Subgroups — C₁₉×#19069 #18025028

Order 4864.

886 conjugacy classes of subgroups.

The subgroup lattice has 862 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
2	C₁₉×#3240	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3172	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×#1661	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1661	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1660	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1659	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×#533	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×#501	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#501	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#497	C₂²	1	1	yes	characteristic
40	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#489	C₂²	1	1	yes	characteristic
44	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#489	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#485	—	2	1	no	—
49	C₁₉×#482	—	2	1	no	—
50	C₁₉×#479	—	2	1	no	—
51	C₁₉×#478	—	2	1	no	—
52	C₁₉×#470	—	2	1	no	—
53	C₁₉×#468	—	2	1	no	—
54	C₁₉×#464	—	2	1	no	—
55	C₁₉×#464	—	2	1	no	—
56	C₁₉×#451	—	2	1	no	—
57	C₁₉×#450	—	2	1	no	—
58	C₄×Q₁₆×C₁₉	—	2	1	no	—
59	C₄×SD₁₆×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	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
79	C₂×Q₁₆×C₁₉	—	2	1	no	—
80	C₂×Q₁₆×C₁₉	—	2	1	no	—
81	C₂×Q₁₆×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×M₁₆×C₁₉	—	2	1	no	—
86	C₁₉×C₄⋊Q₈	—	2	1	no	—
87	C₁₉×C₄⋊Q₈	—	2	1	no	—
88	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₉×#126	—	2	1	no	—
91	C₁₉×#126	—	2	1	no	—
92	C₁₉×#126	—	2	1	no	—
93	C₁₉×#126	—	2	1	no	—
94	C₁₉×#126	—	2	1	no	—
95	C₁₉×#126	—	2	1	no	—
96	C₁₉×#125	—	2	1	no	—
97	C₁₉×#125	C₂³	1	1	yes	characteristic
98	C₁₉×#125	C₂³	1	1	yes	characteristic
99	C₁₉×#124	—	2	1	no	—
100	C₁₉×#124	—	2	1	no	—
101	C₁₉×#124	—	2	1	no	—
102	C₁₉×#124	—	2	1	no	—
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	D₄	1	1	yes	characteristic
108	C₁₉×#124	D₄	1	1	yes	characteristic
109	C₁₉×#124	C₂³	1	1	yes	characteristic
110	C₁₉×#124	C₂³	1	1	yes	characteristic
111	C₁₉×#124	C₂³	1	1	yes	characteristic
112	C₁₉×#124	C₂³	1	1	yes	characteristic
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×#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×C₂²⋊Q₈	—	2	1	no	—
126	C₁₉×C₂²⋊Q₈	—	2	1	no	—
127	C₁₉×C₂²⋊Q₈	—	2	1	no	—
128	C₁₉×C₂²⋊Q₈	—	2	1	no	—
129	C₁₉×C₂²⋊Q₈	—	2	1	no	—
130	C₁₉×C₂²⋊Q₈	—	2	1	no	—
131	C₁₉×C₂²⋊Q₈	—	2	1	no	—
132	C₁₉×C₂²⋊Q₈	—	2	1	no	—
133	C₁₉×C₂²⋊Q₈	—	2	1	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
136	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
137	C₁₉×#121	—	2	1	no	—
138	C₁₉×#121	—	2	1	no	—
139	C₁₉×#121	—	2	1	no	—
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	D₄	1	1	yes	characteristic
146	C₁₉×#121	D₄	1	1	yes	characteristic
147	C₁₉×#120	—	2	1	no	—
148	C₁₉×#120	—	2	1	no	—
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	D₄	1	1	yes	characteristic
156	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
162	C₄×D₄×C₁₉	—	2	1	no	—
163	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
164	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
165	C₁₉×#117	—	2	1	no	—
166	C₁₉×#117	—	2	1	no	—
167	C₁₉×#117	—	2	1	no	—
168	C₁₉×#117	—	2	1	no	—
169	C₁₉×#117	—	2	1	no	—
170	C₁₉×#117	—	2	1	no	—
171	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
