Subgroups — C₁₉×#19068 #18025027

Order 4864.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3545	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3219	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3213	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×#1662	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1661	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×#1656	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1656	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1655	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	C₂²	1	1	yes	characteristic
17	C₁₉×#562	C₂²	1	1	yes	characteristic
18	C₁₉×#562	C₂²	1	1	yes	characteristic
19	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
20	C₁₉×#555	—	2	1	no	—
21	C₁₉×#551	—	2	1	no	—
22	C₁₉×#551	—	2	1	no	—
23	C₁₉×#551	—	2	1	no	—
24	C₁₉×#546	—	2	1	no	—
25	C₁₉×#546	—	2	1	no	—
26	C₁₉×#542	—	2	1	no	—
27	C₁₉×#542	—	2	1	no	—
28	C₁₉×#538	—	2	1	no	—
29	C₁₉×#538	—	2	1	no	—
30	C₁₉×#536	—	2	1	no	—
31	C₁₉×#534	—	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	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
36	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#496	C₂²	1	1	yes	characteristic
39	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
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×#489	C₂²	1	1	yes	characteristic
46	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#469	—	2	1	no	—
49	C₁₉×#468	—	2	1	no	—
50	C₁₉×#464	—	2	1	no	—
51	C₁₉×#463	—	2	1	no	—
52	C₁₉×#463	—	2	1	no	—
53	C₁₉×#463	—	2	1	no	—
54	C₁₉×#452	—	2	1	no	—
55	C₁₉×#449	—	2	1	no	—
56	C₁₉×#448	—	2	1	no	—
57	C₁₉×#447	—	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	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
62	C₄×M₁₆×C₁₉	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×#329	C₂²	1	1	yes	characteristic
68	C₁₉×#329	C₂²	1	1	yes	characteristic
69	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#329	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	—	2	1	no	—
77	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
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×SD₁₆×C₁₉	—	2	1	no	—
86	C₂×D₈×C₁₉	—	2	1	no	—
87	C₂×D₈×C₁₉	—	2	1	no	—
88	C₂×D₈×C₁₉	—	2	1	no	—
89	C₂×D₈×C₁₉	—	2	1	no	—
90	C₂×M₁₆×C₁₉	—	2	1	no	—
91	C₁₉×C₄⋊Q₈	—	2	1	no	—
92	C₁₉×C₄⋊Q₈	—	2	1	no	—
93	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₉×#127	C₂³	1	1	yes	characteristic
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×#125	C₂³	1	1	yes	characteristic
102	C₁₉×#125	C₂³	1	1	yes	characteristic
103	C₁₉×#124	—	2	1	no	—
104	C₁₉×#124	—	2	1	no	—
105	C₁₉×#124	—	2	1	no	—
106	C₁₉×#124	—	2	1	no	—
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	D₄	1	1	yes	characteristic
113	C₁₉×#124	D₄	1	1	yes	characteristic
114	C₁₉×#124	C₂³	1	1	yes	characteristic
115	C₁₉×#124	C₂³	1	1	yes	characteristic
116	C₁₉×#124	C₂³	1	1	yes	characteristic
117	C₁₉×#124	C₂³	1	1	yes	characteristic
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×#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	D₄	1	1	yes	characteristic
139	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
140	C₁₉×#121	—	2	1	no	—
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	—	2	1	no	—
