Subgroups — C₁₉×#19038 #18024997

Order 4864.

876 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3219	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3180	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3171	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1664	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1664	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1660	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1659	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1657	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1657	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1657	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1655	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	C₂²	1	1	yes	characteristic
17	C₁₉×#563	C₂²	1	1	yes	characteristic
18	C₁₉×#563	C₂²	1	1	yes	characteristic
19	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
20	C₁₉×#556	—	2	1	no	—
21	C₁₉×#556	—	2	1	no	—
22	C₁₉×#556	—	2	1	no	—
23	C₁₉×#551	—	2	1	no	—
24	C₁₉×#551	—	2	1	no	—
25	C₁₉×#551	—	2	1	no	—
26	C₁₉×#542	—	2	1	no	—
27	C₁₉×#542	—	2	1	no	—
28	C₁₉×#542	—	2	1	no	—
29	C₁₉×#538	—	2	1	no	—
30	C₁₉×#538	—	2	1	no	—
31	C₁₉×#538	—	2	1	no	—
32	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#529	C₂²	1	1	yes	characteristic
34	C₁₉×#529	C₂²	1	1	yes	characteristic
35	C₁₉×#529	C₂²	1	1	yes	characteristic
36	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#497	C₂²	1	1	yes	characteristic
39	C₁₉×#496	C₂²	1	1	yes	characteristic
40	C₁₉×#496	C₂²	1	1	yes	characteristic
41	C₁₉×#496	C₂²	1	1	yes	characteristic
42	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#489	C₂²	1	1	yes	characteristic
47	C₁₉×#489	C₂²	1	1	yes	characteristic
48	C₁₉×#469	—	2	1	no	—
49	C₁₉×#468	—	2	1	no	—
50	C₁₉×#466	—	2	1	no	—
51	C₁₉×#465	—	2	1	no	—
52	C₁₉×#464	—	2	1	no	—
53	C₁₉×#463	—	2	1	no	—
54	C₁₉×#452	—	2	1	no	—
55	C₁₉×#449	—	2	1	no	—
56	C₁₉×#442	—	2	1	no	—
57	C₁₉×#440	—	2	1	no	—
58	C₄×SD₁₆×C₁₉	—	2	1	no	—
59	C₄×D₈×C₁₉	—	2	1	no	—
60	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
61	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#330	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#330	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#330	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#330	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#330	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#330	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#329	C₂²	1	1	yes	characteristic
70	C₁₉×#329	C₂²	1	1	yes	characteristic
71	C₁₉×#329	C₂²	1	1	yes	characteristic
72	C₁₉×#329	C₂²	1	1	yes	characteristic
73	C₁₉×#329	C₂²	1	1	yes	characteristic
74	C₁₉×#329	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×Q₁₆×C₁₉	—	2	1	no	—
77	C₂×SD₁₆×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	C₂×D₈×C₁₉	—	2	1	no	—
83	C₂×D₈×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂²×C₈×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	C₂³	1	1	yes	characteristic
90	C₁₉×#127	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
105	C₁₉×#125	C₂³	1	1	yes	characteristic
106	C₁₉×#125	C₂³	1	1	yes	characteristic
107	C₁₉×#124	—	2	1	no	—
108	C₁₉×#124	—	2	1	no	—
109	C₁₉×#124	—	2	1	no	—
110	C₁₉×#124	—	2	1	no	—
111	C₁₉×#124	—	2	1	no	—
112	C₁₉×#124	—	2	1	no	—
113	C₁₉×#124	—	2	1	no	—
114	C₁₉×#124	—	2	1	no	—
115	C₁₉×#124	—	2	1	no	—
