Subgroups — C₁₉×#14580 #18020539

Order 4864.

1238 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#400	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1443	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1436	C₂	1	1	yes	maximal, characteristic
13	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1434	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1434	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#400	C₄	1	8	yes	complemented
28	C₁₉×#389	—	2	4	no	—
29	C₁₉×#387	—	2	4	no	—
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
49	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
84	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
93	C₂×C₄²×C₁₉	—	2	2	no	—
94	C₂×C₄²×C₁₉	—	2	2	no	—
95	C₂×C₄²×C₁₉	—	2	2	no	—
96	C₂×C₄²×C₁₉	—	2	2	no	—
97	C₂×C₄²×C₁₉	—	2	2	no	—
98	C₂×C₄²×C₁₉	—	4	1	no	—
99	C₂×C₄²×C₁₉	—	4	1	no	—
100	C₂×C₄²×C₁₉	—	4	1	no	—
101	C₂×C₄²×C₁₉	—	4	1	no	—
102	C₁₉×#95	—	2	2	no	—
103	C₁₉×#95	—	2	2	no	—
104	C₁₉×#95	—	2	2	no	—
105	C₁₉×#95	—	2	2	no	—
106	C₁₉×#95	—	2	2	no	—
107	C₁₉×#95	—	2	2	no	—
108	C₁₉×#95	—	2	2	no	—
109	C₁₉×#95	—	4	1	no	—
110	C₁₉×#95	—	4	1	no	—
111	C₁₉×#95	—	4	1	no	—
112	C₁₉×#95	—	4	1	no	—
113	C₁₉×#95	—	4	1	no	—
114	C₁₉×#95	—	4	1	no	—
115	C₁₉×#95	—	4	1	no	—
116	C₁₉×#95	—	4	1	no	—
117	C₁₉×#95	—	4	1	no	—
118	C₁₉×#95	—	4	1	no	—
119	C₁₉×#95	C₂×C₄	1	4	yes	—
120	C₁₉×#95	C₂×C₄	1	4	yes	—
121	C₁₉×#95	C₂×C₄	1	4	yes	—
122	C₁₉×#95	C₂×C₄	1	4	yes	—
123	C₁₉×#95	C₂×C₄	1	4	yes	—
124	C₁₉×#95	D₄	1	4	yes	—
125	C₁₉×#95	Q₈	1	4	yes	—
126	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	1	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
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	1	no	—
215	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
216	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
218	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
219	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
220	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
222	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
226	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
228	C₂²×C₄×C₁₉	#41	1	2	yes	—
229	C₂²×C₄×C₁₉	#41	1	2	yes	—
230	C₂²×C₄×C₁₉	#41	1	2	yes	—
231	C₂²×C₄×C₁₉	#41	1	2	yes	—
232	C₄⋊C₄×C₁₉	—	2	8	no	—
233	C₄⋊C₄×C₁₉	—	2	8	no	—
234	C₄⋊C₄×C₁₉	—	4	4	no	—
235	C₄⋊C₄×C₁₉	—	4	4	no	—
236	C₄⋊C₄×C₁₉	—	4	4	no	—
237	C₄⋊C₄×C₁₉	—	4	4	no	—
238	C₄⋊C₄×C₁₉	—	4	4	no	—
239	C₄⋊C₄×C₁₉	—	4	4	no	—
240	C₄²×C₁₉	—	4	4	no	—
241	C₄²×C₁₉	—	4	4	no	—
242	C₄²×C₁₉	—	4	4	no	—
243	#14580	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
245	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
246	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
247	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
248	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
249	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
250	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
256	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
257	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
258	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	2	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	2	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	2	no	—
288	C₂×C₄×C₁₉	—	2	2	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	2	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	2	no	—
303	C₂×C₄×C₁₉	—	2	2	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	1	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	1	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	1	no	—