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	—	2	1	no	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	D₄	1	1	yes	characteristic
151	C₁₉×#121	D₄	1	1	yes	characteristic
152	C₁₉×#120	—	2	1	no	—
153	C₁₉×#120	—	2	1	no	—
154	C₁₉×#120	—	2	1	no	—
155	C₁₉×#120	—	2	1	no	—
156	C₁₉×#120	—	2	1	no	—
157	C₁₉×#120	—	2	1	no	—
158	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
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	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×C₄²×C₁₉	C₂³	1	1	yes	characteristic
181	C₁₉×#107	—	2	1	no	—
182	C₁₉×#106	—	2	1	no	—
183	C₁₉×C₄⋊C₈	—	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×#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×#102	—	2	1	no	—
196	C₁₉×#102	—	2	1	no	—
197	C₁₉×C₂²⋊C₈	—	2	1	no	—
198	C₁₉×C₂²⋊C₈	—	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	C₂⁴×C₁₉	—	2	1	no	—
208	#41×C₁₉	—	8	2	no	—
209	#41×C₁₉	—	8	1	no	—
210	#41×C₁₉	—	8	1	no	—
211	C₂×Q₈×C₁₉	—	2	1	no	—
212	C₂×Q₈×C₁₉	—	2	1	no	—
213	C₂×Q₈×C₁₉	—	2	1	no	—
214	C₂×Q₈×C₁₉	—	8	1	no	—
215	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
226	C₂×D₄×C₁₉	—	2	1	no	—
227	C₂×D₄×C₁₉	—	2	1	no	—
228	C₂×D₄×C₁₉	—	2	1	no	—
229	C₂×D₄×C₁₉	—	2	1	no	—
230	C₂×D₄×C₁₉	—	2	1	no	—
231	C₂×D₄×C₁₉	—	2	1	no	—
232	C₂×D₄×C₁₉	—	4	1	no	—
233	C₂×D₄×C₁₉	—	8	1	no	—
234	C₂×D₄×C₁₉	—	8	2	no	—
235	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
237	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
238	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₉	—	2	1	no	—
240	C₂²×C₄×C₁₉	—	2	1	no	—
241	C₂²×C₄×C₁₉	—	2	1	no	—
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	4	1	no	—
248	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	Q₁₆×C₁₉	—	8	1	no	—
252	SD₁₆×C₁₉	—	4	2	no	—
253	SD₁₆×C₁₉	—	8	1	no	—
254	SD₁₆×C₁₉	—	8	1	no	—
255	SD₁₆×C₁₉	—	8	1	no	—
256	SD₁₆×C₁₉	—	8	1	no	—
257	D₈×C₁₉	—	4	2	no	—
258	D₈×C₁₉	—	8	1	no	—
259	D₈×C₁₉	—	8	1	no	—
260	D₈×C₁₉	—	8	1	no	—
261	M₁₆×C₁₉	—	4	2	no	—
262	C₂×C₈×C₁₉	—	2	1	no	—
263	C₂×C₈×C₁₉	—	2	1	no	—
264	C₂×C₈×C₁₉	—	2	1	no	—
265	C₂×C₈×C₁₉	—	2	1	no	—
266	C₂×C₈×C₁₉	—	2	1	no	—
267	C₂×C₈×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	—	2	1	no	—
283	C₄⋊C₄×C₁₉	—	2	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	—	2	1	no	—
310	C₂²⋊C₄×C₁₉	—	2	1	no	—
311	C₂²⋊C₄×C₁₉	—	2	1	no	—
312	C₂²⋊C₄×C₁₉	—	2	1	no	—
313	C₂²⋊C₄×C₁₉	—	2	1	no	—
314	C₂²⋊C₄×C₁₉	—	2	1	no	—
315	C₂²⋊C₄×C₁₉	—	2	1	no	—
316	C₂²⋊C₄×C₁₉	—	4	1	no	—
317	C₂²⋊C₄×C₁₉	—	4	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	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	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
326	#19068	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	2	no	—
332	C₂³×C₁₉	—	4	1	no	—
333	C₂³×C₁₉	—	8	1	no	—
334	C₂³×C₁₉	—	8	1	no	—
335	C₂³×C₁₉	—	8	1	no	—
336	C₂³×C₁₉	—	8	1	no	—
337	C₂³×C₁₉	—	8	1	no	—
338	C₂³×C₁₉	#120	1	1	yes	characteristic
339	Q₈×C₁₉	—	4	1	no	—
340	Q₈×C₁₉	—	4	1	no	—
341	Q₈×C₁₉	—	4	1	no	—
342	Q₈×C₁₉	—	4	1	no	—
343	Q₈×C₁₉	—	4	1	no	—
344	Q₈×C₁₉	—	4	1	no	—
345	Q₈×C₁₉	—	8	1	no	—
346	Q₈×C₁₉	—	8	1	no	—
347	D₄×C₁₉	—	4	1	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	—	4	1	no	—
354	D₄×C₁₉	—	4	1	no	—
355	D₄×C₁₉	—	4	1	no	—
356	D₄×C₁₉	—	4	1	no	—
357	D₄×C₁₉	—	4	2	no	—
358	D₄×C₁₉	—	4	2	no	—
359	D₄×C₁₉	—	8	1	no	—