116	C₁₉×#124	—	2	1	no	—
117	C₁₉×#124	C₂³	1	1	yes	characteristic
118	C₁₉×#124	C₂³	1	1	yes	characteristic
119	C₁₉×#124	C₂³	1	1	yes	characteristic
120	C₁₉×#123	—	2	1	no	—
121	C₁₉×#123	—	2	1	no	—
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×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	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
140	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
141	C₁₉×#121	—	2	1	no	—
142	C₁₉×#121	—	2	1	no	—
143	C₁₉×#121	—	2	1	no	—
144	C₁₉×#121	—	2	1	no	—
145	C₁₉×#121	—	2	1	no	—
146	C₁₉×#121	D₄	1	1	yes	characteristic
147	C₁₉×#121	D₄	1	1	yes	characteristic
148	C₁₉×#121	D₄	1	1	yes	characteristic
149	C₁₉×#120	—	2	1	no	—
150	C₁₉×#120	—	2	1	no	—
151	C₁₉×#120	—	2	1	no	—
152	C₁₉×#120	—	2	1	no	—
153	C₄×Q₈×C₁₉	—	2	1	no	—
154	C₄×Q₈×C₁₉	—	2	1	no	—
155	C₄×Q₈×C₁₉	—	2	1	no	—
156	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
157	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
158	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
159	C₄×D₄×C₁₉	—	2	1	no	—
160	C₄×D₄×C₁₉	—	2	1	no	—
161	C₄×D₄×C₁₉	—	2	1	no	—
162	C₄×D₄×C₁₉	—	2	1	no	—
163	C₄×D₄×C₁₉	—	2	1	no	—
164	C₄×D₄×C₁₉	—	2	1	no	—
165	C₄×D₄×C₁₉	—	2	1	no	—
166	C₄×D₄×C₁₉	—	2	1	no	—
167	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
168	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
169	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
170	C₁₉×#117	—	2	1	no	—
171	C₁₉×#117	—	2	1	no	—
172	C₁₉×#117	—	2	1	no	—
173	C₁₉×#117	—	2	1	no	—
174	C₁₉×#117	—	2	1	no	—
175	C₁₉×#117	—	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×C₄²×C₁₉	C₂³	1	1	yes	characteristic
180	C₁₉×#107	—	2	1	no	—
181	C₁₉×#107	—	2	1	no	—
182	C₁₉×#106	—	2	1	no	—
183	C₁₉×#106	—	2	1	no	—
184	C₁₉×C₄⋊C₈	—	2	1	no	—
185	C₁₉×#103	—	2	1	no	—
186	C₁₉×#103	—	2	1	no	—
187	C₁₉×#103	—	2	1	no	—
188	C₁₉×#103	—	2	1	no	—
189	C₁₉×#102	—	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×#102	—	2	1	no	—
196	C₁₉×#102	—	2	1	no	—
197	C₁₉×C₂²⋊C₈	—	2	1	no	—
198	C₁₉×#97	—	2	1	no	—
199	C₁₉×#97	C₂³	1	1	yes	characteristic
200	C₁₉×#97	C₂³	1	1	yes	characteristic
201	C₁₉×#97	C₂³	1	1	yes	characteristic
202	C₁₉×#97	C₂³	1	1	yes	characteristic
203	C₁₉×#97	C₂³	1	1	yes	characteristic
204	C₁₉×#97	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₁₉	—	2	1	no	—
206	C₂⁴×C₁₉	—	2	1	no	—
207	#41×C₁₉	—	8	1	no	—
208	#41×C₁₉	—	8	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	C₂×D₄	1	1	yes	characteristic
214	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
220	C₂×D₄×C₁₉	—	2	1	no	—
221	C₂×D₄×C₁₉	—	2	1	no	—
222	C₂×D₄×C₁₉	—	2	1	no	—
223	C₂×D₄×C₁₉	—	2	1	no	—
224	C₂×D₄×C₁₉	—	2	1	no	—
225	C₂×D₄×C₁₉	—	4	1	no	—
226	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	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	Q₁₆×C₁₉	—	8	1	no	—
240	SD₁₆×C₁₉	—	4	2	no	—
241	SD₁₆×C₁₉	—	4	2	no	—
242	SD₁₆×C₁₉	—	8	1	no	—
243	SD₁₆×C₁₉	—	8	1	no	—
244	D₈×C₁₉	—	4	2	no	—
245	D₈×C₁₉	—	4	2	no	—
246	D₈×C₁₉	—	8	1	no	—
247	M₁₆×C₁₉	—	4	2	no	—
248	C₂×C₈×C₁₉	—	2	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	C₂×C₈×C₁₉	—	2	1	no	—
254	C₂×C₈×C₁₉	—	4	2	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	C₂×D₄	1	1	yes	characteristic
276	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
277	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
278	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
