Subgroups — C₁₉×#16296 #18022255

Order 4864.

1530 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#396	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#396	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#393	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1440	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1439	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1437	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×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×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#396	—	2	4	no	—
34	C₁₉×#396	—	2	4	no	—
35	C₁₉×#395	—	2	4	no	—
36	C₁₉×#393	—	2	4	no	—
37	C₁₉×#391	—	2	4	no	—
38	C₁₉×#387	—	2	4	no	—
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	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
57	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	—	2	2	no	—
59	C₂²×Q₈×C₁₉	—	2	2	no	—
60	C₂²×Q₈×C₁₉	—	2	2	no	—
61	C₂²×Q₈×C₁₉	—	2	2	no	—
62	C₂²×Q₈×C₁₉	—	2	2	no	—
63	C₂²×Q₈×C₁₉	—	4	1	no	—
64	C₂²×Q₈×C₁₉	—	4	1	no	—
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	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
123	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	complemented
124	C₂×C₄²×C₁₉	—	2	2	no	—
125	C₂×C₄²×C₁₉	—	2	2	no	—
126	C₂×C₄²×C₁₉	—	4	1	no	—
127	C₁₉×#95	—	2	2	no	—
128	C₁₉×#95	—	2	2	no	—
129	C₁₉×#95	—	2	2	no	—
130	C₁₉×#95	—	2	2	no	—
131	C₁₉×#95	—	2	2	no	—
132	C₁₉×#95	—	2	2	no	—
133	C₁₉×#95	—	2	2	no	—
134	C₁₉×#95	—	2	2	no	—
135	C₁₉×#95	—	2	2	no	—
136	C₁₉×#95	—	2	2	no	—
137	C₁₉×#95	—	2	2	no	—
138	C₁₉×#95	—	2	2	no	—
139	C₁₉×#95	—	4	1	no	—
140	C₁₉×#95	—	4	1	no	—
141	C₁₉×#95	—	4	1	no	—
142	C₁₉×#95	—	4	1	no	—
143	C₁₉×#95	D₄	1	4	yes	—
144	C₁₉×#95	D₄	1	4	yes	—
145	C₂⁴×C₁₉	—	2	1	no	—
146	C₂⁴×C₁₉	—	2	1	no	—
147	C₂⁴×C₁₉	—	2	1	no	—
148	C₂⁴×C₁₉	—	2	1	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	C₂⁴×C₁₉	—	2	1	no	—
151	C₂⁴×C₁₉	—	2	1	no	—
152	C₂⁴×C₁₉	—	2	1	no	—
153	C₂⁴×C₁₉	—	2	1	no	—
154	C₂⁴×C₁₉	—	2	1	no	—
155	C₂⁴×C₁₉	—	2	1	no	—
156	C₂⁴×C₁₉	—	2	1	no	—
157	C₂⁴×C₁₉	—	2	1	no	—
158	C₂⁴×C₁₉	—	2	1	no	—
159	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
160	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂×Q₈×C₁₉	—	2	8	no	—
162	C₂×Q₈×C₁₉	—	4	4	no	—
163	C₂×Q₈×C₁₉	—	4	4	no	—
164	C₂×Q₈×C₁₉	—	4	4	no	—
165	C₂×Q₈×C₁₉	—	4	4	no	—
166	C₂×Q₈×C₁₉	—	4	4	no	—
167	C₂×Q₈×C₁₉	—	4	4	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	—	2	1	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	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	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	—	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	—	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	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	1	no	—
247	C₂²×C₄×C₁₉	—	2	1	no	—
248	C₂²×C₄×C₁₉	—	2	1	no	—
249	C₂²×C₄×C₁₉	—	2	1	no	—
250	C₂²×C₄×C₁₉	—	2	1	no	—
251	C₂²×C₄×C₁₉	—	2	1	no	—
252	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
262	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
263	C₂²×C₄×C₁₉	#41	1	2	yes	—
264	C₂²×C₄×C₁₉	#41	1	2	yes	—
265	C₂²×C₄×C₁₉	#41	1	2	yes	—
