Subgroups — C₁₉×#24455 #18030414

Order 4864.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1865	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	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#548	—	2	4	no	—
23	C₁₉×#548	—	2	4	no	—
24	C₂×C₁₉×#124	—	2	1	no	—
25	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#121	—	2	1	no	—
29	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₉	—	2	1	no	—
34	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
36	C₁₉×#469	—	2	4	no	—
37	C₁₉×#449	—	2	4	no	—
38	C₁₉×#448	—	2	4	no	—
39	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
40	C₁₉×#419	—	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×#102	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×#394	—	2	1	no	—
55	C₁₉×#392	—	2	1	no	—
56	C₁₉×#390	—	2	1	no	—
57	C₁₉×#390	C₂²	1	1	yes	characteristic
58	C₁₉×#389	C₂²	1	1	yes	characteristic
59	C₁₉×#388	—	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	—	4	1	no	—
70	C₂×#41×C₁₉	—	4	1	no	—
71	C₂²×Q₈×C₁₉	—	2	1	no	—
72	C₂²×Q₈×C₁₉	—	2	2	no	—
73	C₂²×Q₈×C₁₉	—	2	2	no	—
74	C₂²×Q₈×C₁₉	—	2	2	no	—
75	C₂²×Q₈×C₁₉	—	4	1	no	—
76	C₂²×Q₈×C₁₉	—	4	1	no	—
77	C₂²×Q₈×C₁₉	D₄	1	4	yes	complemented
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	—	2	1	no	—
83	C₂²×D₄×C₁₉	—	2	1	no	—
84	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	—	2	1	no	—
88	C₂³×C₄×C₁₉	—	2	1	no	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₁₉	—	2	2	no	—
92	C₂×SD₁₆×C₁₉	—	2	2	no	—
93	C₂×SD₁₆×C₁₉	—	2	2	no	—
94	C₂×SD₁₆×C₁₉	—	2	2	no	—
95	C₂×SD₁₆×C₁₉	—	4	1	no	—
96	C₂×SD₁₆×C₁₉	—	4	1	no	—
97	C₂×D₈×C₁₉	—	2	2	no	—
98	C₂×D₈×C₁₉	—	2	2	no	—
99	C₂×D₈×C₁₉	—	4	1	no	—
100	C₂×M₁₆×C₁₉	—	2	2	no	—
101	C₂×M₁₆×C₁₉	—	2	2	no	—
102	C₂×M₁₆×C₁₉	—	4	1	no	—
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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×#124	—	2	8	no	—
108	C₁₉×#124	—	2	2	no	—
109	C₁₉×#124	—	2	2	no	—
110	C₁₉×C₂²⋊Q₈	—	2	8	no	—
111	C₁₉×C₂²⋊Q₈	—	2	2	no	—
112	C₁₉×C₂²⋊Q₈	—	2	2	no	—
113	C₁₉×#121	—	2	8	no	—
114	C₁₉×#121	—	2	2	no	—
115	C₁₉×#121	—	2	2	no	—
116	C₁₉×#121	—	2	2	no	—
117	C₁₉×#121	—	2	2	no	—
118	C₁₉×#121	—	4	1	no	—
119	C₁₉×#121	D₄	1	4	yes	complemented
120	C₄×Q₈×C₁₉	—	2	2	no	—
121	C₄×Q₈×C₁₉	—	2	2	no	—
122	C₄×D₄×C₁₉	—	2	8	no	—
123	C₄×D₄×C₁₉	—	2	2	no	—
124	C₄×D₄×C₁₉	—	2	2	no	—
125	C₁₉×#117	—	2	2	no	—
126	C₁₉×#117	—	4	1	no	—
127	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
148	C₂×C₄²×C₁₉	—	2	1	no	—
149	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
150	C₁₉×#106	—	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	—	2	2	no	—
156	C₁₉×#103	D₄	1	4	yes	complemented
157	C₁₉×#102	—	2	2	no	—
158	C₁₉×#102	—	2	2	no	—
159	C₁₉×#102	—	2	2	no	—
160	C₁₉×#102	—	4	1	no	—
161	C₁₉×C₂²⋊C₈	—	2	2	no	—
162	C₁₉×C₂²⋊C₈	—	2	2	no	—
163	C₁₉×C₂²⋊C₈	—	4	1	no	—
164	C₁₉×#95	—	2	1	no	—
165	C₁₉×#95	—	2	1	no	—
166	C₂⁴×C₁₉	—	2	1	no	—
167	C₂⁴×C₁₉	—	2	1	no	—
168	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂×Q₈×C₁₉	—	2	4	no	—
175	C₂×Q₈×C₁₉	—	2	1	no	—
176	C₂×Q₈×C₁₉	—	2	1	no	—
177	C₂×Q₈×C₁₉	—	2	1	no	—
178	C₂×Q₈×C₁₉	—	2	1	no	—
179	C₂×Q₈×C₁₉	—	2	8	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	—	4	2	no	—
185	C₂×Q₈×C₁₉	—	4	2	no	—
186	C₂×Q₈×C₁₉	—	4	4	no	—
187	C₂×Q₈×C₁₉	—	4	4	no	—
