Subgroups — C₁₉×#24446 #18030405

Order 4864.

1458 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2417	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#547	—	2	4	no	—
23	C₁₉×#547	—	2	4	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#123	—	2	1	no	—
26	C₂×C₁₉×#123	—	2	1	no	—
27	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#121	—	2	1	no	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#470	—	2	4	no	—
37	C₁₉×#452	—	2	4	no	—
38	C₁₉×#452	—	2	4	no	—
39	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
40	C₁₉×#417	—	2	4	no	—
41	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₉×#398	—	2	1	no	—
55	C₁₉×#396	—	2	1	no	—
56	C₁₉×#391	C₂²	1	1	yes	characteristic
57	C₁₉×#389	C₂²	1	1	yes	characteristic
58	C₁₉×#386	—	2	1	no	—
59	C₁₉×#380	—	2	1	no	—
60	C₁₉×#380	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₁₉×#340	C₂²	1	1	yes	characteristic
63	C₁₉×#336	C₂²	1	1	yes	characteristic
64	C₁₉×#336	C₂²	1	1	yes	characteristic
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	—	2	2	no	—
69	C₂×#41×C₁₉	—	2	2	no	—
70	C₂×#41×C₁₉	—	2	2	no	—
71	C₂×#41×C₁₉	—	2	2	no	—
72	C₂×#41×C₁₉	—	4	1	no	—
73	C₂×#41×C₁₉	—	4	1	no	—
74	C₂×#41×C₁₉	—	4	1	no	—
75	C₂×#41×C₁₉	—	4	1	no	—
76	C₂×#41×C₁₉	D₄	1	4	yes	—
77	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₉	—	2	1	no	—
81	C₂²×D₄×C₁₉	—	2	1	no	—
82	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₉	—	2	1	no	—
85	C₂³×C₄×C₁₉	—	2	1	no	—
86	C₂³×C₄×C₁₉	—	2	1	no	—
87	C₂³×C₄×C₁₉	—	2	1	no	—
88	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×Q₁₆×C₁₉	—	2	2	no	—
91	C₂×Q₁₆×C₁₉	—	2	2	no	—
92	C₂×Q₁₆×C₁₉	—	2	2	no	—
93	C₂×Q₁₆×C₁₉	—	4	1	no	—
94	C₂×Q₁₆×C₁₉	—	4	1	no	—
95	C₂×Q₁₆×C₁₉	—	4	1	no	—
96	C₂×SD₁₆×C₁₉	—	2	2	no	—
97	C₂×SD₁₆×C₁₉	—	2	2	no	—
98	C₂×SD₁₆×C₁₉	—	2	2	no	—
99	C₂×M₁₆×C₁₉	—	2	2	no	—
100	C₂×M₁₆×C₁₉	—	2	2	no	—
101	C₂×M₁₆×C₁₉	—	4	1	no	—
102	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×C₄⋊Q₈	—	2	2	no	—
107	C₁₉×C₄⋊Q₈	—	2	2	no	—
108	C₁₉×#123	—	2	8	no	—
109	C₁₉×#123	—	2	8	no	—
110	C₁₉×C₂²⋊Q₈	—	2	2	no	—
111	C₁₉×C₂²⋊Q₈	—	2	2	no	—
112	C₁₉×C₂²⋊Q₈	—	2	2	no	—
113	C₁₉×C₂²⋊Q₈	—	2	2	no	—
114	C₁₉×C₂²⋊Q₈	—	2	2	no	—
115	C₁₉×C₂²⋊Q₈	—	2	2	no	—
116	C₁₉×C₂²⋊Q₈	—	4	1	no	—
117	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
118	C₁₉×#121	—	2	8	no	—
119	C₄×D₄×C₁₉	—	2	2	no	—
120	C₄×D₄×C₁₉	—	2	2	no	—
121	C₄×D₄×C₁₉	—	2	2	no	—
122	C₄×D₄×C₁₉	—	2	2	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
148	C₁₉×#106	—	2	2	no	—
149	C₁₉×#103	—	2	2	no	—
150	C₁₉×#103	—	2	2	no	—
151	C₁₉×#103	—	2	2	no	—
152	C₁₉×#103	—	2	2	no	—
153	C₁₉×#103	—	2	2	no	—
154	C₁₉×#103	—	2	2	no	—
155	C₁₉×#103	—	4	1	no	—
156	C₁₉×#102	—	2	2	no	—
157	C₁₉×#102	—	2	2	no	—
158	C₁₉×#102	D₄	1	4	yes	complemented
159	C₁₉×C₂²⋊C₈	—	2	2	no	—
160	C₁₉×C₂²⋊C₈	—	2	2	no	—
161	C₁₉×C₂²⋊C₈	—	4	1	no	—
162	C₁₉×#95	—	2	1	no	—
163	C₁₉×#95	—	2	1	no	—
164	C₁₉×#95	—	2	1	no	—
165	C₁₉×#95	—	2	1	no	—
