q₈×C₁₉	—	4	1	no	—
349	Q₈×C₁₉	—	4	1	no	—
350	Q₈×C₁₉	—	4	1	no	—
351	Q₈×C₁₉	—	8	1	no	—
352	Q₈×C₁₉	—	8	1	no	—
353	Q₈×C₁₉	—	8	1	no	—
354	D₄×C₁₉	—	4	1	no	—
355	D₄×C₁₉	—	4	1	no	—
356	D₄×C₁₉	—	4	1	no	—
357	D₄×C₁₉	—	4	1	no	—
358	D₄×C₁₉	—	4	1	no	—
359	D₄×C₁₉	—	4	1	no	—
360	D₄×C₁₉	—	4	1	no	—
361	D₄×C₁₉	—	8	1	no	—
362	D₄×C₁₉	—	8	1	no	—
363	D₄×C₁₉	—	8	4	no	—
364	C₂×C₄×C₁₉	—	2	1	no	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	2	2	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	—	2	1	no	—
371	C₂×C₄×C₁₉	—	2	1	no	—
372	C₂×C₄×C₁₉	—	2	1	no	—
373	C₂×C₄×C₁₉	—	2	1	no	—
374	C₂×C₄×C₁₉	—	2	1	no	—
375	C₂×C₄×C₁₉	—	2	1	no	—
376	C₂×C₄×C₁₉	—	2	1	no	—
377	C₂×C₄×C₁₉	—	2	1	no	—
378	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
384	C₂×C₄×C₁₉	—	4	1	no	—
385	C₂×C₄×C₁₉	—	4	1	no	—
386	C₂×C₄×C₁₉	—	4	1	no	—
387	C₂×C₄×C₁₉	—	4	1	no	—
388	C₂×C₄×C₁₉	—	4	1	no	—
389	C₂×C₄×C₁₉	—	4	1	no	—
390	C₂×C₄×C₁₉	—	4	1	no	—
391	C₂×C₄×C₁₉	—	8	1	no	—
392	C₂×C₄×C₁₉	—	8	1	no	—
393	C₂×C₄×C₁₉	—	8	1	no	—
394	C₂×C₄×C₁₉	—	8	1	no	—
395	C₂×C₄×C₁₉	—	8	1	no	—
396	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
397	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
398	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
399	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
400	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
402	C₈×C₁₉	—	4	1	no	—
403	C₈×C₁₉	—	4	1	no	—
404	C₈×C₁₉	—	4	1	no	—
405	C₈×C₁₉	—	4	1	no	—
406	#3564	C₂×C₁₉	1	1	yes	characteristic, complemented
407	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
408	#3211	C₂×C₁₉	1	1	yes	characteristic, complemented
409	#2662	C₂×C₁₉	1	1	yes	characteristic, complemented
410	#1606	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#1605	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#1603	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#1602	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#1600	C₂×C₁₉	1	1	yes	characteristic
415	#1599	C₂×C₁₉	1	1	yes	characteristic, complemented
416	#1597	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#1596	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#1509	C₂×C₁₉	1	1	yes	characteristic, complemented
419	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
420	#1473	C₂×C₁₉	1	1	yes	characteristic, complemented
421	C₂²×C₁₉	—	2	1	no	—
422	C₂²×C₁₉	—	2	1	no	—
423	C₂²×C₁₉	—	4	1	no	—
424	C₂²×C₁₉	—	4	1	no	—
425	C₂²×C₁₉	—	4	1	no	—
426	C₂²×C₁₉	—	4	1	no	—
427	C₂²×C₁₉	—	4	1	no	—
428	C₂²×C₁₉	—	4	1	no	—
429	C₂²×C₁₉	—	8	1	no	—
430	C₂²×C₁₉	—	8	1	no	—
431	C₂²×C₁₉	—	8	1	no	—
432	C₂²×C₁₉	—	8	1	no	—
433	C₂²×C₁₉	—	8	1	no	—
434	C₂²×C₁₉	—	8	1	no	—
435	C₂²×C₁₉	—	8	1	no	—
436	C₂²×C₁₉	—	8	1	no	—
437	C₂²×C₁₉	—	8	1	no	—
438	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
439	C₂²×C₁₉	#577	1	1	yes	characteristic
440	C₂²×C₁₉	#578	1	1	yes	characteristic
441	C₄×C₁₉	—	2	1	no	—
442	C₄×C₁₉	—	2	1	no	—
443	C₄×C₁₉	—	2	1	no	—
444	C₄×C₁₉	—	2	1	no	—
445	C₄×C₁₉	—	2	1	no	—
446	C₄×C₁₉	—	2	1	no	—
447	C₄×C₁₉	—	4	2	no	—
448	C₄×C₁₉	—	4	1	no	—
449	C₄×C₁₉	—	4	1	no	—
450	C₄×C₁₉	—	4	1	no	—