188	C₂×Q₈×C₁₉	—	4	4	no	—
189	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
190	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
191	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
192	C₂×Q₈×C₁₉	#41	1	2	yes	—
193	C₂×D₄×C₁₉	—	2	4	no	—
194	C₂×D₄×C₁₉	—	2	2	no	—
195	C₂×D₄×C₁₉	—	2	4	no	—
196	C₂×D₄×C₁₉	—	2	1	no	—
197	C₂×D₄×C₁₉	—	2	1	no	—
198	C₂×D₄×C₁₉	—	2	1	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	—	2	1	no	—
203	C₂×D₄×C₁₉	—	2	1	no	—
204	C₂×D₄×C₁₉	—	2	1	no	—
205	C₂×D₄×C₁₉	—	2	1	no	—
206	C₂×D₄×C₁₉	—	2	1	no	—
207	C₂×D₄×C₁₉	—	4	1	no	—
208	C₂×D₄×C₁₉	—	4	1	no	—
209	C₂×D₄×C₁₉	—	4	2	no	—
210	C₂×D₄×C₁₉	—	4	2	no	—
211	C₂×D₄×C₁₉	—	4	2	no	—
212	C₂×D₄×C₁₉	—	4	2	no	—
213	C₂×D₄×C₁₉	—	4	2	no	—
214	C₂×D₄×C₁₉	—	4	2	no	—
215	C₂×D₄×C₁₉	—	4	2	no	—
216	C₂×D₄×C₁₉	—	8	1	no	—
217	C₂×D₄×C₁₉	—	8	1	no	—
218	C₂×D₄×C₁₉	—	8	1	no	—
219	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
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	4	no	—
226	C₂²×C₄×C₁₉	—	2	4	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	—	2	1	no	—
231	C₂²×C₄×C₁₉	—	2	1	no	—
232	C₂²×C₄×C₁₉	—	2	1	no	—
233	C₂²×C₄×C₁₉	—	2	1	no	—
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	—	2	1	no	—
236	C₂²×C₄×C₁₉	—	2	1	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	4	2	no	—
239	C₂²×C₄×C₁₉	—	4	2	no	—
240	C₂²×C₄×C₁₉	—	4	2	no	—
241	C₂²×C₄×C₁₉	—	4	2	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	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	SD₁₆×C₁₉	—	4	4	no	—
250	SD₁₆×C₁₉	—	4	4	no	—
251	D₈×C₁₉	—	4	4	no	—
252	M₁₆×C₁₉	—	4	4	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	—	2	1	no	—
262	C₂×C₈×C₁₉	—	2	1	no	—
263	C₂×C₈×C₁₉	—	2	1	no	—
264	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₁₉	—	2	4	no	—
266	C₄⋊C₄×C₁₉	—	2	4	no	—
267	C₄⋊C₄×C₁₉	—	2	2	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	—	8	1	no	—
275	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₁₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₉	—	2	2	no	—
281	C₂²⋊C₄×C₁₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₉	—	2	2	no	—
283	C₂²⋊C₄×C₁₉	—	4	2	no	—
284	C₂²⋊C₄×C₁₉	—	4	2	no	—
285	C₂²⋊C₄×C₁₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₉	—	4	2	no	—
287	C₂²⋊C₄×C₁₉	—	8	1	no	—
288	C₂²⋊C₄×C₁₉	—	8	1	no	—
289	C₄²×C₁₉	—	2	4	no	—
290	C₄²×C₁₉	—	2	1	no	—
291	C₄²×C₁₉	—	2	1	no	—
292	C₄²×C₁₉	—	4	2	no	—
293	#24455	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂³×C₁₉	—	2	1	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	2	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	—	2	1	no	—
307	C₂³×C₁₉	—	2	1	no	—
308	C₂³×C₁₉	—	4	1	no	—
309	C₂³×C₁₉	—	4	1	no	—
310	C₂³×C₁₉	—	4	1	no	—
311	C₂³×C₁₉	—	4	1	no	—
312	C₂³×C₁₉	—	4	1	no	—
313	C₂³×C₁₉	—	4	1	no	—
314	C₂³×C₁₉	—	4	1	no	—
315	C₂³×C₁₉	—	4	1	no	—
316	C₂³×C₁₉	—	4	1	no	—
317	C₂³×C₁₉	—	4	1	no	—
318	C₂³×C₁₉	—	4	1	no	—
319	C₂³×C₁₉	—	4	1	no	—
320	C₂³×C₁₉	—	4	1	no	—
321	C₂³×C₁₉	#120	1	2	yes	—
322	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₁₉	—	2	2	no	—
324	Q₈×C₁₉	—	2	2	no	—
325	Q₈×C₁₉	—	2	2	no	—
326	Q₈×C₁₉	—	2	2	no	—
327	Q₈×C₁₉	—	2	2	no	—
328	Q₈×C₁₉	—	4	8	no	—
329	Q₈×C₁₉	—	4	1	no	—
330	Q₈×C₁₉	—	4	1	no	—
331	Q₈×C₁₉	#121	1	4	yes	—
332	D₄×C₁₉	—	2	2	no	—
333	D₄×C₁₉	—	2	2	no	—