172	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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×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×#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×#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	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×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
226	C₂×D₄×C₁₉	—	2	1	no	—
227	C₂×D₄×C₁₉	—	2	1	no	—
228	C₂×D₄×C₁₉	—	8	1	no	—
229	C₂×D₄×C₁₉	—	8	2	no	—
230	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
232	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	—	2	1	no	—
236	C₂²×C₄×C₁₉	—	2	1	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	Q₁₆×C₁₉	—	4	2	no	—
246	Q₁₆×C₁₉	—	8	1	no	—
247	Q₁₆×C₁₉	—	8	1	no	—
248	SD₁₆×C₁₉	—	4	2	no	—
249	SD₁₆×C₁₉	—	8	1	no	—
250	SD₁₆×C₁₉	—	8	1	no	—
251	M₁₆×C₁₉	—	4	2	no	—
252	C₂×C₈×C₁₉	—	2	1	no	—
253	C₂×C₈×C₁₉	—	2	1	no	—
254	C₂×C₈×C₁₉	—	2	1	no	—
255	C₂×C₈×C₁₉	—	2	1	no	—
256	C₂×C₈×C₁₉	—	2	1	no	—
257	C₂×C₈×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	—	4	1	no	—
277	C₄⋊C₄×C₁₉	—	4	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
309	C₂²⋊C₄×C₁₉	—	2	1	no	—
310	C₂²⋊C₄×C₁₉	—	4	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	—	4	1	no	—
316	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
320	#19069	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₁₉	—	2	1	no	—
322	C₂³×C₁₉	—	2	1	no	—
323	C₂³×C₁₉	—	2	1	no	—
324	C₂³×C₁₉	—	2	1	no	—
325	C₂³×C₁₉	—	4	2	no	—
326	C₂³×C₁₉	—	8	1	no	—
327	C₂³×C₁₉	—	8	1	no	—
328	C₂³×C₁₉	—	8	1	no	—
329	C₂³×C₁₉	—	8	1	no	—
330	C₂³×C₁₉	—	8	1	no	—
331	C₂³×C₁₉	#120	1	1	yes	characteristic
332	Q₈×C₁₉	—	4	1	no	—
333	Q₈×C₁₉	—	4	1	no	—
334	Q₈×C₁₉	—	4	1	no	—
335	Q₈×C₁₉	—	4	1	no	—
336	Q₈×C₁₉	—	4	1	no	—
337	Q₈×C₁₉	—	4	1	no	—
338	Q₈×C₁₉	—	4	1	no	—
339	Q₈×C₁₉	—	4	1	no	—
340	Q₈×C₁₉	—	8	1	no	—
341	Q₈×C₁₉	—	8	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	2	no	—
347	D₄×C₁₉	—	4	2	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	1	no	—
354	D₄×C₁₉	—	8	1	no	—
355	D₄×C₁₉	—	8	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	—	2	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	—	4	2	no	—
368	C₂×C₄×C₁₉	—	4	1	no	—
369	C₂×C₄×C₁₉	—	4	1	no	—
370	C₂×C₄×C₁₉	—	8	1	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	—	8	1	no	—
375	C₂×C₄×C₁₉	—	8	1	no	—
376	C₂×C₄×C₁₉	—	8	1	no	—
377	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
378	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
379	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
380	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
383	C₈×C₁₉	—	2	2	no	—
384	C₈×C₁₉	—	4	1	no	—
385	C₈×C₁₉	—	4	1	no	—
386	C₈×C₁₉	—	4	1	no	—
387	C₈×C₁₉	—	4	1	no	—
388	C₈×C₁₉	—	4	1	no	—
389	#3545	C₂×C₁₉	1	1	yes	characteristic
390	#3240	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#3215	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#1664	C₂×C₁₉	1	1	yes	characteristic, complemented
394	#1662	C₂×C₁₉	1	1	yes	characteristic, complemented
395	#1661	C₂×C₁₉	1	1	yes	characteristic, complemented
396	#1661	C₂×C₁₉	1	1	yes	characteristic, complemented
397	#1661	C₂×C₁₉	1	1	yes	characteristic, complemented
398	#1660	C₂×C₁₉	1	1	yes	characteristic, complemented
399	#1659	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#1659	C₂×C₁₉	1	1	yes	characteristic, complemented
401	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#1529	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
404	C₂²×C₁₉	—	2	1	no	—
405	C₂²×C₁₉	—	2	1	no	—
406	C₂²×C₁₉	—	2	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	—	4	1	no	—