279	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
280	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
281	C₂²⋊C₄×C₁₉	—	2	1	no	—
282	C₂²⋊C₄×C₁₉	—	2	1	no	—
283	C₂²⋊C₄×C₁₉	—	2	1	no	—
284	C₂²⋊C₄×C₁₉	—	2	1	no	—
285	C₂²⋊C₄×C₁₉	—	2	1	no	—
286	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	1	no	—
309	C₂²⋊C₄×C₁₉	—	4	1	no	—
310	C₄²×C₁₉	—	2	1	no	—
311	C₄²×C₁₉	—	2	1	no	—
312	C₄²×C₁₉	—	2	1	no	—
313	C₄²×C₁₉	—	2	1	no	—
314	C₄²×C₁₉	—	2	1	no	—
315	C₄²×C₁₉	—	2	1	no	—
316	C₄²×C₁₉	—	2	1	no	—
317	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
321	#19038	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₁₉	—	2	1	no	—
323	C₂³×C₁₉	—	2	1	no	—
324	C₂³×C₁₉	—	2	1	no	—
325	C₂³×C₁₉	—	4	1	no	—
326	C₂³×C₁₉	—	8	1	no	—
327	C₂³×C₁₉	—	8	1	no	—
328	C₂³×C₁₉	—	8	1	no	—
329	C₂³×C₁₉	#120	1	1	yes	characteristic
330	Q₈×C₁₉	—	4	1	no	—
331	Q₈×C₁₉	—	4	1	no	—
332	Q₈×C₁₉	—	4	1	no	—
333	Q₈×C₁₉	—	4	1	no	—
334	Q₈×C₁₉	—	4	1	no	—
335	Q₈×C₁₉	—	8	1	no	—
336	Q₈×C₁₉	—	8	1	no	—
337	Q₈×C₁₉	—	8	1	no	—
338	D₄×C₁₉	—	4	1	no	—
339	D₄×C₁₉	—	4	1	no	—
340	D₄×C₁₉	—	4	1	no	—
341	D₄×C₁₉	—	4	1	no	—
342	D₄×C₁₉	—	4	1	no	—
343	D₄×C₁₉	—	4	1	no	—
344	D₄×C₁₉	—	4	1	no	—
345	D₄×C₁₉	—	4	1	no	—
346	D₄×C₁₉	—	4	1	no	—
347	D₄×C₁₉	—	8	1	no	—
348	D₄×C₁₉	—	8	1	no	—
349	D₄×C₁₉	—	8	1	no	—
350	D₄×C₁₉	—	8	1	no	—
351	D₄×C₁₉	—	8	1	no	—
352	D₄×C₁₉	—	8	1	no	—
353	D₄×C₁₉	—	8	2	no	—
354	C₂×C₄×C₁₉	—	2	1	no	—
355	C₂×C₄×C₁₉	—	2	1	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	—	4	1	no	—
364	C₂×C₄×C₁₉	—	4	1	no	—
365	C₂×C₄×C₁₉	—	4	1	no	—
366	C₂×C₄×C₁₉	—	4	1	no	—
367	C₂×C₄×C₁₉	—	8	1	no	—
368	C₂×C₄×C₁₉	—	8	1	no	—
369	C₂×C₄×C₁₉	—	8	1	no	—
370	C₂×C₄×C₁₉	—	8	2	no	—
371	C₂×C₄×C₁₉	—	8	1	no	—
372	C₂×C₄×C₁₉	—	8	1	no	—
373	C₂×C₄×C₁₉	—	8	1	no	—
374	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
375	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
376	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
377	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
380	C₈×C₁₉	—	2	2	no	—
381	C₈×C₁₉	—	2	2	no	—
382	C₈×C₁₉	—	4	1	no	—
383	C₈×C₁₉	—	4	1	no	—
384	C₈×C₁₉	—	4	1	no	—
385	C₈×C₁₉	—	4	1	no	—
386	#3568	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#3219	C₂×C₁₉	1	1	yes	characteristic, complemented
388	#3180	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#3171	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#1664	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#1664	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#1660	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#1659	C₂×C₁₉	1	1	yes	characteristic, complemented
394	#1657	C₂×C₁₉	1	1	yes	characteristic, complemented
395	#1657	C₂×C₁₉	1	1	yes	characteristic, complemented
396	#1657	C₂×C₁₉	1	1	yes	characteristic, complemented
397	#1655	C₂×C₁₉	1	1	yes	characteristic, complemented
398	#1532	C₂×C₁₉	1	1	yes	characteristic, complemented
399	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
401	C₂²×C₁₉	—	2	1	no	—
402	C₂²×C₁₉	—	2	1	no	—
403	C₂²×C₁₉	—	2	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	1	no	—
413	C₂²×C₁₉	—	8	1	no	—
414	C₂²×C₁₉	—	8	1	no	—
415	C₂²×C₁₉	—	8	1	no	—
416	C₂²×C₁₉	—	16	2	no	—
417	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
418	C₄×C₁₉	—	2	1	no	—
419	C₄×C₁₉	—	2	1	no	—
420	C₄×C₁₉	—	2	1	no	—
421	C₄×C₁₉	—	2	1	no	—
422	C₄×C₁₉	—	2	1	no	—
423	C₄×C₁₉	—	2	1	no	—
424	C₄×C₁₉	—	4	1	no	—
425	C₄×C₁₉	—	4	1	no	—