166	C₂⁴×C₁₉	—	2	1	no	—
167	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
169	#41×C₁₉	—	2	8	no	—
170	#41×C₁₉	—	4	4	no	—
171	#41×C₁₉	—	4	4	no	—
172	#41×C₁₉	—	4	4	no	—
173	#41×C₁₉	—	4	4	no	—
174	#41×C₁₉	—	4	4	no	—
175	#41×C₁₉	—	4	4	no	—
176	#41×C₁₉	—	4	4	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	1	no	—
180	C₂×Q₈×C₁₉	—	2	1	no	—
181	C₂×Q₈×C₁₉	—	2	1	no	—
182	C₂×Q₈×C₁₉	—	2	1	no	—
183	C₂×Q₈×C₁₉	—	2	1	no	—
184	C₂×Q₈×C₁₉	—	2	1	no	—
185	C₂×Q₈×C₁₉	—	2	1	no	—
186	C₂×Q₈×C₁₉	—	2	1	no	—
187	C₂×Q₈×C₁₉	—	2	1	no	—
188	C₂×Q₈×C₁₉	—	2	1	no	—
189	C₂×Q₈×C₁₉	—	2	1	no	—
190	C₂×Q₈×C₁₉	—	2	1	no	—
191	C₂×Q₈×C₁₉	—	2	1	no	—
192	C₂×Q₈×C₁₉	—	2	1	no	—
193	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
194	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₁₉	—	2	4	no	—
196	C₂×D₄×C₁₉	—	2	2	no	—
197	C₂×D₄×C₁₉	—	2	4	no	—
198	C₂×D₄×C₁₉	—	2	2	no	—
199	C₂×D₄×C₁₉	—	2	1	no	—
200	C₂×D₄×C₁₉	—	2	1	no	—
201	C₂×D₄×C₁₉	—	2	1	no	—
202	C₂×D₄×C₁₉	—	4	1	no	—
203	C₂×D₄×C₁₉	—	4	2	no	—
204	C₂×D₄×C₁₉	—	4	2	no	—
205	C₂×D₄×C₁₉	—	4	2	no	—
206	C₂×D₄×C₁₉	—	4	2	no	—
207	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₁₉	#41	1	2	yes	—
210	C₂²×C₄×C₁₉	—	2	1	no	—
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	2	1	no	—
213	C₂²×C₄×C₁₉	—	2	1	no	—
214	C₂²×C₄×C₁₉	—	2	4	no	—
215	C₂²×C₄×C₁₉	—	2	4	no	—
216	C₂²×C₄×C₁₉	—	2	1	no	—
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	4	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	—	2	1	no	—
227	C₂²×C₄×C₁₉	—	2	1	no	—
228	C₂²×C₄×C₁₉	—	2	1	no	—
229	C₂²×C₄×C₁₉	—	2	1	no	—
230	C₂²×C₄×C₁₉	—	4	2	no	—
231	C₂²×C₄×C₁₉	—	4	2	no	—
232	C₂²×C₄×C₁₉	—	4	2	no	—
233	C₂²×C₄×C₁₉	—	4	2	no	—
234	C₂²×C₄×C₁₉	—	4	2	no	—
235	C₂²×C₄×C₁₉	—	4	2	no	—
236	C₂²×C₄×C₁₉	—	4	2	no	—
237	C₂²×C₄×C₁₉	—	4	2	no	—
238	C₂²×C₄×C₁₉	—	8	1	no	—
239	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	Q₁₆×C₁₉	—	4	4	no	—
247	Q₁₆×C₁₉	—	4	4	no	—
248	SD₁₆×C₁₉	—	4	4	no	—
249	M₁₆×C₁₉	—	4	4	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	—	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	C₂×C₈×C₁₉	—	2	1	no	—
259	C₂×C₈×C₁₉	—	2	1	no	—
260	C₂×C₈×C₁₉	—	2	1	no	—
261	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₁₉	—	2	4	no	—
263	C₄⋊C₄×C₁₉	—	2	4	no	—
264	C₄⋊C₄×C₁₉	—	2	4	no	—
265	C₄⋊C₄×C₁₉	—	2	2	no	—
266	C₄⋊C₄×C₁₉	—	2	4	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	—	4	2	no	—
274	C₄⋊C₄×C₁₉	—	4	2	no	—
275	C₄⋊C₄×C₁₉	—	4	2	no	—
276	C₄⋊C₄×C₁₉	—	8	1	no	—
277	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₁₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₉	—	2	2	no	—
283	C₂²⋊C₄×C₁₉	—	2	2	no	—
284	C₂²⋊C₄×C₁₉	—	4	2	no	—
285	C₂²⋊C₄×C₁₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₉	—	8	1	no	—
287	C₄²×C₁₉	—	2	1	no	—
288	C₄²×C₁₉	—	2	1	no	—
289	#24446	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂³×C₁₉	—	2	2	no	—
291	C₂³×C₁₉	—	2	1	no	—
292	C₂³×C₁₉	—	2	2	no	—