325	C₂×C₄×C₁₉	—	4	1	no	—
326	C₂×C₄×C₁₉	—	4	1	no	—
327	C₂×C₄×C₁₉	—	4	1	no	—
328	C₂×C₄×C₁₉	—	4	1	no	—
329	C₂×C₄×C₁₉	—	4	1	no	—
330	C₂×C₄×C₁₉	—	4	1	no	—
331	C₂×C₄×C₁₉	—	4	1	no	—
332	C₂×C₄×C₁₉	—	4	1	no	—
333	C₂×C₄×C₁₉	—	4	1	no	—
334	C₂×C₄×C₁₉	—	4	1	no	—
335	C₂×C₄×C₁₉	—	4	1	no	—
336	C₂×C₄×C₁₉	—	4	1	no	—
337	C₂×C₄×C₁₉	—	4	1	no	—
338	C₂×C₄×C₁₉	—	4	1	no	—
339	C₂×C₄×C₁₉	—	4	1	no	—
340	C₂×C₄×C₁₉	—	4	1	no	—
341	C₂×C₄×C₁₉	—	4	1	no	—
342	C₂×C₄×C₁₉	—	4	1	no	—
343	C₂×C₄×C₁₉	—	4	1	no	—
344	C₂×C₄×C₁₉	—	4	1	no	—
345	C₂×C₄×C₁₉	—	4	1	no	—
346	C₂×C₄×C₁₉	—	4	1	no	—
347	C₂×C₄×C₁₉	—	4	1	no	—
348	C₂×C₄×C₁₉	—	4	1	no	—
349	C₂×C₄×C₁₉	—	4	1	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	—	4	1	no	—
359	C₂×C₄×C₁₉	—	4	1	no	—
360	C₂×C₄×C₁₉	—	4	1	no	—
361	C₂×C₄×C₁₉	—	4	1	no	—
362	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
363	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
364	C₂×#400	C₂×C₁₉	1	1	yes	characteristic
365	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
366	C₂×#387	C₂×C₁₉	1	1	yes	characteristic
367	#1444	C₂×C₁₉	1	1	yes	characteristic
368	#1444	C₂×C₁₉	1	1	yes	characteristic
369	#1444	C₂×C₁₉	1	1	yes	characteristic
370	#1443	C₂×C₁₉	1	1	yes	characteristic
371	#1442	C₂×C₁₉	1	1	yes	characteristic
372	#1436	C₂×C₁₉	1	1	yes	characteristic
373	#1436	C₂×C₁₉	1	1	yes	characteristic
374	#1436	C₂×C₁₉	1	1	yes	characteristic
375	#1436	C₂×C₁₉	1	1	yes	characteristic
376	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
377	#1434	C₂×C₁₉	1	1	yes	characteristic
378	#1434	C₂×C₁₉	1	1	yes	characteristic
379	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
380	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
381	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
382	C₂²×C₁₉	#520	1	1	yes	characteristic
383	C₂²×C₁₉	#520	1	1	yes	characteristic
384	C₂²×C₁₉	#520	1	1	yes	characteristic
385	C₂²×C₁₉	#520	1	1	yes	characteristic
386	C₂²×C₁₉	#535	1	1	yes	characteristic
387	C₂²×C₁₉	#536	1	1	yes	characteristic
388	C₂²×C₁₉	#538	1	1	yes	characteristic
389	C₂²×C₁₉	#539	1	1	yes	characteristic
390	C₂²×C₁₉	#540	1	1	yes	characteristic
391	C₂²×C₁₉	#541	1	1	yes	characteristic
392	C₂²×C₁₉	#541	1	1	yes	characteristic
393	C₂²×C₁₉	#542	1	1	yes	characteristic
394	C₂²×C₁₉	#542	1	1	yes	characteristic
395	C₂²×C₁₉	#542	1	1	yes	characteristic
396	C₂²×C₁₉	#544	1	1	yes	characteristic
397	C₂²×C₁₉	#544	1	1	yes	characteristic
398	C₂²×C₁₉	#546	1	1	yes	characteristic
399	C₂²×C₁₉	#546	1	1	yes	characteristic
400	C₂²×C₁₉	#547	1	1	yes	characteristic
401	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
402	C₂²×C₁₉	#551	1	1	yes	characteristic
403	C₂²×C₁₉	#552	1	1	yes	characteristic
404	C₂²×C₁₉	#552	1	1	yes	characteristic
405	C₂²×C₁₉	#552	1	1	yes	characteristic
406	C₂²×C₁₉	#553	1	1	yes	characteristic
407	C₂²×C₁₉	#554	1	1	yes	characteristic
408	C₂²×C₁₉	#554	1	1	yes	characteristic
409	C₂²×C₁₉	#557	1	1	yes	characteristic
410	C₂²×C₁₉	#560	1	1	yes	characteristic
411	C₂²×C₁₉	#563	1	1	yes	characteristic
412	C₂²×C₁₉	#563	1	1	yes	characteristic
413	C₂²×C₁₉	#563	1	1	yes	characteristic
414	C₄×C₁₉	—	2	4	no	—
415	C₄×C₁₉	—	2	4	no	—
416	C₄×C₁₉	—	4	2	no	—
417	C₄×C₁₉	—	4	2	no	—
418	C₄×C₁₉	—	4	2	no	—
419	C₄×C₁₉	—	4	2	no	—
420	C₄×C₁₉	—	4	2	no	—
421	C₄×C₁₉	—	4	2	no	—
422	C₄×C₁₉	—	4	2	no	—
423	C₄×C₁₉	—	4	2	no	—
424	C₄×C₁₉	—	4	2	no	—
425	C₄×C₁₉	—	4	2	no	—
426	C₄×C₁₉	—	4	2	no	—
427	C₄×C₁₉	—	8	1	no	—
428	C₄×C₁₉	—	8	1	no	—
429	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
432	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
438	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