360	D₄×C₁₉	—	8	1	no	—
361	D₄×C₁₉	—	8	1	no	—
362	D₄×C₁₉	—	8	1	no	—
363	D₄×C₁₉	—	8	1	no	—
364	D₄×C₁₉	—	8	1	no	—
365	D₄×C₁₉	—	8	1	no	—
366	D₄×C₁₉	—	8	1	no	—
367	D₄×C₁₉	—	8	2	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	—	4	1	no	—
377	C₂×C₄×C₁₉	—	4	1	no	—
378	C₂×C₄×C₁₉	—	4	1	no	—
379	C₂×C₄×C₁₉	—	4	2	no	—
380	C₂×C₄×C₁₉	—	4	1	no	—
381	C₂×C₄×C₁₉	—	8	1	no	—
382	C₂×C₄×C₁₉	—	8	1	no	—
383	C₂×C₄×C₁₉	—	8	2	no	—
384	C₂×C₄×C₁₉	—	8	1	no	—
385	C₂×C₄×C₁₉	—	8	1	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	#120	1	1	yes	characteristic
390	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
391	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
392	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
395	C₈×C₁₉	—	2	2	no	—
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	C₈×C₁₉	—	4	1	no	—
401	#3545	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#3219	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#3213	C₂×C₁₉	1	1	yes	characteristic, complemented
404	#3171	C₂×C₁₉	1	1	yes	characteristic, complemented
405	#1664	C₂×C₁₉	1	1	yes	characteristic, complemented
406	#1662	C₂×C₁₉	1	1	yes	characteristic, complemented
407	#1661	C₂×C₁₉	1	1	yes	characteristic, complemented
408	#1659	C₂×C₁₉	1	1	yes	characteristic, complemented
409	#1657	C₂×C₁₉	1	1	yes	characteristic, complemented
410	#1656	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#1656	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#1655	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
415	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
416	C₂²×C₁₉	—	2	1	no	—
417	C₂²×C₁₉	—	2	1	no	—
418	C₂²×C₁₉	—	2	1	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	1	no	—
426	C₂²×C₁₉	—	4	1	no	—
427	C₂²×C₁₉	—	4	1	no	—
428	C₂²×C₁₉	—	4	1	no	—
429	C₂²×C₁₉	—	4	1	no	—
430	C₂²×C₁₉	—	4	1	no	—
431	C₂²×C₁₉	—	8	1	no	—
432	C₂²×C₁₉	—	8	1	no	—
433	C₂²×C₁₉	—	8	1	no	—
434	C₂²×C₁₉	—	16	2	no	—
435	C₂²×C₁₉	—	16	2	no	—
436	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
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	—	2	1	no	—
442	C₄×C₁₉	—	2	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	#563	C₂²×C₁₉	1	1	yes	characteristic
453	#562	C₂²×C₁₉	1	1	yes	characteristic
454	#562	C₂²×C₁₉	1	1	yes	characteristic
455	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
456	#555	—	2	1	no	—
457	#551	—	2	1	no	—
458	#551	—	2	1	no	—
459	#551	—	2	1	no	—
460	#546	—	2	1	no	—
461	#546	—	2	1	no	—
462	#542	—	2	1	no	—
463	#542	—	2	1	no	—
464	#538	—	2	1	no	—
465	#538	—	2	1	no	—
466	#536	—	2	1	no	—
467	#534	—	2	1	no	—
468	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
469	#529	C₂²×C₁₉	1	1	yes	characteristic
470	#529	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
472	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
473	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
474	#496	C₂²×C₁₉	1	1	yes	characteristic
475	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
476	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
477	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
478	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
479	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
480	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
