Subgroups — C₁₉×#18445 #18024404

Order 4864.

848 conjugacy classes of subgroups.

The subgroup lattice has 838 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
2	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3232	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2664	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1618	C₂	1	1	yes	maximal, characteristic
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×#1612	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1611	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1609	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1608	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×#125	C₂²	1	1	yes	characteristic
36	C₁₉×#501	—	2	1	no	—
37	C₁₉×#499	—	2	1	no	—
38	C₁₉×#491	—	2	1	no	—
39	C₁₉×#488	—	2	1	no	—
40	C₁₉×#484	C₂²	1	1	yes	characteristic
41	C₁₉×#484	C₂²	1	1	yes	characteristic
42	C₁₉×#484	C₂²	1	1	yes	characteristic
43	C₁₉×#483	C₂²	1	1	yes	characteristic
44	C₁₉×#483	C₂²	1	1	yes	characteristic
45	C₁₉×#483	C₂²	1	1	yes	characteristic
46	C₁₉×#481	C₂²	1	1	yes	characteristic
47	C₁₉×#480	C₂²	1	1	yes	characteristic
48	C₁₉×#479	—	2	1	no	—
49	C₁₉×#479	—	2	1	no	—
50	C₁₉×#479	—	2	1	no	—
51	C₁₉×#478	—	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×#398	—	2	1	no	—
57	C₁₉×#398	C₂²	1	1	yes	characteristic
58	C₁₉×#397	C₂²	1	1	yes	characteristic
59	C₁₉×#396	—	2	1	no	—
60	C₁₉×#389	—	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	C₁₉×C₄⋊Q₈	—	2	1	no	—
76	C₁₉×C₄⋊Q₈	—	2	1	no	—
77	C₁₉×C₄⋊Q₈	—	2	1	no	—
78	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
79	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
80	C₁₉×#126	—	2	1	no	—
81	C₁₉×#126	—	2	1	no	—
82	C₁₉×#126	—	2	1	no	—
83	C₁₉×#126	—	2	1	no	—
84	C₁₉×#126	—	2	1	no	—
85	C₁₉×#126	—	2	1	no	—
86	C₁₉×#126	—	2	1	no	—
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×#125	—	2	1	no	—
94	C₁₉×#125	—	2	1	no	—
95	C₁₉×#125	—	2	1	no	—
96	C₁₉×#125	—	2	1	no	—
97	C₁₉×#125	—	2	1	no	—
98	C₁₉×#125	—	2	1	no	—
99	C₁₉×#125	—	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	D₄	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	D₄	1	1	yes	characteristic
111	C₁₉×#123	—	2	1	no	—
112	C₁₉×#123	—	2	1	no	—
113	C₁₉×#123	—	2	1	no	—
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×C₂²⋊Q₈	—	2	1	no	—
120	C₁₉×C₂²⋊Q₈	—	2	1	no	—
121	C₁₉×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
134	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₉×#121	—	2	1	no	—
137	C₁₉×#121	C₂³	1	1	yes	characteristic
138	C₁₉×#120	—	2	1	no	—
139	C₄×Q₈×C₁₉	—	2	1	no	—
140	C₄×Q₈×C₁₉	—	2	1	no	—
141	C₄×Q₈×C₁₉	—	2	1	no	—
142	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
143	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
144	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
145	C₄×D₄×C₁₉	—	2	1	no	—
146	C₄×D₄×C₁₉	—	2	1	no	—
147	C₄×D₄×C₁₉	—	2	1	no	—
148	C₄×D₄×C₁₉	—	2	1	no	—
149	C₄×D₄×C₁₉	—	2	1	no	—
150	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
151	C₁₉×#117	—	2	1	no	—
152	C₁₉×#117	—	2	1	no	—
153	C₁₉×#117	—	2	1	no	—
154	C₁₉×#117	—	2	1	no	—
155	C₁₉×#117	—	2	1	no	—
156	C₁₉×#117	—	2	1	no	—
157	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
169	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