439	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
440	#400	C₄×C₁₉	1	8	yes	complemented
441	#389	—	2	4	no	—
442	#387	—	2	4	no	—
443	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
444	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
447	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
449	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
450	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
451	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
454	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
455	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
463	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
465	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
466	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
467	C₂×C₁₉	#2326	1	1	yes	characteristic
468	C₂×C₁₉	#2330	1	1	yes	characteristic
469	C₂×C₁₉	#2334	1	1	yes	characteristic
470	C₂×C₁₉	#2359	1	1	yes	characteristic
471	C₂×C₁₉	#2360	1	1	yes	characteristic
472	C₂×C₁₉	#2370	1	1	yes	characteristic
473	C₂×C₁₉	#2383	1	1	yes	characteristic
474	C₂×C₁₉	#2698	1	1	yes	characteristic
475	C₂×C₁₉	#2703	1	1	yes	characteristic
476	C₂×C₁₉	#2713	1	1	yes	characteristic
477	C₂×C₁₉	#2720	1	1	yes	characteristic
478	C₂×C₁₉	#2738	1	1	yes	characteristic
479	C₂×C₁₉	#2742	1	1	yes	characteristic
480	C₂×C₁₉	#2766	1	1	yes	characteristic
481	C₂×C₁₉	#2774	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	—	2	2	no	—
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	2	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	4	1	no	—
510	C₂×C₄⋊C₄	—	4	1	no	—
511	C₂×C₄⋊C₄	—	4	1	no	—
512	C₂×C₄⋊C₄	—	4	1	no	—
513	C₂×C₄⋊C₄	—	4	1	no	—
514	C₂×C₄⋊C₄	—	4	1	no	—
515	C₂×C₄⋊C₄	—	4	1	no	—
516	C₂×C₄⋊C₄	—	4	1	no	—
517	C₂×C₄⋊C₄	—	4	1	no	—
518	C₂×C₄⋊C₄	—	4	1	no	—
519	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
520	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
521	C₂×C₄²	—	2	2	no	—
522	C₂×C₄²	—	2	2	no	—
523	C₂×C₄²	—	2	2	no	—
524	C₂×C₄²	—	2	2	no	—
525	C₂×C₄²	—	2	2	no	—
526	C₂×C₄²	—	4	1	no	—
527	C₂×C₄²	—	4	1	no	—
528	C₂×C₄²	—	4	1	no	—
529	C₂×C₄²	—	4	1	no	—
530	#95	—	2	2	no	—
531	#95	—	2	2	no	—
532	#95	—	2	2	no	—
533	#95	—	2	2	no	—
534	#95	—	2	2	no	—
535	#95	—	2	2	no	—
536	#95	—	2	2	no	—
537	#95	—	4	1	no	—
538	#95	—	4	1	no	—
539	#95	—	4	1	no	—
540	#95	—	4	1	no	—
541	#95	—	4	1	no	—
542	#95	—	4	1	no	—
543	#95	—	4	1	no	—
544	#95	—	4	1	no	—
545	#95	—	4	1	no	—
546	#95	—	4	1	no	—
547	#95	C₂×C₄×C₁₉	1	4	yes	—
548	#95	C₂×C₄×C₁₉	1	4	yes	—
549	#95	C₂×C₄×C₁₉	1	4	yes	—
550	#95	C₂×C₄×C₁₉	1	4	yes	—
551	#95	C₂×C₄×C₁₉	1	4	yes	—
552	#95	D₄×C₁₉	1	4	yes	—
553	#95	Q₈×C₁₉	1	4	yes	—
554	C₁₉	#14580	1	1	yes	characteristic, direct product factor, Sylow
555	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
645	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
646	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
647	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
648	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
649	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
650	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
651	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
652	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
653	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
654	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
655	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
656	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
657	C₂²×C₄	#41×C₁₉	1	2	yes	—
658	C₂²×C₄	#41×C₁₉	1	2	yes	—