293	C₂³×C₁₉	—	2	1	no	—
294	C₂³×C₁₉	—	2	2	no	—
295	C₂³×C₁₉	—	2	1	no	—
296	C₂³×C₁₉	—	2	1	no	—
297	C₂³×C₁₉	—	2	1	no	—
298	C₂³×C₁₉	—	2	1	no	—
299	C₂³×C₁₉	—	2	1	no	—
300	C₂³×C₁₉	—	2	1	no	—
301	C₂³×C₁₉	—	2	1	no	—
302	C₂³×C₁₉	—	2	1	no	—
303	C₂³×C₁₉	—	2	1	no	—
304	C₂³×C₁₉	—	2	1	no	—
305	C₂³×C₁₉	—	2	1	no	—
306	C₂³×C₁₉	—	4	1	no	—
307	C₂³×C₁₉	—	4	1	no	—
308	C₂³×C₁₉	—	4	1	no	—
309	C₂³×C₁₉	—	4	1	no	—
310	C₂³×C₁₉	#120	1	2	yes	—
311	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₁₉	—	2	2	no	—
313	Q₈×C₁₉	—	2	2	no	—
314	Q₈×C₁₉	—	2	2	no	—
315	Q₈×C₁₉	—	2	2	no	—
316	Q₈×C₁₉	—	4	1	no	—
317	Q₈×C₁₉	—	4	1	no	—
318	Q₈×C₁₉	—	4	1	no	—
319	Q₈×C₁₉	—	4	1	no	—
320	Q₈×C₁₉	—	4	1	no	—
321	Q₈×C₁₉	—	4	1	no	—
322	Q₈×C₁₉	—	4	1	no	—
323	Q₈×C₁₉	—	4	1	no	—
324	D₄×C₁₉	—	2	2	no	—
325	D₄×C₁₉	—	2	2	no	—
326	D₄×C₁₉	—	2	2	no	—
327	D₄×C₁₉	—	4	4	no	—
328	D₄×C₁₉	—	4	8	no	—
329	D₄×C₁₉	—	4	8	no	—
330	D₄×C₁₉	#121	1	4	yes	—
331	C₂×C₄×C₁₉	—	2	1	no	—
332	C₂×C₄×C₁₉	—	2	1	no	—
333	C₂×C₄×C₁₉	—	2	1	no	—
334	C₂×C₄×C₁₉	—	2	1	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	2	no	—
338	C₂×C₄×C₁₉	—	2	2	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	1	no	—
342	C₂×C₄×C₁₉	—	2	2	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	2	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	8	no	—
350	C₂×C₄×C₁₉	—	4	8	no	—
351	C₂×C₄×C₁₉	—	4	8	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	—	4	1	no	—
365	C₂×C₄×C₁₉	—	4	1	no	—
366	C₂×C₄×C₁₉	—	4	1	no	—
367	C₂×C₄×C₁₉	—	4	1	no	—
368	C₂×C₄×C₁₉	—	4	1	no	—
369	C₂×C₄×C₁₉	—	4	1	no	—
370	C₂×C₄×C₁₉	—	4	1	no	—
371	C₂×C₄×C₁₉	—	4	1	no	—
372	C₂×C₄×C₁₉	—	4	1	no	—
373	C₂×C₄×C₁₉	—	8	4	no	—
374	C₂×C₄×C₁₉	#120	1	2	yes	—
375	C₂×C₄×C₁₉	#137	1	2	yes	—
376	C₂×C₄×C₁₉	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
381	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
382	C₈×C₁₉	—	2	2	no	—
383	C₈×C₁₉	—	4	1	no	—
384	C₈×C₁₉	—	4	1	no	—
385	C₈×C₁₉	—	4	1	no	—
386	C₂×#547	C₂×C₁₉	1	1	yes	characteristic
387	C₂×#470	C₂×C₁₉	1	1	yes	characteristic, complemented
388	C₂×#452	C₂×C₁₉	1	1	yes	characteristic, complemented
389	C₂×#452	C₂×C₁₉	1	1	yes	characteristic, complemented
390	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#2417	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#2043	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#2035	C₂×C₁₉	1	1	yes	characteristic, complemented
394	#2016	C₂×C₁₉	1	1	yes	characteristic, complemented
395	#2001	C₂×C₁₉	1	1	yes	characteristic, complemented
396	#1877	C₂×C₁₉	1	1	yes	characteristic, complemented
397	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
398	#1870	C₂×C₁₉	1	1	yes	characteristic, complemented
399	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
401	C₂²×C₁₉	—	2	2	no	—
402	C₂²×C₁₉	—	2	4	no	—
403	C₂²×C₁₉	—	2	2	no	—
404	C₂²×C₁₉	—	2	2	no	—
405	C₂²×C₁₉	—	4	1	no	—
406	C₂²×C₁₉	—	4	2	no	—
407	C₂²×C₁₉	—	4	2	no	—
408	C₂²×C₁₉	—	4	1	no	—