266	C₄⋊C₄×C₁₉	—	2	8	no	—
267	C₄⋊C₄×C₁₉	—	4	4	no	—
268	C₄⋊C₄×C₁₉	—	4	4	no	—
269	C₄⋊C₄×C₁₉	—	4	4	no	—
270	C₄⋊C₄×C₁₉	—	4	4	no	—
271	C₄⋊C₄×C₁₉	—	4	4	no	—
272	C₄⋊C₄×C₁₉	—	4	4	no	—
273	C₄⋊C₄×C₁₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₉	—	4	4	no	—
275	C₂²⋊C₄×C₁₉	—	4	4	no	—
276	C₂²⋊C₄×C₁₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₉	—	4	4	no	—
278	C₂²⋊C₄×C₁₉	—	4	4	no	—
279	C₂²⋊C₄×C₁₉	—	4	4	no	—
280	C₂²⋊C₄×C₁₉	—	4	4	no	—
281	C₄²×C₁₉	—	4	4	no	—
282	#16296	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂³×C₁₉	—	2	2	no	—
284	C₂³×C₁₉	—	2	2	no	—
285	C₂³×C₁₉	—	2	2	no	—
286	C₂³×C₁₉	—	2	2	no	—
287	C₂³×C₁₉	—	2	2	no	—
288	C₂³×C₁₉	—	2	2	no	—
289	C₂³×C₁₉	—	2	2	no	—
290	C₂³×C₁₉	—	4	1	no	—
291	C₂³×C₁₉	—	4	1	no	—
292	C₂³×C₁₉	—	4	1	no	—
293	C₂³×C₁₉	—	4	1	no	—
294	C₂³×C₁₉	—	4	1	no	—
295	C₂³×C₁₉	—	4	1	no	—
296	C₂³×C₁₉	—	4	1	no	—
297	C₂³×C₁₉	—	4	1	no	—
298	C₂³×C₁₉	—	4	1	no	—
299	C₂³×C₁₉	—	4	1	no	—
300	C₂³×C₁₉	—	4	1	no	—
301	C₂³×C₁₉	—	4	1	no	—
302	C₂³×C₁₉	—	4	1	no	—
303	C₂³×C₁₉	—	4	1	no	—
304	C₂³×C₁₉	—	4	1	no	—
305	C₂³×C₁₉	—	4	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	—	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	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
320	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
322	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
323	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
324	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
325	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
328	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
330	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
331	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
332	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
333	Q₈×C₁₉	—	4	16	no	—
334	C₂×C₄×C₁₉	—	2	2	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	2	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	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	2	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
347	C₂×C₄×C₁₉	—	2	2	no	—
348	C₂×C₄×C₁₉	—	2	2	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	2	no	—
355	C₂×C₄×C₁₉	—	2	2	no	—
356	C₂×C₄×C₁₉	—	2	2	no	—
357	C₂×C₄×C₁₉	—	2	2	no	—
358	C₂×C₄×C₁₉	—	2	2	no	—
359	C₂×C₄×C₁₉	—	2	2	no	—
360	C₂×C₄×C₁₉	—	2	2	no	—
361	C₂×C₄×C₁₉	—	2	2	no	—
362	C₂×C₄×C₁₉	—	2	2	no	—
363	C₂×C₄×C₁₉	—	2	2	no	—
364	C₂×C₄×C₁₉	—	2	2	no	—
365	C₂×C₄×C₁₉	—	2	2	no	—
366	C₂×C₄×C₁₉	—	2	2	no	—
367	C₂×C₄×C₁₉	—	2	2	no	—
368	C₂×C₄×C₁₉	—	2	2	no	—
369	C₂×C₄×C₁₉	—	2	2	no	—
370	C₂×C₄×C₁₉	—	2	2	no	—
371	C₂×C₄×C₁₉	—	2	2	no	—
372	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
385	C₂×C₄×C₁₉	—	4	1	no	—
386	C₂×C₄×C₁₉	—	4	1	no	—
387	C₂×C₄×C₁₉	—	4	1	no	—
388	C₂×C₄×C₁₉	—	4	1	no	—
389	C₂×C₄×C₁₉	—	4	1	no	—
390	C₂×C₄×C₁₉	—	4	1	no	—
391	C₂×C₄×C₁₉	—	4	1	no	—
392	C₂×C₄×C₁₉	—	4	1	no	—
393	C₂×C₄×C₁₉	—	4	1	no	—
394	C₂×C₄×C₁₉	—	4	1	no	—
395	C₂×C₄×C₁₉	—	4	1	no	—
396	C₂×C₄×C₁₉	—	4	1	no	—
397	C₂×C₄×C₁₉	—	4	1	no	—
398	C₂×C₄×C₁₉	—	4	1	no	—
399	C₂×C₄×C₁₉	—	4	1	no	—
400	C₂×C₄×C₁₉	—	4	1	no	—
401	C₂×C₄×C₁₉	—	4	1	no	—
402	C₂×C₄×C₁₉	—	4	1	no	—
403	C₂×C₄×C₁₉	—	4	1	no	—