170	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
171	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₉	—	2	1	no	—
175	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
176	C₁₉×#107	—	2	1	no	—
177	C₁₉×#107	—	2	1	no	—
178	C₁₉×#107	—	2	1	no	—
179	C₁₉×#107	—	2	1	no	—
180	C₁₉×#106	—	2	1	no	—
181	C₁₉×#106	—	2	1	no	—
182	C₁₉×#106	—	2	1	no	—
183	C₁₉×#106	—	2	1	no	—
184	C₁₉×C₄⋊C₈	—	2	1	no	—
185	C₁₉×C₄⋊C₈	—	2	1	no	—
186	C₁₉×#103	—	2	1	no	—
187	C₁₉×#103	—	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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×#97	—	2	1	no	—
199	C₄×C₈×C₁₉	—	2	1	no	—
200	C₁₉×#95	—	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	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₁₉	—	2	1	no	—
208	C₂×Q₈×C₁₉	—	2	1	no	—
209	C₂×Q₈×C₁₉	—	2	1	no	—
210	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₁₉	—	2	1	no	—
214	C₂×D₄×C₁₉	—	2	1	no	—
215	C₂×D₄×C₁₉	—	2	1	no	—
216	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₉	—	2	1	no	—
218	C₂²×C₄×C₁₉	—	2	1	no	—
219	C₂²×C₄×C₁₉	—	2	1	no	—
220	C₂²×C₄×C₁₉	—	2	1	no	—
221	C₂²×C₄×C₁₉	—	2	1	no	—
222	C₂²×C₄×C₁₉	—	2	1	no	—
223	C₂²×C₄×C₁₉	—	2	1	no	—
224	C₂²×C₄×C₁₉	—	2	1	no	—
225	C₂²×C₄×C₁₉	—	2	1	no	—
226	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₁₉	—	2	1	no	—
237	C₄⋊C₄×C₁₉	—	2	1	no	—
238	C₄⋊C₄×C₁₉	—	2	1	no	—
239	C₄⋊C₄×C₁₉	—	2	1	no	—
240	C₄⋊C₄×C₁₉	—	2	1	no	—
241	C₄⋊C₄×C₁₉	—	2	1	no	—
242	C₄⋊C₄×C₁₉	—	2	1	no	—
243	C₄⋊C₄×C₁₉	—	2	1	no	—
244	C₄⋊C₄×C₁₉	—	2	1	no	—
245	C₄⋊C₄×C₁₉	—	2	1	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	—	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	—	4	2	no	—
270	C₄⋊C₄×C₁₉	—	4	2	no	—
271	C₄⋊C₄×C₁₉	—	4	1	no	—
272	C₄⋊C₄×C₁₉	—	4	1	no	—
273	C₄⋊C₄×C₁₉	—	4	1	no	—
274	C₄⋊C₄×C₁₉	—	4	1	no	—
275	C₄⋊C₄×C₁₉	—	8	1	no	—
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
302	C₂²⋊C₄×C₁₉	—	8	1	no	—
303	C₄²×C₁₉	—	2	1	no	—
304	C₄²×C₁₉	—	2	1	no	—
305	C₄²×C₁₉	—	2	1	no	—
306	C₄²×C₁₉	—	2	1	no	—
307	C₄²×C₁₉	—	2	1	no	—
308	C₄²×C₁₉	—	2	1	no	—
309	C₄²×C₁₉	—	2	1	no	—
310	C₄²×C₁₉	—	8	1	no	—
311	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
315	#18445	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂³×C₁₉	—	2	1	no	—
317	C₂³×C₁₉	—	2	1	no	—
318	C₂³×C₁₉	—	2	1	no	—
319	C₂³×C₁₉	—	2	1	no	—
320	C₂³×C₁₉	—	4	1	no	—
321	C₂³×C₁₉	—	4	1	no	—
322	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₁₉	—	4	1	no	—
324	Q₈×C₁₉	—	4	1	no	—
325	Q₈×C₁₉	—	4	1	no	—
326	Q₈×C₁₉	—	8	1	no	—
327	Q₈×C₁₉	—	8	1	no	—
328	Q₈×C₁₉	—	8	1	no	—
329	D₄×C₁₉	—	4	1	no	—
330	D₄×C₁₉	—	4	1	no	—
331	D₄×C₁₉	—	4	1	no	—
332	D₄×C₁₉	—	8	1	no	—
333	D₄×C₁₉	—	8	1	no	—
334	C₂×C₄×C₁₉	—	2	1	no	—
335	C₂×C₄×C₁₉	—	2	1	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	1	no	—
338	C₂×C₄×C₁₉	—	2	1	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	1	no	—
341	C₂×C₄×C₁₉	—	2	1	no	—
342	C₂×C₄×C₁₉	—	2	1	no	—
343	C₂×C₄×C₁₉	—	2	1	no	—
344	C₂×C₄×C₁₉	—	2	1	no	—
345	C₂×C₄×C₁₉	—	2	1	no	—
346	C₂×C₄×C₁₉	—	2	1	no	—
347	C₂×C₄×C₁₉	—	2	1	no	—
348	C₂×C₄×C₁₉	—	2	1	no	—
349	C₂×C₄×C₁₉	—	4	1	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	—	4	1	no	—
359	C₂×C₄×C₁₉	—	4	1	no	—
360	C₂×C₄×C₁₉	—	4	1	no	—
361	C₂×C₄×C₁₉	—	4	1	no	—
362	C₂×C₄×C₁₉	—	4	1	no	—
363	C₂×C₄×C₁₉	—	4	1	no	—