409	C₂²×C₁₉	—	4	2	no	—
410	C₂²×C₁₉	—	4	2	no	—
411	C₂²×C₁₉	—	4	1	no	—
412	C₂²×C₁₉	—	4	2	no	—
413	C₂²×C₁₉	—	4	1	no	—
414	C₂²×C₁₉	—	4	2	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	—	4	1	no	—
420	C₂²×C₁₉	—	4	1	no	—
421	C₂²×C₁₉	—	4	1	no	—
422	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
423	C₂²×C₁₉	D₄²	1	1	yes	characteristic
424	C₂²×C₁₉	#546	1	1	yes	characteristic
425	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
426	C₂²×C₁₉	#575	1	1	yes	characteristic
427	C₂²×C₁₉	#577	1	1	yes	characteristic
428	C₂²×C₁₉	#578	1	1	yes	characteristic
429	C₄×C₁₉	—	2	2	no	—
430	C₄×C₁₉	—	2	2	no	—
431	C₄×C₁₉	—	4	1	no	—
432	C₄×C₁₉	—	4	2	no	—
433	C₄×C₁₉	—	4	2	no	—
434	C₄×C₁₉	—	4	2	no	—
435	C₄×C₁₉	—	4	2	no	—
436	C₄×C₁₉	—	4	1	no	—
437	C₄×C₁₉	—	8	1	no	—
438	C₄×C₁₉	—	8	1	no	—
439	C₄×C₁₉	—	8	1	no	—
440	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
441	C₄×C₁₉	#534	1	1	yes	characteristic
442	C₄×C₁₉	D₄²	1	1	yes	characteristic
443	C₄×C₁₉	#546	1	1	yes	characteristic
444	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
445	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
446	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
447	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
448	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
449	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
450	#547	—	2	4	no	—
451	#547	—	2	4	no	—
452	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#123	—	2	1	no	—
454	C₂×#123	—	2	1	no	—
455	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×#121	—	2	1	no	—
460	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
462	C₂²×C₄⋊C₄	—	2	1	no	—
463	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
464	#470	—	2	4	no	—
465	#452	—	2	4	no	—
466	#452	—	2	4	no	—
467	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
468	#417	—	2	4	no	—
469	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
470	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
472	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
473	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
475	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
476	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
477	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
478	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
481	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
482	#398	—	2	1	no	—
483	#396	—	2	1	no	—
484	#391	C₂²×C₁₉	1	1	yes	characteristic
485	#389	C₂²×C₁₉	1	1	yes	characteristic
486	#386	—	2	1	no	—
487	#380	—	2	1	no	—
488	#380	C₂²×C₁₉	1	1	yes	characteristic
489	#340	C₂²×C₁₉	1	1	yes	characteristic
490	#340	C₂²×C₁₉	1	1	yes	characteristic
491	#336	C₂²×C₁₉	1	1	yes	characteristic
492	#336	C₂²×C₁₉	1	1	yes	characteristic
493	C₂×C₁₉	—	4	2	no	—
494	C₂×C₁₉	—	4	4	no	—
495	C₂×C₁₉	—	8	1	no	—
496	C₂×C₁₉	#2410	1	1	yes	characteristic