414	C₂²×C₁₉	—	4	1	no	—
415	C₂²×C₁₉	—	4	1	no	—
416	C₂²×C₁₉	—	4	1	no	—
417	C₂²×C₁₉	—	4	1	no	—
418	C₂²×C₁₉	—	4	1	no	—
419	C₂²×C₁₉	—	16	2	no	—
420	C₂²×C₁₉	—	16	2	no	—
421	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
422	C₄×C₁₉	—	2	1	no	—
423	C₄×C₁₉	—	2	1	no	—
424	C₄×C₁₉	—	2	1	no	—
425	C₄×C₁₉	—	2	1	no	—
426	C₄×C₁₉	—	2	1	no	—
427	C₄×C₁₉	—	2	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	—	4	1	no	—
434	C₄×C₁₉	—	4	1	no	—
435	C₄×C₁₉	—	4	1	no	—
436	C₄×C₁₉	—	8	1	no	—
437	C₄×C₁₉	—	8	1	no	—
438	#563	C₂²×C₁₉	1	1	yes	characteristic
439	#562	C₂²×C₁₉	1	1	yes	characteristic
440	#562	C₂²×C₁₉	1	1	yes	characteristic
441	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
442	#555	—	2	1	no	—
443	#551	—	2	1	no	—
444	#551	—	2	1	no	—
445	#551	—	2	1	no	—
446	#546	—	2	1	no	—
447	#546	—	2	1	no	—
448	#542	—	2	1	no	—
449	#542	—	2	1	no	—
450	#538	—	2	1	no	—
451	#538	—	2	1	no	—
452	#536	—	2	1	no	—
453	#534	—	2	1	no	—
454	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
455	#529	C₂²×C₁₉	1	1	yes	characteristic
456	#529	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
458	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
459	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
460	#501	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#497	C₂²×C₁₉	1	1	yes	characteristic
462	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
463	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
465	#489	C₂²×C₁₉	1	1	yes	characteristic
466	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
467	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
468	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
469	#489	C₂²×C₁₉	1	1	yes	characteristic, complemented
470	#485	—	2	1	no	—
471	#482	—	2	1	no	—
472	#479	—	2	1	no	—
473	#478	—	2	1	no	—
474	#470	—	2	1	no	—
475	#468	—	2	1	no	—
476	#464	—	2	1	no	—
477	#464	—	2	1	no	—
478	#451	—	2	1	no	—
479	#450	—	2	1	no	—
480	C₄×Q₁₆	—	2	1	no	—
481	C₄×SD₁₆	—	2	1	no	—
482	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
483	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
484	C₄×M₁₆	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	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	#330	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	#329	C₂²×C₁₉	1	1	yes	characteristic
490	#329	C₂²×C₁₉	1	1	yes	characteristic
491	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
492	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
493	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
494	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
495	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
496	#329	C₂²×C₁₉	1	1	yes	characteristic, complemented
497	C₂×C₁₉	—	4	1	no	—
498	C₂×C₁₉	—	8	1	no	—
499	C₂×C₁₉	—	8	1	no	—
500	C₂×C₁₉	—	8	1	no	—
501	C₂×C₁₉	—	8	1	no	—
502	C₂×C₁₉	#3018	1	1	yes	characteristic
503	C₂×C₁₉	#3019	1	1	yes	characteristic
504	C₂×C₁₉	#3022	1	1	yes	characteristic
505	C₂×#41	—	2	1	no	—
506	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
509	C₂×Q₁₆	—	2	1	no	—
510	C₂×Q₁₆	—	2	1	no	—
511	C₂×Q₁₆	—	2	1	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×SD₁₆	—	2	1	no	—
514	C₂×SD₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	1	no	—
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
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	#125	—	2	1	no	—
527	#125	C₂³×C₁₉	1	1	yes	characteristic
528	#125	C₂³×C₁₉	1	1	yes	characteristic
529	#124	—	2	1	no	—
530	#124	—	2	1	no	—
531	#124	—	2	1	no	—