426	C₄×C₁₉	—	4	1	no	—
427	C₄×C₁₉	—	4	1	no	—
428	C₄×C₁₉	—	4	1	no	—
429	C₄×C₁₉	—	4	1	no	—
430	C₄×C₁₉	—	4	1	no	—
431	C₄×C₁₉	—	4	1	no	—
432	C₄×C₁₉	—	4	1	no	—
433	C₄×C₁₉	—	8	1	no	—
434	#563	C₂²×C₁₉	1	1	yes	characteristic
435	#563	C₂²×C₁₉	1	1	yes	characteristic
436	#563	C₂²×C₁₉	1	1	yes	characteristic
437	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
438	#556	—	2	1	no	—
439	#556	—	2	1	no	—
440	#556	—	2	1	no	—
441	#551	—	2	1	no	—
442	#551	—	2	1	no	—
443	#551	—	2	1	no	—
444	#542	—	2	1	no	—
445	#542	—	2	1	no	—
446	#542	—	2	1	no	—
447	#538	—	2	1	no	—
448	#538	—	2	1	no	—
449	#538	—	2	1	no	—
450	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	#529	C₂²×C₁₉	1	1	yes	characteristic
452	#529	C₂²×C₁₉	1	1	yes	characteristic
453	#529	C₂²×C₁₉	1	1	yes	characteristic
454	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
455	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	#497	C₂²×C₁₉	1	1	yes	characteristic
457	#496	C₂²×C₁₉	1	1	yes	characteristic
458	#496	C₂²×C₁₉	1	1	yes	characteristic
459	#496	C₂²×C₁₉	1	1	yes	characteristic
460	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
462	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
463	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	#489	C₂²×C₁₉	1	1	yes	characteristic
465	#489	C₂²×C₁₉	1	1	yes	characteristic
466	#469	—	2	1	no	—
467	#468	—	2	1	no	—
468	#466	—	2	1	no	—
469	#465	—	2	1	no	—
470	#464	—	2	1	no	—
471	#463	—	2	1	no	—
472	#452	—	2	1	no	—
473	#449	—	2	1	no	—
474	#442	—	2	1	no	—
475	#440	—	2	1	no	—
476	C₄×SD₁₆	—	2	1	no	—
477	C₄×D₈	—	2	1	no	—
478	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
479	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
480	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
481	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
482	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
483	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
484	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
485	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
486	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
487	#329	C₂²×C₁₉	1	1	yes	characteristic
488	#329	C₂²×C₁₉	1	1	yes	characteristic
489	#329	C₂²×C₁₉	1	1	yes	characteristic
490	#329	C₂²×C₁₉	1	1	yes	characteristic
491	#329	C₂²×C₁₉	1	1	yes	characteristic
492	#329	C₂²×C₁₉	1	1	yes	characteristic
493	C₂×C₁₉	—	4	1	no	—
494	C₂×C₁₉	—	8	1	no	—
495	C₂×C₁₉	—	8	1	no	—
496	C₂×C₁₉	—	8	1	no	—
497	C₂×C₁₉	—	16	1	no	—
498	C₂×C₁₉	#3018	1	1	yes	characteristic
499	C₂×C₁₉	#3018	1	1	yes	characteristic
500	C₂×C₁₉	#3021	1	1	yes	characteristic
501	C₂×#41	—	2	1	no	—
502	C₂×Q₁₆	—	2	1	no	—
503	C₂×SD₁₆	—	2	1	no	—
504	C₂×SD₁₆	—	2	1	no	—
505	C₂×SD₁₆	—	2	1	no	—
506	C₂×SD₁₆	—	2	1	no	—
507	C₂×D₈	—	2	1	no	—
508	C₂×D₈	—	2	1	no	—
509	C₂×D₈	—	2	1	no	—
510	C₂×M₁₆	—	2	1	no	—
511	C₂²×C₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
516	#127	C₂³×C₁₉	1	1	yes	characteristic
517	#126	—	2	1	no	—
518	#126	—	2	1	no	—
519	#126	—	2	1	no	—
520	#126	—	2	1	no	—
521	#126	—	2	1	no	—
522	#126	—	2	1	no	—
523	#126	—	2	1	no	—
524	#126	—	2	1	no	—
525	#126	—	2	1	no	—
526	#126	—	2	1	no	—
527	#126	—	2	1	no	—
528	#126	—	2	1	no	—
529	#126	—	2	1	no	—
530	#125	C₂³×C₁₉	1	1	yes	characteristic
531	#125	C₂³×C₁₉	1	1	yes	characteristic
532	#125	C₂³×C₁₉	1	1	yes	characteristic
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	—	2	1	no	—