497	C₂×C₁₉	#3007	1	1	yes	characteristic
498	C₂×C₁₉	#3013	1	1	yes	characteristic
499	C₂×C₁₉	#3267	1	1	yes	characteristic
500	C₂×C₁₉	#3276	1	1	yes	characteristic
501	C₂×C₁₉	#3315	1	1	yes	characteristic
502	C₂×C₁₉	#3331	1	1	yes	characteristic
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	4	1	no	—
511	C₂×#41	—	4	1	no	—
512	C₂×#41	—	4	1	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	D₄×C₁₉	1	4	yes	—
515	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	—	2	1	no	—
525	C₂³×C₄	—	2	1	no	—
526	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
528	C₂×Q₁₆	—	2	2	no	—
529	C₂×Q₁₆	—	2	2	no	—
530	C₂×Q₁₆	—	2	2	no	—
531	C₂×Q₁₆	—	4	1	no	—
532	C₂×Q₁₆	—	4	1	no	—
533	C₂×Q₁₆	—	4	1	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×M₁₆	—	2	2	no	—
538	C₂×M₁₆	—	2	2	no	—
539	C₂×M₁₆	—	4	1	no	—
540	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	2	no	—
546	#123	—	2	8	no	—
547	#123	—	2	8	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	4	1	no	—
555	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
556	#121	—	2	8	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₂×C₄⋊C₄	—	2	8	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	2	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	4	1	no	—
572	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
586	#106	—	2	2	no	—
587	#103	—	2	2	no	—
588	#103	—	2	2	no	—
589	#103	—	2	2	no	—
590	#103	—	2	2	no	—
591	#103	—	2	2	no	—
592	#103	—	2	2	no	—
593	#103	—	4	1	no	—
594	#102	—	2	2	no	—
595	#102	—	2	2	no	—
596	#102	D₄×C₁₉	1	4	yes	complemented
597	C₂²⋊C₈	—	2	2	no	—
598	C₂²⋊C₈	—	2	2	no	—
599	C₂²⋊C₈	—	4	1	no	—
600	#95	—	2	1	no	—
601	#95	—	2	1	no	—
602	#95	—	2	1	no	—
603	#95	—	2	1	no	—
604	C₁₉	#24446	1	1	yes	characteristic, direct product factor, Sylow
605	C₂⁴	—	2	1	no	—
606	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
607	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
608	#41	—	2	8	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	4	no	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
633	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	4	1	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
647	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
648	C₂×D₄	#41×C₁₉	1	2	yes	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	8	1	no	—
678	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
683	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
685	Q₁₆	—	4	4	no	—
686	Q₁₆	—	4	4	no	—
687	SD₁₆	—	4	4	no	—
688	M₁₆	—	4	4	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	8	1	no	—
716	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	8	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	C₁₉×#120	1	2	yes	—
749	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
750	Q₈	—	2	2	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	1	no	—
755	Q₈	—	4	1	no	—