532	#124	—	2	1	no	—
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	—	2	1	no	—
536	#124	—	2	1	no	—
537	#124	D₄×C₁₉	1	1	yes	characteristic
538	#124	D₄×C₁₉	1	1	yes	characteristic
539	#124	C₂³×C₁₉	1	1	yes	characteristic
540	#124	C₂³×C₁₉	1	1	yes	characteristic
541	#124	C₂³×C₁₉	1	1	yes	characteristic
542	#124	C₂³×C₁₉	1	1	yes	characteristic
543	#123	—	2	1	no	—
544	#123	—	2	1	no	—
545	#123	—	2	1	no	—
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	—	2	1	no	—
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	—	2	1	no	—
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	D₄×C₁₉	1	1	yes	characteristic
576	#121	D₄×C₁₉	1	1	yes	characteristic
577	#120	—	2	1	no	—
578	#120	—	2	1	no	—
579	#120	—	2	1	no	—
580	#120	—	2	1	no	—
581	#120	—	2	1	no	—
582	#120	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
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	#117	—	2	1	no	—
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	C₂×C₂²⋊C₄	—	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×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
607	#107	—	2	1	no	—
608	#107	—	2	1	no	—
609	#107	—	2	1	no	—
610	#106	—	2	1	no	—
611	#106	—	2	1	no	—
612	#106	—	2	1	no	—
613	C₄⋊C₈	—	2	1	no	—
614	C₄⋊C₈	—	2	1	no	—
615	#103	—	2	1	no	—
616	#103	—	2	1	no	—
617	#103	—	2	1	no	—
618	#103	—	2	1	no	—
619	#103	—	2	1	no	—
620	#103	—	2	1	no	—
621	#103	—	2	1	no	—
622	#102	—	2	1	no	—
623	#102	—	2	1	no	—
624	#102	—	2	1	no	—
625	#102	—	2	1	no	—
626	#102	—	2	1	no	—
627	C₂²⋊C₈	—	2	1	no	—
628	C₂²⋊C₈	—	2	1	no	—
629	#97	C₂³×C₁₉	1	1	yes	characteristic
630	#97	C₂³×C₁₉	1	1	yes	characteristic
631	#97	C₂³×C₁₉	1	1	yes	characteristic
632	#97	C₂³×C₁₉	1	1	yes	characteristic
633	#97	C₂³×C₁₉	1	1	yes	characteristic
634	#97	C₂³×C₁₉	1	1	yes	characteristic
635	C₄×C₈	—	2	1	no	—
636	C₁₉	#19069	1	1	yes	characteristic, direct product factor, Sylow
637	C₂⁴	—	2	1	no	—
638	C₂⁴	—	2	1	no	—
639	#41	—	8	2	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	8	1	no	—
645	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
647	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
648	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	8	1	no	—
660	C₂×D₄	—	8	2	no	—
661	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
662	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
663	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
664	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
676	Q₁₆	—	4	2	no	—
677	Q₁₆	—	8	1	no	—
678	Q₁₆	—	8	1	no	—
679	SD₁₆	—	4	2	no	—
680	SD₁₆	—	8	1	no	—
681	SD₁₆	—	8	1	no	—
682	M₁₆	—	4	2	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	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	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	1	no	—
709	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
710	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
711	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	—	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	—	4	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	1	no	—
746	C₄²	—	4	1	no	—
747	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
750	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	8	1	no	—
757	C₂³	—	8	1	no	—
758	C₂³	—	8	1	no	—
759	C₂³	—	8	1	no	—
760	C₂³	—	8	1	no	—
761	C₂³	C₁₉×#120	1	1	yes	characteristic
762	Q₈	—	4	1	no	—
763	Q₈	—	4	1	no	—
764	Q₈	—	4	1	no	—
765	Q₈	—	4	1	no	—
766	Q₈	—	4	1	no	—
767	Q₈	—	4	1	no	—
768	Q₈	—	4	1	no	—
769	Q₈	—	4	1	no	—
770	Q₈	—	8	1	no	—