451	C₄×C₁₉	—	4	1	no	—
452	C₄×C₁₉	—	4	1	no	—
453	C₄×C₁₉	—	4	1	no	—
454	C₄×C₁₉	—	4	1	no	—
455	C₄×C₁₉	—	4	1	no	—
456	C₄×C₁₉	—	4	1	no	—
457	C₄×C₁₉	—	4	1	no	—
458	C₄×C₁₉	—	8	1	no	—
459	C₄×C₁₉	—	8	1	no	—
460	#563	—	2	1	no	—
461	#563	—	2	1	no	—
462	#556	—	2	1	no	—
463	#554	—	2	1	no	—
464	#552	—	2	1	no	—
465	#552	—	2	1	no	—
466	#551	—	2	1	no	—
467	#551	—	2	1	no	—
468	#544	C₂²×C₁₉	1	1	yes	characteristic
469	#543	C₂²×C₁₉	1	1	yes	characteristic
470	#542	—	2	1	no	—
471	#541	—	2	1	no	—
472	#541	—	2	1	no	—
473	#539	—	2	1	no	—
474	#539	C₂²×C₁₉	1	1	yes	characteristic
475	#538	C₂²×C₁₉	1	1	yes	characteristic
476	#533	C₂²×C₁₉	1	1	yes	characteristic
477	#529	C₂²×C₁₉	1	1	yes	characteristic
478	C₂×#126	C₂²×C₁₉	1	1	yes	characteristic
479	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
480	#497	—	2	1	no	—
481	#495	—	2	1	no	—
482	#489	—	2	1	no	—
483	#488	—	2	1	no	—
484	#464	—	2	1	no	—
485	#464	—	2	1	no	—
486	#464	—	2	1	no	—
487	#463	—	2	1	no	—
488	#451	C₂²×C₁₉	1	1	yes	characteristic
489	#451	C₂²×C₁₉	1	1	yes	characteristic
490	#451	C₂²×C₁₉	1	1	yes	characteristic
491	#450	C₂²×C₁₉	1	1	yes	characteristic
492	#450	C₂²×C₁₉	1	1	yes	characteristic
493	#450	C₂²×C₁₉	1	1	yes	characteristic
494	#448	C₂²×C₁₉	1	1	yes	characteristic
495	#447	C₂²×C₁₉	1	1	yes	characteristic
496	#432	C₂²×C₁₉	1	1	yes	characteristic
497	#431	C₂²×C₁₉	1	1	yes	characteristic
498	#396	—	2	1	no	—
499	#395	C₂²×C₁₉	1	1	yes	characteristic
500	#394	—	2	1	no	—
501	#394	C₂²×C₁₉	1	1	yes	characteristic
502	#393	C₂²×C₁₉	1	1	yes	characteristic
503	#392	C₂²×C₁₉	1	1	yes	characteristic
504	#390	—	2	1	no	—
505	#388	—	2	1	no	—
506	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
507	#328	C₂²×C₁₉	1	1	yes	characteristic
508	#328	C₂²×C₁₉	1	1	yes	characteristic
509	#328	C₂²×C₁₉	1	1	yes	characteristic
510	#328	C₂²×C₁₉	1	1	yes	characteristic
511	#328	C₂²×C₁₉	1	1	yes	characteristic
512	#328	C₂²×C₁₉	1	1	yes	characteristic
513	#327	C₂²×C₁₉	1	1	yes	characteristic
514	#327	C₂²×C₁₉	1	1	yes	characteristic
515	#324	C₂²×C₁₉	1	1	yes	characteristic
516	#324	C₂²×C₁₉	1	1	yes	characteristic
517	#323	C₂²×C₁₉	1	1	yes	characteristic
518	#323	C₂²×C₁₉	1	1	yes	characteristic
519	C₂×C₁₉	—	2	1	no	—
520	C₂×C₁₉	—	2	1	no	—
521	C₂×C₁₉	—	8	1	no	—
522	C₂×C₁₉	—	8	1	no	—
523	C₂×C₁₉	—	16	1	no	—
524	C₂×C₁₉	#3013	1	1	yes	characteristic
525	C₂×C₁₉	#3018	1	1	yes	characteristic
526	C₂×C₁₉	#3027	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
530	C₂×Q₁₆	—	2	1	no	—
531	C₂×Q₁₆	—	2	1	no	—
532	C₂×Q₁₆	—	2	1	no	—
533	C₂×SD₁₆	—	2	1	no	—
534	C₂×SD₁₆	—	2	1	no	—
535	C₂×SD₁₆	—	2	1	no	—
536	C₂×SD₁₆	—	2	1	no	—
537	C₂×D₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
542	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
543	#126	—	2	1	no	—
544	#126	—	2	1	no	—
545	#126	—	2	1	no	—
546	#126	—	2	1	no	—
547	#126	—	2	1	no	—
548	#126	—	2	1	no	—
549	#126	—	2	1	no	—
550	#126	—	2	1	no	—
551	#126	—	2	1	no	—
552	#126	—	2	1	no	—
553	#126	—	2	1	no	—
554	#126	—	2	1	no	—
555	#126	—	2	1	no	—
556	#125	—	2	1	no	—
557	#125	—	2	1	no	—
558	#125	—	2	1	no	—