404	C₂×C₄×C₁₉	—	4	1	no	—
405	C₂×C₄×C₁₉	—	4	1	no	—
406	C₂×C₄×C₁₉	—	4	1	no	—
407	C₂×C₄×C₁₉	—	4	1	no	—
408	C₂×C₄×C₁₉	—	4	1	no	—
409	C₂×C₄×C₁₉	—	4	1	no	—
410	C₂×C₄×C₁₉	—	4	1	no	—
411	C₂×C₄×C₁₉	—	4	1	no	—
412	C₂×C₄×C₁₉	—	4	1	no	—
413	C₂×C₄×C₁₉	—	4	1	no	—
414	C₂×C₄×C₁₉	—	4	1	no	—
415	C₂×C₄×C₁₉	—	4	1	no	—
416	C₂×C₄×C₁₉	—	4	1	no	—
417	C₂×C₄×C₁₉	—	4	1	no	—
418	C₂×C₄×C₁₉	—	4	1	no	—
419	C₂×C₄×C₁₉	—	4	1	no	—
420	C₂×C₄×C₁₉	—	4	1	no	—
421	C₂×C₄×C₁₉	—	4	1	no	—
422	C₂×C₄×C₁₉	—	4	1	no	—
423	C₂×C₄×C₁₉	—	4	1	no	—
424	C₂×C₄×C₁₉	—	4	1	no	—
425	C₂×C₄×C₁₉	—	4	1	no	—
426	C₂×C₄×C₁₉	—	4	1	no	—
427	C₂×C₄×C₁₉	—	4	1	no	—
428	C₂×C₄×C₁₉	—	4	1	no	—
429	C₂×C₄×C₁₉	—	4	1	no	—
430	C₂×C₄×C₁₉	—	4	1	no	—
431	C₂×C₄×C₁₉	#121	1	4	yes	—
432	C₂×#396	C₂×C₁₉	1	1	yes	characteristic
433	C₂×#396	C₂×C₁₉	1	1	yes	characteristic
434	C₂×#395	C₂×C₁₉	1	1	yes	characteristic, complemented
435	C₂×#393	C₂×C₁₉	1	1	yes	characteristic
436	C₂×#391	C₂×C₁₉	1	1	yes	characteristic, complemented
437	C₂×#387	C₂×C₁₉	1	1	yes	characteristic, complemented
438	#1444	C₂×C₁₉	1	1	yes	characteristic, complemented
439	#1442	C₂×C₁₉	1	1	yes	characteristic, complemented
440	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
441	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
442	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
443	#1440	C₂×C₁₉	1	1	yes	characteristic
444	#1439	C₂×C₁₉	1	1	yes	characteristic
445	#1439	C₂×C₁₉	1	1	yes	characteristic
446	#1437	C₂×C₁₉	1	1	yes	characteristic
447	C₂²×C₁₉	—	4	2	no	—
448	C₂²×C₁₉	—	4	2	no	—
449	C₂²×C₁₉	—	4	2	no	—
450	C₂²×C₁₉	—	4	2	no	—
451	C₂²×C₁₉	—	4	2	no	—
452	C₂²×C₁₉	—	4	2	no	—
453	C₂²×C₁₉	—	4	2	no	—
454	C₂²×C₁₉	—	8	1	no	—
455	C₂²×C₁₉	—	8	1	no	—
456	C₂²×C₁₉	—	8	1	no	—
457	C₂²×C₁₉	—	8	1	no	—
458	C₂²×C₁₉	—	8	1	no	—
459	C₂²×C₁₉	—	8	1	no	—
460	C₂²×C₁₉	—	8	1	no	—
461	C₂²×C₁₉	—	8	1	no	—
462	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
463	C₂²×C₁₉	#525	1	1	yes	characteristic
464	C₂²×C₁₉	#533	1	1	yes	characteristic
465	C₂²×C₁₉	#535	1	1	yes	characteristic
466	C₂²×C₁₉	#536	1	1	yes	characteristic
467	C₂²×C₁₉	#536	1	1	yes	characteristic
468	C₂²×C₁₉	#537	1	1	yes	characteristic
469	C₂²×C₁₉	#537	1	1	yes	characteristic
470	C₂²×C₁₉	#537	1	1	yes	characteristic
471	C₂²×C₁₉	#538	1	1	yes	characteristic
472	C₂²×C₁₉	#538	1	1	yes	characteristic
473	C₂²×C₁₉	#541	1	1	yes	characteristic
474	C₂²×C₁₉	#541	1	1	yes	characteristic
475	C₂²×C₁₉	#542	1	1	yes	characteristic
476	C₂²×C₁₉	#542	1	1	yes	characteristic
477	C₂²×C₁₉	#542	1	1	yes	characteristic
478	C₂²×C₁₉	#542	1	1	yes	characteristic
479	C₂²×C₁₉	#543	1	1	yes	characteristic
480	C₂²×C₁₉	#544	1	1	yes	characteristic
481	C₂²×C₁₉	D₄²	1	1	yes	characteristic
482	C₂²×C₁₉	D₄²	1	1	yes	characteristic
483	C₂²×C₁₉	#546	1	1	yes	characteristic
484	C₂²×C₁₉	#546	1	1	yes	characteristic
485	C₂²×C₁₉	#546	1	1	yes	characteristic
486	C₂²×C₁₉	#547	1	1	yes	characteristic
487	C₂²×C₁₉	#548	1	1	yes	characteristic
488	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
489	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
490	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
491	C₂²×C₁₉	#554	1	1	yes	characteristic