364	C₂×C₄×C₁₉	—	8	1	no	—
365	C₂×C₄×C₁₉	—	8	1	no	—
366	C₂×C₄×C₁₉	—	8	1	no	—
367	C₂×C₄×C₁₉	—	8	1	no	—
368	C₂×C₄×C₁₉	—	8	1	no	—
369	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
370	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
371	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
372	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
373	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
375	C₈×C₁₉	—	4	1	no	—
376	C₈×C₁₉	—	4	1	no	—
377	C₈×C₁₉	—	4	1	no	—
378	C₈×C₁₉	—	4	1	no	—
379	#3564	C₂×C₁₉	1	1	yes	characteristic
380	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#3232	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#2664	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#1618	C₂×C₁₉	1	1	yes	characteristic
384	#1617	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#1615	C₂×C₁₉	1	1	yes	characteristic, complemented
386	#1614	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#1612	C₂×C₁₉	1	1	yes	characteristic
388	#1611	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#1609	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#1608	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#1509	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#1473	C₂×C₁₉	1	1	yes	characteristic, complemented
394	C₂²×C₁₉	—	2	1	no	—
395	C₂²×C₁₉	—	2	1	no	—
396	C₂²×C₁₉	—	4	1	no	—
397	C₂²×C₁₉	—	4	1	no	—
398	C₂²×C₁₉	—	4	1	no	—
399	C₂²×C₁₉	—	4	1	no	—
400	C₂²×C₁₉	—	4	1	no	—
401	C₂²×C₁₉	—	4	1	no	—
402	C₂²×C₁₉	—	8	1	no	—
403	C₂²×C₁₉	—	8	1	no	—
404	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
405	C₂²×C₁₉	#577	1	1	yes	characteristic
406	C₂²×C₁₉	#578	1	1	yes	characteristic
407	C₄×C₁₉	—	2	1	no	—
408	C₄×C₁₉	—	2	1	no	—
409	C₄×C₁₉	—	2	1	no	—
410	C₄×C₁₉	—	2	1	no	—
411	C₄×C₁₉	—	2	1	no	—
412	C₄×C₁₉	—	2	1	no	—
413	C₄×C₁₉	—	4	2	no	—
414	C₄×C₁₉	—	4	1	no	—
415	C₄×C₁₉	—	4	1	no	—
416	C₄×C₁₉	—	4	1	no	—
417	C₄×C₁₉	—	4	1	no	—
418	C₄×C₁₉	—	4	1	no	—
419	C₄×C₁₉	—	4	1	no	—
420	C₄×C₁₉	—	4	1	no	—
421	C₄×C₁₉	—	4	1	no	—
422	C₄×C₁₉	—	4	1	no	—
423	C₄×C₁₉	—	4	1	no	—
424	C₄×C₁₉	—	8	1	no	—
425	C₄×C₁₉	—	8	1	no	—
426	C₄×C₁₉	—	8	1	no	—
427	#563	—	2	1	no	—
428	#563	—	2	1	no	—
429	#556	—	2	1	no	—
430	#554	—	2	1	no	—
431	#552	—	2	1	no	—
432	#552	—	2	1	no	—
433	#551	—	2	1	no	—
434	#551	—	2	1	no	—
435	#544	C₂²×C₁₉	1	1	yes	characteristic
436	#543	C₂²×C₁₉	1	1	yes	characteristic
437	#542	—	2	1	no	—
438	#541	—	2	1	no	—
439	#541	—	2	1	no	—
440	#539	—	2	1	no	—
441	#539	C₂²×C₁₉	1	1	yes	characteristic
442	#538	C₂²×C₁₉	1	1	yes	characteristic
443	#533	C₂²×C₁₉	1	1	yes	characteristic
444	#529	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#126	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
447	#501	—	2	1	no	—
448	#499	—	2	1	no	—
449	#491	—	2	1	no	—
450	#488	—	2	1	no	—
451	#484	C₂²×C₁₉	1	1	yes	characteristic
452	#484	C₂²×C₁₉	1	1	yes	characteristic
453	#484	C₂²×C₁₉	1	1	yes	characteristic
454	#483	C₂²×C₁₉	1	1	yes	characteristic
455	#483	C₂²×C₁₉	1	1	yes	characteristic
456	#483	C₂²×C₁₉	1	1	yes	characteristic
457	#481	C₂²×C₁₉	1	1	yes	characteristic
458	#480	C₂²×C₁₉	1	1	yes	characteristic
459	#479	—	2	1	no	—
460	#479	—	2	1	no	—
461	#479	—	2	1	no	—
462	#478	—	2	1	no	—
463	#432	C₂²×C₁₉	1	1	yes	characteristic