334	D₄×C₁₉	—	4	8	no	—
335	D₄×C₁₉	—	4	4	no	—
336	D₄×C₁₉	—	4	8	no	—
337	D₄×C₁₉	—	4	1	no	—
338	D₄×C₁₉	—	4	1	no	—
339	D₄×C₁₉	—	4	1	no	—
340	D₄×C₁₉	—	4	1	no	—
341	D₄×C₁₉	—	4	1	no	—
342	D₄×C₁₉	—	4	1	no	—
343	D₄×C₁₉	—	8	4	no	—
344	D₄×C₁₉	—	8	4	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	1	no	—
347	C₂×C₄×C₁₉	—	2	2	no	—
348	C₂×C₄×C₁₉	—	2	1	no	—
349	C₂×C₄×C₁₉	—	2	2	no	—
350	C₂×C₄×C₁₉	—	2	2	no	—
351	C₂×C₄×C₁₉	—	2	2	no	—
352	C₂×C₄×C₁₉	—	2	2	no	—
353	C₂×C₄×C₁₉	—	2	2	no	—
354	C₂×C₄×C₁₉	—	2	1	no	—
355	C₂×C₄×C₁₉	—	2	1	no	—
356	C₂×C₄×C₁₉	—	2	2	no	—
357	C₂×C₄×C₁₉	—	2	2	no	—
358	C₂×C₄×C₁₉	—	2	1	no	—
359	C₂×C₄×C₁₉	—	2	2	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	—	2	1	no	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	4	8	no	—
367	C₂×C₄×C₁₉	—	4	8	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	—	4	1	no	—
374	C₂×C₄×C₁₉	—	4	1	no	—
375	C₂×C₄×C₁₉	—	4	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	1	no	—
380	C₂×C₄×C₁₉	—	4	1	no	—
381	C₂×C₄×C₁₉	—	4	1	no	—
382	C₂×C₄×C₁₉	—	4	1	no	—
383	C₂×C₄×C₁₉	—	4	1	no	—
384	C₂×C₄×C₁₉	#120	1	2	yes	—
385	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
389	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
391	C₈×C₁₉	—	2	2	no	—
392	C₈×C₁₉	—	4	1	no	—
393	C₈×C₁₉	—	4	1	no	—
394	C₈×C₁₉	—	4	1	no	—
395	C₂×#548	C₂×C₁₉	1	1	yes	characteristic, complemented
396	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
397	C₂×#449	C₂×C₁₉	1	1	yes	characteristic, complemented
398	C₂×#448	C₂×C₁₉	1	1	yes	characteristic, complemented
399	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
400	#2414	C₂×C₁₉	1	1	yes	characteristic, complemented
401	#2042	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#2035	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#2012	C₂×C₁₉	1	1	yes	characteristic, complemented
404	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
405	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
406	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
407	#1870	C₂×C₁₉	1	1	yes	characteristic, complemented
408	#1865	C₂×C₁₉	1	1	yes	characteristic, complemented
409	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
410	C₂²×C₁₉	—	2	2	no	—
411	C₂²×C₁₉	—	2	2	no	—
412	C₂²×C₁₉	—	2	2	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	2	no	—
418	C₂²×C₁₉	—	4	1	no	—
419	C₂²×C₁₉	—	4	1	no	—
420	C₂²×C₁₉	—	4	2	no	—
421	C₂²×C₁₉	—	4	1	no	—
422	C₂²×C₁₉	—	4	2	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	—	8	1	no	—
428	C₂²×C₁₉	—	8	1	no	—
429	C₂²×C₁₉	—	8	1	no	—
430	C₂²×C₁₉	—	8	1	no	—
431	C₂²×C₁₉	—	8	1	no	—
432	C₂²×C₁₉	—	8	1	no	—
433	C₂²×C₁₉	—	8	1	no	—
434	C₂²×C₁₉	—	8	1	no	—
435	C₂²×C₁₉	—	8	1	no	—
436	C₂²×C₁₉	—	8	1	no	—
437	C₂²×C₁₉	—	8	1	no	—
438	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
439	C₂²×C₁₉	D₄²	1	1	yes	characteristic
440	C₂²×C₁₉	#546	1	1	yes	characteristic
441	C₂²×C₁₉	#575	1	1	yes	characteristic
442	C₂²×C₁₉	#575	1	1	yes	characteristic
443	C₂²×C₁₉	#577	1	1	yes	characteristic
444	C₂²×C₁₉	#577	1	1	yes	characteristic
445	C₄×C₁₉	—	2	2	no	—
446	C₄×C₁₉	—	2	4	no	—
447	C₄×C₁₉	—	4	1	no	—
448	C₄×C₁₉	—	4	2	no	—
449	C₄×C₁₉	—	4	1	no	—
450	C₄×C₁₉	—	4	2	no	—
451	C₄×C₁₉	—	4	1	no	—
452	C₄×C₁₉	—	4	2	no	—
453	C₄×C₁₉	—	8	1	no	—
454	C₄×C₁₉	—	8	1	no	—