559	#125	—	2	1	no	—
560	#125	—	2	1	no	—
561	#125	—	2	1	no	—
562	#125	—	2	1	no	—
563	#125	—	2	1	no	—
564	#125	—	2	1	no	—
565	#125	D₄×C₁₉	1	1	yes	characteristic, complemented
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	—	2	1	no	—
569	#124	—	2	1	no	—
570	#124	—	2	1	no	—
571	#124	—	2	1	no	—
572	#124	—	2	1	no	—
573	#124	D₄×C₁₉	1	1	yes	characteristic, complemented
574	#123	—	2	1	no	—
575	#123	—	2	1	no	—
576	#123	—	2	1	no	—
577	#123	—	2	1	no	—
578	#123	—	2	1	no	—
579	#123	—	2	1	no	—
580	#123	—	2	1	no	—
581	#123	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
597	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
598	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
599	#121	—	2	1	no	—
600	#121	C₂³×C₁₉	1	1	yes	characteristic
601	#120	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
606	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
607	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
614	#117	—	2	1	no	—
615	#117	—	2	1	no	—
616	#117	—	2	1	no	—
617	#117	—	2	1	no	—
618	#117	—	2	1	no	—
619	#117	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
638	C₄⋊C₈	—	2	1	no	—
639	C₄⋊C₈	—	2	1	no	—
640	#103	—	2	1	no	—
641	#103	—	2	1	no	—
642	#103	—	2	1	no	—
643	#103	—	2	1	no	—
644	#102	—	2	1	no	—
645	#102	—	2	1	no	—
646	#102	—	2	1	no	—
647	#102	—	2	1	no	—
648	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
649	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
650	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
651	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
652	#97	—	2	1	no	—
653	C₄×C₈	—	2	1	no	—
654	#95	—	2	1	no	—
655	#95	—	2	1	no	—
656	#95	C₂³×C₁₉	1	1	yes	characteristic
657	#95	C₂³×C₁₉	1	1	yes	characteristic
658	C₁₉	#18435	1	1	yes	characteristic, direct product factor, Sylow
659	C₂⁴	—	2	1	no	—
660	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	8	1	no	—
667	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
668	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
669	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	8	1	no	—
677	C₂×D₄	—	8	1	no	—
678	C₂×D₄	—	8	1	no	—
679	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
694	Q₁₆	—	8	1	no	—
695	Q₁₆	—	8	1	no	—
696	Q₁₆	—	8	1	no	—
697	SD₁₆	—	8	1	no	—
698	SD₁₆	—	8	1	no	—
699	SD₁₆	—	8	1	no	—
700	SD₁₆	—	8	1	no	—
701	D₈	—	8	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	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	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	8	1	no	—
737	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
738	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
739	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	1	no	—
766	C₂²⋊C₄	—	4	1	no	—
767	C₂²⋊C₄	—	8	1	no	—
768	C₂²⋊C₄	—	8	1	no	—
769	C₂²⋊C₄	—	8	1	no	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	8	1	no	—
778	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	1	no	—
794	C₂³	—	4	1	no	—
795	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
796	Q₈	—	4	1	no	—
797	Q₈	—	4	1	no	—
798	Q₈	—	4	1	no	—
799	Q₈	—	4	1	no	—