464	#431	C₂²×C₁₉	1	1	yes	characteristic
465	#400	C₂²×C₁₉	1	1	yes	characteristic
466	#399	C₂²×C₁₉	1	1	yes	characteristic
467	#398	—	2	1	no	—
468	#398	C₂²×C₁₉	1	1	yes	characteristic
469	#397	C₂²×C₁₉	1	1	yes	characteristic
470	#396	—	2	1	no	—
471	#389	—	2	1	no	—
472	#388	—	2	1	no	—
473	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
474	#328	C₂²×C₁₉	1	1	yes	characteristic
475	#328	C₂²×C₁₉	1	1	yes	characteristic
476	#328	C₂²×C₁₉	1	1	yes	characteristic
477	#328	C₂²×C₁₉	1	1	yes	characteristic
478	#328	C₂²×C₁₉	1	1	yes	characteristic
479	#328	C₂²×C₁₉	1	1	yes	characteristic
480	#327	C₂²×C₁₉	1	1	yes	characteristic
481	#327	C₂²×C₁₉	1	1	yes	characteristic
482	#324	C₂²×C₁₉	1	1	yes	characteristic
483	#324	C₂²×C₁₉	1	1	yes	characteristic
484	#323	C₂²×C₁₉	1	1	yes	characteristic
485	#323	C₂²×C₁₉	1	1	yes	characteristic
486	C₂×C₁₉	—	2	1	no	—
487	C₂×C₁₉	—	2	1	no	—
488	C₂×C₁₉	—	8	1	no	—
489	C₂×C₁₉	—	8	1	no	—
490	C₂×C₁₉	#3013	1	1	yes	characteristic
491	C₂×C₁₉	#3018	1	1	yes	characteristic
492	C₂×C₁₉	#3028	1	1	yes	characteristic
493	C₄⋊Q₈	—	2	1	no	—
494	C₄⋊Q₈	—	2	1	no	—
495	C₄⋊Q₈	—	2	1	no	—
496	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
497	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
498	#126	—	2	1	no	—
499	#126	—	2	1	no	—
500	#126	—	2	1	no	—
501	#126	—	2	1	no	—
502	#126	—	2	1	no	—
503	#126	—	2	1	no	—
504	#126	—	2	1	no	—
505	#126	—	2	1	no	—
506	#126	—	2	1	no	—
507	#126	—	2	1	no	—
508	#126	—	2	1	no	—
509	#126	—	2	1	no	—
510	#126	—	2	1	no	—
511	#125	—	2	1	no	—
512	#125	—	2	1	no	—
513	#125	—	2	1	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#125	—	2	1	no	—
518	#125	—	2	1	no	—
519	#125	—	2	1	no	—
520	#125	—	2	1	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	—	2	1	no	—
524	#125	D₄×C₁₉	1	1	yes	characteristic
525	#124	—	2	1	no	—
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	D₄×C₁₉	1	1	yes	characteristic
529	#123	—	2	1	no	—
530	#123	—	2	1	no	—
531	#123	—	2	1	no	—
532	#123	—	2	1	no	—
533	#123	—	2	1	no	—
534	#123	—	2	1	no	—
535	#123	—	2	1	no	—
536	#123	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
552	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
553	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
554	#121	—	2	1	no	—
555	#121	C₂³×C₁₉	1	1	yes	characteristic
556	#120	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
561	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
562	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
569	#117	—	2	1	no	—
570	#117	—	2	1	no	—
571	#117	—	2	1	no	—
572	#117	—	2	1	no	—
573	#117	—	2	1	no	—
574	#117	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
594	#107	—	2	1	no	—
595	#107	—	2	1	no	—
596	#107	—	2	1	no	—
597	#107	—	2	1	no	—
598	#106	—	2	1	no	—
599	#106	—	2	1	no	—
600	#106	—	2	1	no	—
601	#106	—	2	1	no	—
602	C₄⋊C₈	—	2	1	no	—
603	C₄⋊C₈	—	2	1	no	—
604	#103	—	2	1	no	—
605	#103	—	2	1	no	—
606	#103	—	2	1	no	—
607	#103	—	2	1	no	—
608	#103	—	2	1	no	—
609	#103	—	2	1	no	—
610	#102	—	2	1	no	—
611	#102	—	2	1	no	—
612	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
613	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
614	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
615	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
616	#97	—	2	1	no	—