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	—	4	1	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	8	no	—
768	D₄	C₁₉×#121	1	4	yes	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	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	—	4	8	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	C₁₉×#120	1	2	yes	—
813	C₂×C₄	C₁₉×#137	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
817	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
818	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
819	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	4	1	no	—
822	C₈	—	4	1	no	—
823	C₈	—	4	1	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
846	C₂²	D₄²×C₁₉	1	1	yes	characteristic
847	C₂²	C₁₉×#546	1	1	yes	characteristic
848	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
849	C₂²	C₁₉×#575	1	1	yes	characteristic
850	C₂²	C₁₉×#577	1	1	yes	characteristic
851	C₂²	C₁₉×#578	1	1	yes	characteristic
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	8	1	no	—
861	C₄	—	8	1	no	—
862	C₄	—	8	1	no	—
863	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
864	C₄	C₁₉×#534	1	1	yes	characteristic
865	C₄	D₄²×C₁₉	1	1	yes	characteristic
866	C₄	C₁₉×#546	1	1	yes	characteristic
867	C₂	—	4	2	no	—
868	C₂	—	4	4	no	—
869	C₂	—	8	1	no	—
870	C₂	C₁₉×#2410	1	1	yes	characteristic
871	C₂	C₁₉×#3007	1	1	yes	characteristic
872	C₂	C₁₉×#3013	1	1	yes	characteristic
873	C₂	C₁₉×#3267	1	1	yes	characteristic
874	C₂	C₁₉×#3276	1	1	yes	characteristic
875	C₂	C₁₉×#3315	1	1	yes	characteristic
876	C₂	C₁₉×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#547	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₉×#470	C₂	semidirect
3. C₂×C₁₉×#452	C₂	semidirect
4. C₂×C₁₉×#452	C₂	semidirect
5. C₂×C₁₉×#417	C₂	semidirect
6. C₁₉×#2417	C₂	semidirect
7. C₁₉×#2043	C₂	semidirect
8. C₁₉×#2035	C₂	semidirect
9. C₁₉×#2016	C₂	semidirect
10. C₁₉×#2001	C₂	semidirect
11. C₁₉×#1877	C₂	semidirect
12. C₁₉×#1872	C₂	semidirect
13. C₁₉×#1870	C₂	semidirect
14. C₁₉×#1864	C₂	semidirect
15. C₁₉×#1788	C₂	semidirect
158. C₁₉×#102	D₄	semidirect
289. #24446	C₁₉	direct (N × H)
387. C₂×#470	C₂×C₁₉	semidirect
388. C₂×#452	C₂×C₁₉	semidirect
389. C₂×#452	C₂×C₁₉	semidirect
390. C₂×#417	C₂×C₁₉	semidirect
391. #2417	C₂×C₁₉	semidirect
392. #2043	C₂×C₁₉	semidirect
393. #2035	C₂×C₁₉	semidirect
394. #2016	C₂×C₁₉	semidirect
395. #2001	C₂×C₁₉	semidirect
396. #1877	C₂×C₁₉	semidirect
397. #1872	C₂×C₁₉	semidirect
398. #1870	C₂×C₁₉	semidirect
399. #1864	C₂×C₁₉	semidirect
400. #1788	C₂×C₁₉	semidirect
596. #102	D₄×C₁₉	semidirect
604. C₁₉	#24446	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#547	2
C₂×C₁₉×#470	2
C₂×C₁₉×#452	2
C₂×C₁₉×#417	2
C₁₉×#2417	2
C₁₉×#2043	2
C₁₉×#2035	2
C₁₉×#2016	2
C₁₉×#2001	2
C₁₉×#1877	2
C₁₉×#1872	2
C₁₉×#1870	2
C₁₉×#1864	2
C₁₉×#1788	2
#24446	19

Subgroups — C19×#24446 #18030405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24446 #18030405