481	#489	C₂²×C₁₉	1	1	yes	characteristic
482	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
483	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
484	#469	—	2	1	no	—
485	#468	—	2	1	no	—
486	#464	—	2	1	no	—
487	#463	—	2	1	no	—
488	#463	—	2	1	no	—
489	#463	—	2	1	no	—
490	#452	—	2	1	no	—
491	#449	—	2	1	no	—
492	#448	—	2	1	no	—
493	#447	—	2	1	no	—
494	C₄×SD₁₆	—	2	1	no	—
495	C₄×D₈	—	2	1	no	—
496	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
497	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
498	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
499	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
500	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
501	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
502	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
503	#329	C₂²×C₁₉	1	1	yes	characteristic
504	#329	C₂²×C₁₉	1	1	yes	characteristic
505	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
506	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
507	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
508	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
509	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
510	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
511	C₂×C₁₉	—	4	1	no	—
512	C₂×C₁₉	—	8	1	no	—
513	C₂×C₁₉	—	8	1	no	—
514	C₂×C₁₉	—	8	1	no	—
515	C₂×C₁₉	—	8	1	no	—
516	C₂×C₁₉	—	16	1	no	—
517	C₂×C₁₉	#3018	1	1	yes	characteristic
518	C₂×C₁₉	#3019	1	1	yes	characteristic
519	C₂×C₁₉	#3021	1	1	yes	characteristic
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	2	1	no	—
522	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
525	C₂×Q₁₆	—	2	1	no	—
526	C₂×SD₁₆	—	2	1	no	—
527	C₂×SD₁₆	—	2	1	no	—
528	C₂×SD₁₆	—	2	1	no	—
529	C₂×SD₁₆	—	2	1	no	—
530	C₂×SD₁₆	—	2	1	no	—
531	C₂×D₈	—	2	1	no	—
532	C₂×D₈	—	2	1	no	—
533	C₂×D₈	—	2	1	no	—
534	C₂×D₈	—	2	1	no	—
535	C₂×M₁₆	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
539	#127	C₂³×C₁₉	1	1	yes	characteristic
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	C₂³×C₁₉	1	1	yes	characteristic
547	#125	C₂³×C₁₉	1	1	yes	characteristic
548	#124	—	2	1	no	—
549	#124	—	2	1	no	—
550	#124	—	2	1	no	—
551	#124	—	2	1	no	—
552	#124	—	2	1	no	—
553	#124	—	2	1	no	—
554	#124	—	2	1	no	—
555	#124	—	2	1	no	—
556	#124	—	2	1	no	—
557	#124	D₄×C₁₉	1	1	yes	characteristic
558	#124	D₄×C₁₉	1	1	yes	characteristic
559	#124	C₂³×C₁₉	1	1	yes	characteristic
560	#124	C₂³×C₁₉	1	1	yes	characteristic
561	#124	C₂³×C₁₉	1	1	yes	characteristic
562	#124	C₂³×C₁₉	1	1	yes	characteristic
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	#123	—	2	1	no	—
569	#123	—	2	1	no	—
570	#123	—	2	1	no	—
571	#123	—	2	1	no	—
572	#123	—	2	1	no	—
573	#123	—	2	1	no	—
574	#123	—	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	—	2	1	no	—
583	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
584	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	D₄×C₁₉	1	1	yes	characteristic
596	#121	D₄×C₁₉	1	1	yes	characteristic
597	#120	—	2	1	no	—
598	#120	—	2	1	no	—
599	#120	—	2	1	no	—
600	#120	—	2	1	no	—
601	#120	—	2	1	no	—
602	#120	—	2	1	no	—
603	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
604	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
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