617	C₄×C₈	—	2	1	no	—
618	#95	—	2	1	no	—
619	#95	—	2	1	no	—
620	#95	—	2	1	no	—
621	#95	—	2	1	no	—
622	#95	C₂³×C₁₉	1	1	yes	characteristic
623	#95	C₂³×C₁₉	1	1	yes	characteristic
624	C₁₉	#18445	1	1	yes	characteristic, direct product factor, Sylow
625	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	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	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	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	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	1	no	—
694	C₄⋊C₄	—	8	1	no	—
695	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
696	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
698	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
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	—	4	2	no	—
721	C₂²⋊C₄	—	8	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	—	2	1	no	—
729	C₄²	—	8	1	no	—
730	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
741	Q₈	—	4	1	no	—
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	8	1	no	—
745	Q₈	—	8	1	no	—
746	Q₈	—	8	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	8	1	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	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	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	8	1	no	—
783	C₂×C₄	—	8	1	no	—
784	C₂×C₄	—	8	1	no	—
785	C₂×C₄	—	8	1	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
788	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
789	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
790	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₈	—	4	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
808	C₂²	C₁₉×#577	1	1	yes	characteristic
809	C₂²	C₁₉×#578	1	1	yes	characteristic
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	8	1	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₂	—	2	1	no	—
831	C₂	—	2	1	no	—
832	C₂	—	8	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₁₉×#3013	1	1	yes	characteristic
835	C₂	C₁₉×#3018	1	1	yes	characteristic
836	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#538	C₂²
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
2. C₁₉×#3236	C₂	semidirect
3. C₁₉×#3232	C₂	semidirect
4. C₁₉×#2664	C₂	semidirect
6. C₁₉×#1617	C₂	semidirect
7. C₁₉×#1615	C₂	semidirect
8. C₁₉×#1614	C₂	semidirect
10. C₁₉×#1611	C₂	semidirect
11. C₁₉×#1609	C₂	semidirect
12. C₁₉×#1608	C₂	semidirect
13. C₁₉×#1509	C₂	semidirect
14. C₁₉×#1503	C₂	semidirect
15. C₁₉×#1473	C₂	semidirect
315. #18445	C₁₉	direct (N × H)
380. #3236	C₂×C₁₉	semidirect
381. #3232	C₂×C₁₉	semidirect
382. #2664	C₂×C₁₉	semidirect
384. #1617	C₂×C₁₉	semidirect
385. #1615	C₂×C₁₉	semidirect
386. #1614	C₂×C₁₉	semidirect
388. #1611	C₂×C₁₉	semidirect
389. #1609	C₂×C₁₉	semidirect
390. #1608	C₂×C₁₉	semidirect
391. #1509	C₂×C₁₉	semidirect
392. #1503	C₂×C₁₉	semidirect
393. #1473	C₂×C₁₉	semidirect
624. C₁₉	#18445	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×#3236	2
C₁₉×#3232	2
C₁₉×#2664	2
C₁₉×#1618	2
C₁₉×#1617	2
C₁₉×#1615	2
C₁₉×#1614	2
C₁₉×#1612	2
C₁₉×#1611	2
C₁₉×#1609	2
C₁₉×#1608	2
C₁₉×#1509	2
C₁₉×#1503	2
C₁₉×#1473	2
#18445	19

Subgroups — C19×#18445 #18024404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18445 #18024404