536	#124	—	2	1	no	—
537	#124	—	2	1	no	—
538	#124	—	2	1	no	—
539	#124	—	2	1	no	—
540	#124	—	2	1	no	—
541	#124	—	2	1	no	—
542	#124	—	2	1	no	—
543	#124	C₂³×C₁₉	1	1	yes	characteristic
544	#124	C₂³×C₁₉	1	1	yes	characteristic
545	#124	C₂³×C₁₉	1	1	yes	characteristic
546	#123	—	2	1	no	—
547	#123	—	2	1	no	—
548	#123	—	2	1	no	—
549	#123	—	2	1	no	—
550	#123	—	2	1	no	—
551	#123	—	2	1	no	—
552	#123	—	2	1	no	—
553	#123	—	2	1	no	—
554	#123	—	2	1	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
565	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
566	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	D₄×C₁₉	1	1	yes	characteristic
573	#121	D₄×C₁₉	1	1	yes	characteristic
574	#121	D₄×C₁₉	1	1	yes	characteristic
575	#120	—	2	1	no	—
576	#120	—	2	1	no	—
577	#120	—	2	1	no	—
578	#120	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
583	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
584	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
594	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
595	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
596	#117	—	2	1	no	—
597	#117	—	2	1	no	—
598	#117	—	2	1	no	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
606	#107	—	2	1	no	—
607	#107	—	2	1	no	—
608	#106	—	2	1	no	—
609	#106	—	2	1	no	—
610	C₄⋊C₈	—	2	1	no	—
611	#103	—	2	1	no	—
612	#103	—	2	1	no	—
613	#103	—	2	1	no	—
614	#103	—	2	1	no	—
615	#102	—	2	1	no	—
616	#102	—	2	1	no	—
617	#102	—	2	1	no	—
618	#102	—	2	1	no	—
619	#102	—	2	1	no	—
620	#102	—	2	1	no	—
621	#102	—	2	1	no	—
622	#102	—	2	1	no	—
623	C₂²⋊C₈	—	2	1	no	—
624	#97	—	2	1	no	—
625	#97	C₂³×C₁₉	1	1	yes	characteristic
626	#97	C₂³×C₁₉	1	1	yes	characteristic
627	#97	C₂³×C₁₉	1	1	yes	characteristic
628	#97	C₂³×C₁₉	1	1	yes	characteristic
629	#97	C₂³×C₁₉	1	1	yes	characteristic
630	#97	C₂³×C₁₉	1	1	yes	characteristic
631	C₄×C₈	—	2	1	no	—
632	C₁₉	#19038	1	1	yes	characteristic, direct product factor, Sylow
633	C₂⁴	—	2	1	no	—
634	#41	—	8	1	no	—
635	#41	—	8	1	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
641	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
642	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
654	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
655	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
666	Q₁₆	—	8	1	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	8	1	no	—
670	SD₁₆	—	8	1	no	—
671	D₈	—	4	2	no	—
672	D₈	—	4	2	no	—
673	D₈	—	8	1	no	—
674	M₁₆	—	4	2	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	—	4	2	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	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	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
703	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
704	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
706	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
707	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	4	1	no	—
736	C₂²⋊C₄	—	4	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	1	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
747	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	8	1	no	—
753	C₂³	—	8	1	no	—
754	C₂³	—	8	1	no	—
755	C₂³	C₁₉×#120	1	1	yes	characteristic
756	Q₈	—	4	1	no	—
757	Q₈	—	4	1	no	—
758	Q₈	—	4	1	no	—
759	Q₈	—	4	1	no	—
760	Q₈	—	4	1	no	—
761	Q₈	—	8	1	no	—
762	Q₈	—	8	1	no	—