455	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
456	C₄×C₁₉	#534	1	1	yes	characteristic
457	C₄×C₁₉	D₄²	1	1	yes	characteristic
458	C₄×C₁₉	#546	1	1	yes	characteristic
459	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
460	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
461	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
462	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
463	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
464	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
465	#548	—	2	4	no	—
466	#548	—	2	4	no	—
467	C₂×#124	—	2	1	no	—
468	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×C₂²⋊Q₈	—	2	1	no	—
470	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
471	C₂×#121	—	2	1	no	—
472	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
473	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
475	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
476	C₂×C₄×D₄	—	2	1	no	—
477	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
478	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
479	#469	—	2	4	no	—
480	#449	—	2	4	no	—
481	#448	—	2	4	no	—
482	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
483	#419	—	2	4	no	—
484	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
485	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
486	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
487	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
488	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
489	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
490	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
491	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
492	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
493	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
494	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
495	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
496	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
497	#394	—	2	1	no	—
498	#392	—	2	1	no	—
499	#390	—	2	1	no	—
500	#390	C₂²×C₁₉	1	1	yes	characteristic
501	#389	C₂²×C₁₉	1	1	yes	characteristic
502	#388	—	2	1	no	—
503	#380	C₂²×C₁₉	1	1	yes	characteristic
504	#340	C₂²×C₁₉	1	1	yes	characteristic
505	#340	C₂²×C₁₉	1	1	yes	characteristic
506	#336	C₂²×C₁₉	1	1	yes	characteristic
507	#336	C₂²×C₁₉	1	1	yes	characteristic
508	C₂×C₁₉	—	4	2	no	—
509	C₂×C₁₉	—	8	1	no	—
510	C₂×C₁₉	—	8	2	no	—
511	C₂×C₁₉	—	16	1	no	—
512	C₂×C₁₉	#2410	1	1	yes	characteristic
513	C₂×C₁₉	#3005	1	1	yes	characteristic
514	C₂×C₁₉	#3010	1	1	yes	characteristic
515	C₂×C₁₉	#3271	1	1	yes	characteristic
516	C₂×C₁₉	#3275	1	1	yes	characteristic
517	C₂×C₁₉	#3321	1	1	yes	characteristic
518	C₂×C₁₉	#3326	1	1	yes	characteristic
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	4	1	no	—
524	C₂×#41	—	4	1	no	—
525	C₂²×Q₈	—	2	1	no	—
526	C₂²×Q₈	—	2	2	no	—
527	C₂²×Q₈	—	2	2	no	—
528	C₂²×Q₈	—	2	2	no	—
529	C₂²×Q₈	—	4	1	no	—
530	C₂²×Q₈	—	4	1	no	—
531	C₂²×Q₈	D₄×C₁₉	1	4	yes	complemented
532	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
545	C₂×SD₁₆	—	2	2	no	—
546	C₂×SD₁₆	—	2	2	no	—
547	C₂×SD₁₆	—	2	2	no	—
548	C₂×SD₁₆	—	2	2	no	—
549	C₂×SD₁₆	—	4	1	no	—
550	C₂×SD₁₆	—	4	1	no	—
551	C₂×D₈	—	2	2	no	—