614	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
626	#107	—	2	1	no	—
627	#106	—	2	1	no	—
628	C₄⋊C₈	—	2	1	no	—
629	C₄⋊C₈	—	2	1	no	—
630	#103	—	2	1	no	—
631	#103	—	2	1	no	—
632	#103	—	2	1	no	—
633	#103	—	2	1	no	—
634	#103	—	2	1	no	—
635	#102	—	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	#102	—	2	1	no	—
642	C₂²⋊C₈	—	2	1	no	—
643	C₂²⋊C₈	—	2	1	no	—
644	#97	C₂³×C₁₉	1	1	yes	characteristic
645	#97	C₂³×C₁₉	1	1	yes	characteristic
646	#97	C₂³×C₁₉	1	1	yes	characteristic
647	#97	C₂³×C₁₉	1	1	yes	characteristic
648	#97	C₂³×C₁₉	1	1	yes	characteristic
649	#97	C₂³×C₁₉	1	1	yes	characteristic
650	C₄×C₈	—	2	1	no	—
651	C₁₉	#19068	1	1	yes	characteristic, direct product factor, Sylow
652	C₂⁴	—	2	1	no	—
653	C₂⁴	—	2	1	no	—
654	#41	—	8	2	no	—
655	#41	—	8	1	no	—
656	#41	—	8	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	8	1	no	—
661	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
662	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
663	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
664	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
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	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	4	1	no	—
679	C₂×D₄	—	8	1	no	—
680	C₂×D₄	—	8	2	no	—
681	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
682	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
683	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
684	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
697	Q₁₆	—	8	1	no	—
698	SD₁₆	—	4	2	no	—
699	SD₁₆	—	8	1	no	—
700	SD₁₆	—	8	1	no	—
701	SD₁₆	—	8	1	no	—
702	SD₁₆	—	8	1	no	—
703	D₈	—	4	2	no	—
704	D₈	—	8	1	no	—
705	D₈	—	8	1	no	—
706	D₈	—	8	1	no	—
707	M₁₆	—	4	2	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	—	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	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	—	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	1	no	—
763	C₂²⋊C₄	—	4	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	C₂⁴×C₁₉	1	1	yes	characteristic
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	1	no	—
780	C₂³	—	8	1	no	—
781	C₂³	—	8	1	no	—
782	C₂³	—	8	1	no	—
783	C₂³	C₁₉×#120	1	1	yes	characteristic
784	Q₈	—	4	1	no	—
785	Q₈	—	4	1	no	—
786	Q₈	—	4	1	no	—
787	Q₈	—	4	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	8	1	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	4	1	no	—
793	D₄	—	4	1	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	—	4	1	no	—
800	D₄	—	4	1	no	—
801	D₄	—	4	1	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	2	no	—
804	D₄	—	8	1	no	—
805	D₄	—	8	1	no	—
806	D₄	—	8	1	no	—
807	D₄	—	8	1	no	—
808	D₄	—	8	1	no	—
809	D₄	—	8	1	no	—
810	D₄	—	8	1	no	—
811	D₄	—	8	1	no	—
812	D₄	—	8	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	8	1	no	—
827	C₂×C₄	—	8	1	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	1	no	—
831	C₂×C₄	—	8	1	no	—
832	C₂×C₄	—	8	1	no	—
833	C₂×C₄	—	8	1	no	—
834	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
835	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
836	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
840	C₈	—	2	2	no	—
841	C₈	—	4	1	no	—
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	—	2	1	no	—