492	C₂²×C₁₉	#556	1	1	yes	characteristic
493	C₂²×C₁₉	#562	1	1	yes	characteristic
494	C₂²×C₁₉	#562	1	1	yes	characteristic
495	C₂²×C₁₉	#563	1	1	yes	characteristic
496	C₂²×C₁₉	#563	1	1	yes	characteristic
497	C₄×C₁₉	—	2	4	no	—
498	C₄×C₁₉	—	4	2	no	—
499	C₄×C₁₉	—	4	2	no	—
500	C₄×C₁₉	—	4	2	no	—
501	C₄×C₁₉	—	4	2	no	—
502	C₄×C₁₉	—	4	2	no	—
503	C₄×C₁₉	—	4	2	no	—
504	C₄×C₁₉	—	4	2	no	—
505	C₄×C₁₉	—	4	2	no	—
506	C₄×C₁₉	—	4	2	no	—
507	C₄×C₁₉	—	4	2	no	—
508	C₄×C₁₉	—	4	2	no	—
509	C₄×C₁₉	—	8	1	no	—
510	C₄×C₁₉	—	8	1	no	—
511	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
512	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
513	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
514	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
515	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
516	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
517	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
518	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
519	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
520	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
521	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
522	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
523	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
524	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
525	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
526	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
527	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
528	#396	—	2	4	no	—
529	#396	—	2	4	no	—
530	#395	—	2	4	no	—
531	#393	—	2	4	no	—
532	#391	—	2	4	no	—
533	#387	—	2	4	no	—
534	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
535	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
536	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
537	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
538	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
539	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
540	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
541	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
542	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
543	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
544	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
545	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
546	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
547	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
548	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
549	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
550	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
551	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
552	C₂×C₁₉	—	8	2	no	—
553	C₂×C₁₉	#2424	1	1	yes	characteristic
554	C₂×C₁₉	#2429	1	1	yes	characteristic
555	C₂×C₁₉	#2465	1	1	yes	characteristic
556	C₂×C₁₉	#2620	1	1	yes	characteristic
557	C₂×C₁₉	#2637	1	1	yes	characteristic
558	C₂×C₁₉	#2665	1	1	yes	characteristic
559	C₂×C₁₉	#2672	1	1	yes	characteristic
560	C₂×C₁₉	#2676	1	1	yes	characteristic
561	C₂×C₁₉	#2677	1	1	yes	characteristic