552	C₂×D₈	—	2	2	no	—
553	C₂×D₈	—	4	1	no	—
554	C₂×M₁₆	—	2	2	no	—
555	C₂×M₁₆	—	2	2	no	—
556	C₂×M₁₆	—	4	1	no	—
557	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
559	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
561	#124	—	2	8	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	C₂²⋊Q₈	—	2	8	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	#121	—	2	8	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	4	1	no	—
573	#121	D₄×C₁₉	1	4	yes	complemented
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×D₄	—	2	8	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	#117	—	2	2	no	—
580	#117	—	4	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	—	2	1	no	—
603	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
604	#106	—	2	2	no	—
605	#103	—	2	2	no	—
606	#103	—	2	2	no	—
607	#103	—	2	2	no	—
608	#103	—	2	2	no	—
609	#103	—	2	2	no	—
610	#103	D₄×C₁₉	1	4	yes	complemented
611	#102	—	2	2	no	—
612	#102	—	2	2	no	—
613	#102	—	2	2	no	—
614	#102	—	4	1	no	—
615	C₂²⋊C₈	—	2	2	no	—
616	C₂²⋊C₈	—	2	2	no	—
617	C₂²⋊C₈	—	4	1	no	—
618	#95	—	2	1	no	—
619	#95	—	2	1	no	—
620	C₁₉	#24455	1	1	yes	characteristic, direct product factor, Sylow
621	C₂⁴	—	2	1	no	—
622	C₂⁴	—	2	1	no	—
623	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
625	#41	—	4	4	no	—
626	#41	—	4	4	no	—
627	#41	—	4	4	no	—
628	#41	—	4	4	no	—
629	C₂×Q₈	—	2	4	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	8	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	4	2	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	4	no	—
642	C₂×Q₈	—	4	4	no	—
643	C₂×Q₈	—	4	4	no	—
644	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
645	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
646	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
647	C₂×Q₈	#41×C₁₉	1	2	yes	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	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	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	4	1	no	—
663	C₂×D₄	—	4	1	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	8	1	no	—
672	C₂×D₄	—	8	1	no	—
673	C₂×D₄	—	8	1	no	—
674	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
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	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
702	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
704	SD₁₆	—	4	4	no	—
705	SD₁₆	—	4	4	no	—
706	D₈	—	4	4	no	—
707	M₁₆	—	4	4	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	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	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	—	8	1	no	—
730	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	8	1	no	—
743	C₂²⋊C₄	—	8	1	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	1	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	4	2	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	1	no	—
764	C₂³	—	4	1	no	—
765	C₂³	—	4	1	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	1	no	—
772	C₂³	—	4	1	no	—
773	C₂³	—	4	1	no	—
774	C₂³	—	4	1	no	—
775	C₂³	C₁₉×#120	1	2	yes	—
776	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	2	no	—
782	Q₈	—	4	8	no	—
783	Q₈	—	4	1	no	—
784	Q₈	—	4	1	no	—
785	Q₈	C₁₉×#121	1	4	yes	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	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	—	8	4	no	—