659	C₂²×C₄	#41×C₁₉	1	2	yes	—
660	C₂²×C₄	#41×C₁₉	1	2	yes	—
661	C₄⋊C₄	—	2	8	no	—
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	4	4	no	—
664	C₄⋊C₄	—	4	4	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄²	—	4	4	no	—
670	C₄²	—	4	4	no	—
671	C₄²	—	4	4	no	—
672	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
673	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
674	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
675	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
676	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
677	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
678	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
679	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
684	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
685	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
686	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
791	C₂×C₄	C₄×Q₈×C₁₉	1	4	yes	—
792	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
793	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
794	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
795	C₂²	C₁₉×#520	1	1	yes	characteristic
796	C₂²	C₁₉×#520	1	1	yes	characteristic
797	C₂²	C₁₉×#520	1	1	yes	characteristic
798	C₂²	C₁₉×#520	1	1	yes	characteristic
799	C₂²	C₁₉×#535	1	1	yes	characteristic
800	C₂²	C₁₉×#536	1	1	yes	characteristic
801	C₂²	C₁₉×#538	1	1	yes	characteristic
802	C₂²	C₁₉×#539	1	1	yes	characteristic
803	C₂²	C₁₉×#540	1	1	yes	characteristic
804	C₂²	C₁₉×#541	1	1	yes	characteristic
805	C₂²	C₁₉×#541	1	1	yes	characteristic
806	C₂²	C₁₉×#542	1	1	yes	characteristic
807	C₂²	C₁₉×#542	1	1	yes	characteristic
808	C₂²	C₁₉×#542	1	1	yes	characteristic
809	C₂²	C₁₉×#544	1	1	yes	characteristic
810	C₂²	C₁₉×#544	1	1	yes	characteristic
811	C₂²	C₁₉×#546	1	1	yes	characteristic
812	C₂²	C₁₉×#546	1	1	yes	characteristic
813	C₂²	C₁₉×#547	1	1	yes	characteristic
814	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
815	C₂²	C₁₉×#551	1	1	yes	characteristic
816	C₂²	C₁₉×#552	1	1	yes	characteristic
817	C₂²	C₁₉×#552	1	1	yes	characteristic
818	C₂²	C₁₉×#552	1	1	yes	characteristic
819	C₂²	C₁₉×#553	1	1	yes	characteristic
820	C₂²	C₁₉×#554	1	1	yes	characteristic
821	C₂²	C₁₉×#554	1	1	yes	characteristic
822	C₂²	C₁₉×#557	1	1	yes	characteristic
823	C₂²	C₁₉×#560	1	1	yes	characteristic
824	C₂²	C₁₉×#563	1	1	yes	characteristic
825	C₂²	C₁₉×#563	1	1	yes	characteristic
826	C₂²	C₁₉×#563	1	1	yes	characteristic
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	8	1	no	—
841	C₄	—	8	1	no	—
842	C₂	C₁₉×#2326	1	1	yes	characteristic
843	C₂	C₁₉×#2330	1	1	yes	characteristic
844	C₂	C₁₉×#2334	1	1	yes	characteristic
845	C₂	C₁₉×#2359	1	1	yes	characteristic
846	C₂	C₁₉×#2360	1	1	yes	characteristic
847	C₂	C₁₉×#2370	1	1	yes	characteristic
848	C₂	C₁₉×#2383	1	1	yes	characteristic
849	C₂	C₁₉×#2698	1	1	yes	characteristic
850	C₂	C₁₉×#2703	1	1	yes	characteristic
851	C₂	C₁₉×#2713	1	1	yes	characteristic
852	C₂	C₁₉×#2720	1	1	yes	characteristic
853	C₂	C₁₉×#2738	1	1	yes	characteristic
854	C₂	C₁₉×#2742	1	1	yes	characteristic
855	C₂	C₁₉×#2766	1	1	yes	characteristic
856	C₂	C₁₉×#2774	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
27. C₁₉×#400	C₄	semidirect
243. #14580	C₁₉	direct (N × H)
440. #400	C₄×C₁₉	semidirect
554. C₁₉	#14580	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×#400	2
C₂×C₁₉×#389	2
C₂×C₁₉×#387	2
C₁₉×#1444	2
C₁₉×#1443	2
C₁₉×#1442	2
C₁₉×#1436	2
C₁₉×C₄⋊#95	2
C₁₉×#1434	2
#14580	19

Subgroups — C19×#14580 #18020539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14580 #18020539