800	Q₈	—	4	1	no	—
801	Q₈	—	4	1	no	—
802	Q₈	—	4	1	no	—
803	Q₈	—	8	1	no	—
804	Q₈	—	8	1	no	—
805	Q₈	—	8	1	no	—
806	D₄	—	4	1	no	—
807	D₄	—	4	1	no	—
808	D₄	—	4	1	no	—
809	D₄	—	4	1	no	—
810	D₄	—	4	1	no	—
811	D₄	—	4	1	no	—
812	D₄	—	4	1	no	—
813	D₄	—	8	1	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	4	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	8	1	no	—
844	C₂×C₄	—	8	1	no	—
845	C₂×C₄	—	8	1	no	—
846	C₂×C₄	—	8	1	no	—
847	C₂×C₄	—	8	1	no	—
848	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
849	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
850	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
851	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
854	C₈	—	4	1	no	—
855	C₈	—	4	1	no	—
856	C₈	—	4	1	no	—
857	C₈	—	4	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	1	no	—
869	C₂²	—	8	1	no	—
870	C₂²	—	8	1	no	—
871	C₂²	—	8	1	no	—
872	C₂²	—	8	1	no	—
873	C₂²	—	8	1	no	—
874	C₂²	—	8	1	no	—
875	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
876	C₂²	C₁₉×#577	1	1	yes	characteristic
877	C₂²	C₁₉×#578	1	1	yes	characteristic
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	8	1	no	—
896	C₄	—	8	1	no	—
897	C₂	—	2	1	no	—
898	C₂	—	2	1	no	—
899	C₂	—	8	1	no	—
900	C₂	—	8	1	no	—
901	C₂	—	16	1	no	—
902	C₂	C₁₉×#3013	1	1	yes	characteristic
903	C₂	C₁₉×#3018	1	1	yes	characteristic
904	C₂	C₁₉×#3027	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×#3215	C₂	semidirect
3. C₁₉×#3211	C₂	semidirect
4. C₁₉×#2662	C₂	semidirect
5. C₁₉×#1606	C₂	semidirect
6. C₁₉×#1605	C₂	semidirect
7. C₁₉×#1603	C₂	semidirect
8. C₁₉×#1602	C₂	semidirect
10. C₁₉×#1599	C₂	semidirect
11. C₁₉×#1597	C₂	semidirect
12. C₁₉×#1596	C₂	semidirect
13. C₁₉×#1509	C₂	semidirect
14. C₁₉×#1503	C₂	semidirect
15. C₁₉×#1473	C₂	semidirect
89. C₁₉×C₄⋊Q₈	D₄	semidirect
90. C₁₉×C₄⋊Q₈	D₄	semidirect
113. C₁₉×#125	D₄	semidirect
121. C₁₉×#124	D₄	semidirect
153. C₄×Q₈×C₁₉	D₄	semidirect
154. C₄×Q₈×C₁₉	D₄	semidirect
155. C₄×Q₈×C₁₉	D₄	semidirect
161. C₄×D₄×C₁₉	D₄	semidirect
329. #18435	C₁₉	direct (N × H)
406. #3564	C₂×C₁₉	semidirect
407. #3215	C₂×C₁₉	semidirect
408. #3211	C₂×C₁₉	semidirect
409. #2662	C₂×C₁₉	semidirect
410. #1606	C₂×C₁₉	semidirect
411. #1605	C₂×C₁₉	semidirect
412. #1603	C₂×C₁₉	semidirect
413. #1602	C₂×C₁₉	semidirect
415. #1599	C₂×C₁₉	semidirect
416. #1597	C₂×C₁₉	semidirect
417. #1596	C₂×C₁₉	semidirect
418. #1509	C₂×C₁₉	semidirect
419. #1503	C₂×C₁₉	semidirect
420. #1473	C₂×C₁₉	semidirect
541. C₄⋊Q₈	D₄×C₁₉	semidirect
542. C₄⋊Q₈	D₄×C₁₉	semidirect
565. #125	D₄×C₁₉	semidirect
573. #124	D₄×C₁₉	semidirect
605. C₄×Q₈	D₄×C₁₉	semidirect
606. C₄×Q₈	D₄×C₁₉	semidirect
607. C₄×Q₈	D₄×C₁₉	semidirect
613. C₄×D₄	D₄×C₁₉	semidirect
658. C₁₉	#18435	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×#3215	2
C₁₉×#3211	2
C₁₉×#2662	2
C₁₉×#1606	2
C₁₉×#1605	2
C₁₉×#1603	2
C₁₉×#1602	2
C₁₉×#1600	2
C₁₉×#1599	2
C₁₉×#1597	2
C₁₉×#1596	2
C₁₉×#1509	2
C₁₉×#1503	2
C₁₉×#1473	2
#18435	19

Subgroups — C19×#18435 #18024394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18435 #18024394