763	Q₈	—	8	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	4	1	no	—
770	D₄	—	4	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	8	1	no	—
774	D₄	—	8	1	no	—
775	D₄	—	8	1	no	—
776	D₄	—	8	1	no	—
777	D₄	—	8	1	no	—
778	D₄	—	8	1	no	—
779	D₄	—	8	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	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	—	8	1	no	—
794	C₂×C₄	—	8	1	no	—
795	C₂×C₄	—	8	1	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	1	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	—	8	1	no	—
800	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
801	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
802	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	4	1	no	—
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₈	—	4	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	16	2	no	—
828	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	1	no	—
844	C₄	—	8	1	no	—
845	C₂	—	4	1	no	—
846	C₂	—	8	1	no	—
847	C₂	—	8	1	no	—
848	C₂	—	8	1	no	—
849	C₂	—	16	1	no	—
850	C₂	C₁₉×#3018	1	1	yes	characteristic
851	C₂	C₁₉×#3018	1	1	yes	characteristic
852	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ 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×#3568	C₂	semidirect
2. C₁₉×#3219	C₂	semidirect
3. C₁₉×#3180	C₂	semidirect
4. C₁₉×#3171	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1664	C₂	semidirect
7. C₁₉×#1660	C₂	semidirect
8. C₁₉×#1659	C₂	semidirect
9. C₁₉×#1657	C₂	semidirect
10. C₁₉×#1657	C₂	semidirect
11. C₁₉×#1657	C₂	semidirect
12. C₁₉×#1655	C₂	semidirect
13. C₁₉×#1532	C₂	semidirect
14. C₁₉×#1529	C₂	semidirect
15. C₁₉×#1524	C₂	semidirect
32. C₁₉×#532	C₂²	semidirect
36. C₁₉×#501	C₂²	semidirect
37. C₁₉×#501	C₂²	semidirect
42. C₁₉×#491	C₂²	semidirect
43. C₁₉×#490	C₂²	semidirect
44. C₁₉×#490	C₂²	semidirect
45. C₁₉×#490	C₂²	semidirect
60. C₁₉×#432	C₂²	semidirect
61. C₄×M₁₆×C₁₉	C₂²	semidirect
62. C₂×C₁₉×#97	C₂²	semidirect
63. C₁₉×#330	C₂²	semidirect
64. C₁₉×#330	C₂²	semidirect
65. C₁₉×#330	C₂²	semidirect
66. C₁₉×#330	C₂²	semidirect
67. C₁₉×#330	C₂²	semidirect
68. C₁₉×#330	C₂²	semidirect
321. #19038	C₁₉	direct (N × H)
386. #3568	C₂×C₁₉	semidirect
387. #3219	C₂×C₁₉	semidirect
388. #3180	C₂×C₁₉	semidirect
389. #3171	C₂×C₁₉	semidirect
390. #1664	C₂×C₁₉	semidirect
391. #1664	C₂×C₁₉	semidirect
392. #1660	C₂×C₁₉	semidirect
393. #1659	C₂×C₁₉	semidirect
394. #1657	C₂×C₁₉	semidirect
395. #1657	C₂×C₁₉	semidirect
396. #1657	C₂×C₁₉	semidirect
397. #1655	C₂×C₁₉	semidirect
398. #1532	C₂×C₁₉	semidirect
399. #1529	C₂×C₁₉	semidirect
400. #1524	C₂×C₁₉	semidirect
450. #532	C₂²×C₁₉	semidirect
454. #501	C₂²×C₁₉	semidirect
455. #501	C₂²×C₁₉	semidirect
460. #491	C₂²×C₁₉	semidirect
461. #490	C₂²×C₁₉	semidirect
462. #490	C₂²×C₁₉	semidirect
463. #490	C₂²×C₁₉	semidirect
478. #432	C₂²×C₁₉	semidirect
479. C₄×M₁₆	C₂²×C₁₉	semidirect
480. C₂×#97	C₂²×C₁₉	semidirect
481. #330	C₂²×C₁₉	semidirect
482. #330	C₂²×C₁₉	semidirect
483. #330	C₂²×C₁₉	semidirect
484. #330	C₂²×C₁₉	semidirect
485. #330	C₂²×C₁₉	semidirect
486. #330	C₂²×C₁₉	semidirect
632. C₁₉	#19038	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×#3568	2
C₁₉×#3219	2
C₁₉×#3180	2
C₁₉×#3171	2
C₁₉×#1664	2
C₁₉×#1660	2
C₁₉×#1659	2
C₁₉×#1657	2
C₁₉×#1655	2
C₁₉×#1532	2
C₁₉×#1529	2
C₁₉×#1524	2
#19038	19

Subgroups — C19×#19038 #18024997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19038 #18024997