562	C₂×C₁₉	#2683	1	1	yes	characteristic
563	C₂×C₁₉	#2692	1	1	yes	characteristic
564	C₂×C₁₉	#2704	1	1	yes	characteristic
565	C₂×C₁₉	#2715	1	1	yes	characteristic
566	C₂×C₁₉	#2716	1	1	yes	characteristic
567	C₂×C₁₉	#2831	1	1	yes	characteristic
568	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
569	C₂²×Q₈	—	2	2	no	—
570	C₂²×Q₈	—	2	2	no	—
571	C₂²×Q₈	—	2	2	no	—
572	C₂²×Q₈	—	2	2	no	—
573	C₂²×Q₈	—	2	2	no	—
574	C₂²×Q₈	—	4	1	no	—
575	C₂²×Q₈	—	4	1	no	—
576	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	—	2	2	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	—	2	2	no	—
598	C₂×C₄⋊C₄	—	2	2	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	—	2	2	no	—
604	C₂×C₄⋊C₄	—	4	1	no	—
605	C₂×C₄⋊C₄	—	4	1	no	—
606	C₂×C₄⋊C₄	—	4	1	no	—
607	C₂×C₄⋊C₄	—	4	1	no	—
608	C₂×C₄⋊C₄	—	4	1	no	—
609	C₂×C₄⋊C₄	—	4	1	no	—
610	C₂×C₄⋊C₄	—	4	1	no	—
611	C₂×C₄⋊C₄	—	4	1	no	—
612	C₂×C₄⋊C₄	—	4	1	no	—
613	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
614	C₂×C₂²⋊C₄	—	2	2	no	—
615	C₂×C₂²⋊C₄	—	2	2	no	—
616	C₂×C₂²⋊C₄	—	2	2	no	—
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₂²⋊C₄	—	2	2	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₂²⋊C₄	—	2	2	no	—
621	C₂×C₂²⋊C₄	—	2	2	no	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₂²⋊C₄	—	2	2	no	—
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	4	1	no	—
627	C₂×C₂²⋊C₄	—	4	1	no	—
628	C₂×C₂²⋊C₄	—	4	1	no	—
629	C₂×C₂²⋊C₄	—	4	1	no	—
630	C₂×C₂²⋊C₄	—	4	1	no	—
631	C₂×C₂²⋊C₄	—	4	1	no	—
632	C₂×C₂²⋊C₄	—	4	1	no	—
633	C₂×C₂²⋊C₄	—	4	1	no	—
634	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	complemented
635	C₂×C₄²	—	2	2	no	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	—	4	1	no	—
638	#95	—	2	2	no	—
639	#95	—	2	2	no	—
640	#95	—	2	2	no	—
641	#95	—	2	2	no	—
642	#95	—	2	2	no	—
643	#95	—	2	2	no	—
644	#95	—	2	2	no	—
645	#95	—	2	2	no	—
646	#95	—	2	2	no	—
647	#95	—	2	2	no	—
648	#95	—	2	2	no	—
649	#95	—	2	2	no	—
650	#95	—	4	1	no	—
651	#95	—	4	1	no	—
652	#95	—	4	1	no	—
653	#95	—	4	1	no	—
654	#95	D₄×C₁₉	1	4	yes	—
655	#95	D₄×C₁₉	1	4	yes	—
656	C₁₉	#16296	1	1	yes	characteristic, direct product factor, Sylow
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	1	no	—
659	C₂⁴	—	2	1	no	—
660	C₂⁴	—	2	1	no	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	2	1	no	—
663	C₂⁴	—	2	1	no	—
664	C₂⁴	—	2	1	no	—
665	C₂⁴	—	2	1	no	—
666	C₂⁴	—	2	1	no	—
667	C₂⁴	—	2	1	no	—
668	C₂⁴	—	2	1	no	—
669	C₂⁴	—	2	1	no	—
670	C₂⁴	—	2	1	no	—
671	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
672	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
673	C₂×Q₈	—	2	8	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	4	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	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	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
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	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
765	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
766	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
767	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
769	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