771	Q₈	—	8	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	4	1	no	—
774	D₄	—	4	1	no	—
775	D₄	—	4	1	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	8	1	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	1	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	1	no	—
784	D₄	—	8	1	no	—
785	D₄	—	8	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	—	8	1	no	—
802	C₂×C₄	—	8	1	no	—
803	C₂×C₄	—	8	1	no	—
804	C₂×C₄	—	8	1	no	—
805	C₂×C₄	—	8	1	no	—
806	C₂×C₄	—	8	1	no	—
807	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
808	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
809	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
813	C₈	—	2	2	no	—
814	C₈	—	4	1	no	—
815	C₈	—	4	1	no	—
816	C₈	—	4	1	no	—
817	C₈	—	4	1	no	—
818	C₈	—	4	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	16	2	no	—
835	C₂²	—	16	2	no	—
836	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
837	C₄	—	2	1	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	8	1	no	—
852	C₄	—	8	1	no	—
853	C₂	—	4	1	no	—
854	C₂	—	8	1	no	—
855	C₂	—	8	1	no	—
856	C₂	—	8	1	no	—
857	C₂	—	8	1	no	—
858	C₂	C₁₉×#3018	1	1	yes	characteristic
859	C₂	C₁₉×#3019	1	1	yes	characteristic
860	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3545	C₂
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
2. C₁₉×#3240	C₂	semidirect
3. C₁₉×#3215	C₂	semidirect
4. C₁₉×#3172	C₂	semidirect
5. C₁₉×#1664	C₂	semidirect
6. C₁₉×#1662	C₂	semidirect
7. C₁₉×#1661	C₂	semidirect
8. C₁₉×#1661	C₂	semidirect
9. C₁₉×#1661	C₂	semidirect
10. C₁₉×#1660	C₂	semidirect
11. C₁₉×#1659	C₂	semidirect
12. C₁₉×#1659	C₂	semidirect
13. C₁₉×#1535	C₂	semidirect
14. C₁₉×#1529	C₂	semidirect
15. C₁₉×#1527	C₂	semidirect
32. C₁₉×#533	C₂²	semidirect
36. C₁₉×#501	C₂²	semidirect
37. C₁₉×#501	C₂²	semidirect
38. C₁₉×#501	C₂²	semidirect
40. C₁₉×#497	C₂²	semidirect
41. C₁₉×#497	C₂²	semidirect
42. C₁₉×#491	C₂²	semidirect
44. C₁₉×#489	C₂²	semidirect
45. C₁₉×#489	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
320. #19069	C₁₉	direct (N × H)
390. #3240	C₂×C₁₉	semidirect
391. #3215	C₂×C₁₉	semidirect
392. #3172	C₂×C₁₉	semidirect
393. #1664	C₂×C₁₉	semidirect
394. #1662	C₂×C₁₉	semidirect
395. #1661	C₂×C₁₉	semidirect
396. #1661	C₂×C₁₉	semidirect
397. #1661	C₂×C₁₉	semidirect
398. #1660	C₂×C₁₉	semidirect
399. #1659	C₂×C₁₉	semidirect
400. #1659	C₂×C₁₉	semidirect
401. #1535	C₂×C₁₉	semidirect
402. #1529	C₂×C₁₉	semidirect
403. #1527	C₂×C₁₉	semidirect
454. #533	C₂²×C₁₉	semidirect
458. #501	C₂²×C₁₉	semidirect
459. #501	C₂²×C₁₉	semidirect
460. #501	C₂²×C₁₉	semidirect
462. #497	C₂²×C₁₉	semidirect
463. #497	C₂²×C₁₉	semidirect
464. #491	C₂²×C₁₉	semidirect
466. #489	C₂²×C₁₉	semidirect
467. #489	C₂²×C₁₉	semidirect
468. #489	C₂²×C₁₉	semidirect
469. #489	C₂²×C₁₉	semidirect
482. #432	C₂²×C₁₉	semidirect
483. #432	C₂²×C₁₉	semidirect
484. C₄×M₁₆	C₂²×C₁₉	semidirect
485. #330	C₂²×C₁₉	semidirect
486. #330	C₂²×C₁₉	semidirect
487. #330	C₂²×C₁₉	semidirect
488. #330	C₂²×C₁₉	semidirect
491. #329	C₂²×C₁₉	semidirect
492. #329	C₂²×C₁₉	semidirect
493. #329	C₂²×C₁₉	semidirect
494. #329	C₂²×C₁₉	semidirect
495. #329	C₂²×C₁₉	semidirect
496. #329	C₂²×C₁₉	semidirect
636. C₁₉	#19069	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×#3240	2
C₁₉×#3215	2
C₁₉×#3172	2
C₁₉×#1664	2
C₁₉×#1662	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1659	2
C₁₉×#1535	2
C₁₉×#1529	2
C₁₉×#1527	2
#19069	19

Subgroups — C19×#19069 #18025028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19069 #18025028