849	C₂²	—	4	1	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	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	16	2	no	—
865	C₂²	—	16	2	no	—
866	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
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	—	2	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	—	8	1	no	—
882	C₂	—	4	1	no	—
883	C₂	—	8	1	no	—
884	C₂	—	8	1	no	—
885	C₂	—	8	1	no	—
886	C₂	—	8	1	no	—
887	C₂	—	16	1	no	—
888	C₂	C₁₉×#3018	1	1	yes	characteristic
889	C₂	C₁₉×#3019	1	1	yes	characteristic
890	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×#3545	C₂	semidirect
2. C₁₉×#3219	C₂	semidirect
3. C₁₉×#3213	C₂	semidirect
4. C₁₉×#3171	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1662	C₂	semidirect
7. C₁₉×#1661	C₂	semidirect
8. C₁₉×#1659	C₂	semidirect
9. C₁₉×#1657	C₂	semidirect
10. C₁₉×#1656	C₂	semidirect
11. C₁₉×#1656	C₂	semidirect
12. C₁₉×#1655	C₂	semidirect
13. C₁₉×#1535	C₂	semidirect
14. C₁₉×#1529	C₂	semidirect
15. C₁₉×#1527	C₂	semidirect
32. C₁₉×#532	C₂²	semidirect
36. C₁₉×#501	C₂²	semidirect
37. C₁₉×#497	C₂²	semidirect
39. C₁₉×#496	C₂²	semidirect
40. C₁₉×#496	C₂²	semidirect
41. C₁₉×#496	C₂²	semidirect
42. C₁₉×#491	C₂²	semidirect
43. C₁₉×#490	C₂²	semidirect
44. C₁₉×#490	C₂²	semidirect
46. C₁₉×#489	C₂²	semidirect
47. C₁₉×#489	C₂²	semidirect
60. C₁₉×#432	C₂²	semidirect
61. C₁₉×#432	C₂²	semidirect
62. C₄×M₁₆×C₁₉	C₂²	semidirect
63. C₁₉×#330	C₂²	semidirect
64. C₁₉×#330	C₂²	semidirect
65. C₁₉×#330	C₂²	semidirect
66. C₁₉×#330	C₂²	semidirect
69. C₁₉×#329	C₂²	semidirect
70. C₁₉×#329	C₂²	semidirect
71. C₁₉×#329	C₂²	semidirect
72. C₁₉×#329	C₂²	semidirect
73. C₁₉×#329	C₂²	semidirect
74. C₁₉×#329	C₂²	semidirect
326. #19068	C₁₉	direct (N × H)
401. #3545	C₂×C₁₉	semidirect
402. #3219	C₂×C₁₉	semidirect
403. #3213	C₂×C₁₉	semidirect
404. #3171	C₂×C₁₉	semidirect
405. #1664	C₂×C₁₉	semidirect
406. #1662	C₂×C₁₉	semidirect
407. #1661	C₂×C₁₉	semidirect
408. #1659	C₂×C₁₉	semidirect
409. #1657	C₂×C₁₉	semidirect
410. #1656	C₂×C₁₉	semidirect
411. #1656	C₂×C₁₉	semidirect
412. #1655	C₂×C₁₉	semidirect
413. #1535	C₂×C₁₉	semidirect
414. #1529	C₂×C₁₉	semidirect
415. #1527	C₂×C₁₉	semidirect
468. #532	C₂²×C₁₉	semidirect
472. #501	C₂²×C₁₉	semidirect
473. #497	C₂²×C₁₉	semidirect
475. #496	C₂²×C₁₉	semidirect
476. #496	C₂²×C₁₉	semidirect
477. #496	C₂²×C₁₉	semidirect
478. #491	C₂²×C₁₉	semidirect
479. #490	C₂²×C₁₉	semidirect
480. #490	C₂²×C₁₉	semidirect
482. #489	C₂²×C₁₉	semidirect
483. #489	C₂²×C₁₉	semidirect
496. #432	C₂²×C₁₉	semidirect
497. #432	C₂²×C₁₉	semidirect
498. C₄×M₁₆	C₂²×C₁₉	semidirect
499. #330	C₂²×C₁₉	semidirect
500. #330	C₂²×C₁₉	semidirect
501. #330	C₂²×C₁₉	semidirect
502. #330	C₂²×C₁₉	semidirect
505. #329	C₂²×C₁₉	semidirect
506. #329	C₂²×C₁₉	semidirect
507. #329	C₂²×C₁₉	semidirect
508. #329	C₂²×C₁₉	semidirect
509. #329	C₂²×C₁₉	semidirect
510. #329	C₂²×C₁₉	semidirect
651. C₁₉	#19068	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×#3545	2
C₁₉×#3219	2
C₁₉×#3213	2
C₁₉×#3171	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1659	2
C₁₉×#1657	2
C₁₉×#1656	2
C₁₉×#1655	2
C₁₉×#1535	2
C₁₉×#1529	2
C₁₉×#1527	2
#19068	19

Subgroups — C19×#19068 #18025027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19068 #18025027