798	D₄	—	8	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	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	—	4	8	no	—
821	C₂×C₄	—	4	8	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	C₁₉×#120	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
842	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
843	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	4	1	no	—
847	C₈	—	4	1	no	—
848	C₈	—	4	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	1	no	—
869	C₂²	—	8	1	no	—
870	C₂²	—	8	1	no	—
871	C₂²	—	8	1	no	—
872	C₂²	—	8	1	no	—
873	C₂²	—	8	1	no	—
874	C₂²	—	8	1	no	—
875	C₂²	—	8	1	no	—
876	C₂²	—	8	1	no	—
877	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
878	C₂²	D₄²×C₁₉	1	1	yes	characteristic
879	C₂²	C₁₉×#546	1	1	yes	characteristic
880	C₂²	C₁₉×#575	1	1	yes	characteristic
881	C₂²	C₁₉×#575	1	1	yes	characteristic
882	C₂²	C₁₉×#577	1	1	yes	characteristic
883	C₂²	C₁₉×#577	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	4	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	8	1	no	—
893	C₄	—	8	1	no	—
894	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
895	C₄	C₁₉×#534	1	1	yes	characteristic
896	C₄	D₄²×C₁₉	1	1	yes	characteristic
897	C₄	C₁₉×#546	1	1	yes	characteristic
898	C₂	—	4	2	no	—
899	C₂	—	8	1	no	—
900	C₂	—	8	2	no	—
901	C₂	—	16	1	no	—
902	C₂	C₁₉×#2410	1	1	yes	characteristic
903	C₂	C₁₉×#3005	1	1	yes	characteristic
904	C₂	C₁₉×#3010	1	1	yes	characteristic
905	C₂	C₁₉×#3271	1	1	yes	characteristic
906	C₂	C₁₉×#3275	1	1	yes	characteristic
907	C₂	C₁₉×#3321	1	1	yes	characteristic
908	C₂	C₁₉×#3326	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
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
1. C₂×C₁₉×#548	C₂	semidirect
2. C₂×C₁₉×#469	C₂	semidirect
3. C₂×C₁₉×#449	C₂	semidirect
4. C₂×C₁₉×#448	C₂	semidirect
5. C₂×C₁₉×#419	C₂	semidirect
6. C₁₉×#2414	C₂	semidirect
7. C₁₉×#2042	C₂	semidirect
8. C₁₉×#2035	C₂	semidirect
9. C₁₉×#2012	C₂	semidirect
10. C₁₉×#2000	C₂	semidirect
11. C₁₉×#1880	C₂	semidirect
12. C₁₉×#1875	C₂	semidirect
13. C₁₉×#1870	C₂	semidirect
14. C₁₉×#1865	C₂	semidirect
15. C₁₉×#1788	C₂	semidirect
77. C₂²×Q₈×C₁₉	D₄	semidirect
119. C₁₉×#121	D₄	semidirect
156. C₁₉×#103	D₄	semidirect
293. #24455	C₁₉	direct (N × H)
395. C₂×#548	C₂×C₁₉	semidirect
396. C₂×#469	C₂×C₁₉	semidirect
397. C₂×#449	C₂×C₁₉	semidirect
398. C₂×#448	C₂×C₁₉	semidirect
399. C₂×#419	C₂×C₁₉	semidirect
400. #2414	C₂×C₁₉	semidirect
401. #2042	C₂×C₁₉	semidirect
402. #2035	C₂×C₁₉	semidirect
403. #2012	C₂×C₁₉	semidirect
404. #2000	C₂×C₁₉	semidirect
405. #1880	C₂×C₁₉	semidirect
406. #1875	C₂×C₁₉	semidirect
407. #1870	C₂×C₁₉	semidirect
408. #1865	C₂×C₁₉	semidirect
409. #1788	C₂×C₁₉	semidirect
531. C₂²×Q₈	D₄×C₁₉	semidirect
573. #121	D₄×C₁₉	semidirect
610. #103	D₄×C₁₉	semidirect
620. C₁₉	#24455	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×#548	2
C₂×C₁₉×#469	2
C₂×C₁₉×#449	2
C₂×C₁₉×#448	2
C₂×C₁₉×#419	2
C₁₉×#2414	2
C₁₉×#2042	2
C₁₉×#2035	2
C₁₉×#2012	2
C₁₉×#2000	2
C₁₉×#1880	2
C₁₉×#1875	2
C₁₉×#1870	2
C₁₉×#1865	2
C₁₉×#1788	2
#24455	19

Subgroups — C19×#24455 #18030414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24455 #18030414