770	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
771	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
772	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
773	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
774	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
775	C₂²×C₄	#41×C₁₉	1	2	yes	—
776	C₂²×C₄	#41×C₁₉	1	2	yes	—
777	C₂²×C₄	#41×C₁₉	1	2	yes	—
778	C₄⋊C₄	—	2	8	no	—
779	C₄⋊C₄	—	4	4	no	—
780	C₄⋊C₄	—	4	4	no	—
781	C₄⋊C₄	—	4	4	no	—
782	C₄⋊C₄	—	4	4	no	—
783	C₄⋊C₄	—	4	4	no	—
784	C₄⋊C₄	—	4	4	no	—
785	C₄⋊C₄	—	4	4	no	—
786	C₂²⋊C₄	—	4	4	no	—
787	C₂²⋊C₄	—	4	4	no	—
788	C₂²⋊C₄	—	4	4	no	—
789	C₂²⋊C₄	—	4	4	no	—
790	C₂²⋊C₄	—	4	4	no	—
791	C₂²⋊C₄	—	4	4	no	—
792	C₂²⋊C₄	—	4	4	no	—
793	C₄²	—	4	4	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	1	no	—
810	C₂³	—	4	1	no	—
811	C₂³	—	4	1	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	1	no	—
815	C₂³	—	4	1	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
830	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
832	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
833	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
834	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
835	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
836	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
838	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
839	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
840	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
841	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
842	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
843	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
844	Q₈	—	4	16	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	1	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	1	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	1	no	—
940	C₂×C₄	—	4	1	no	—
941	C₂×C₄	—	4	1	no	—
942	C₂×C₄	C₁₉×#121	1	4	yes	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	8	1	no	—
951	C₂²	—	8	1	no	—
952	C₂²	—	8	1	no	—
953	C₂²	—	8	1	no	—
954	C₂²	—	8	1	no	—
955	C₂²	—	8	1	no	—
956	C₂²	—	8	1	no	—
957	C₂²	—	8	1	no	—
958	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
959	C₂²	C₁₉×#525	1	1	yes	characteristic
960	C₂²	C₁₉×#533	1	1	yes	characteristic
961	C₂²	C₁₉×#535	1	1	yes	characteristic
962	C₂²	C₁₉×#536	1	1	yes	characteristic
963	C₂²	C₁₉×#536	1	1	yes	characteristic
964	C₂²	C₁₉×#537	1	1	yes	characteristic
965	C₂²	C₁₉×#537	1	1	yes	characteristic
966	C₂²	C₁₉×#537	1	1	yes	characteristic
967	C₂²	C₁₉×#538	1	1	yes	characteristic
968	C₂²	C₁₉×#538	1	1	yes	characteristic
969	C₂²	C₁₉×#541	1	1	yes	characteristic
970	C₂²	C₁₉×#541	1	1	yes	characteristic
971	C₂²	C₁₉×#542	1	1	yes	characteristic
972	C₂²	C₁₉×#542	1	1	yes	characteristic
973	C₂²	C₁₉×#542	1	1	yes	characteristic
974	C₂²	C₁₉×#542	1	1	yes	characteristic
975	C₂²	C₁₉×#543	1	1	yes	characteristic
976	C₂²	C₁₉×#544	1	1	yes	characteristic
977	C₂²	D₄²×C₁₉	1	1	yes	characteristic
978	C₂²	D₄²×C₁₉	1	1	yes	characteristic
979	C₂²	C₁₉×#546	1	1	yes	characteristic
980	C₂²	C₁₉×#546	1	1	yes	characteristic
981	C₂²	C₁₉×#546	1	1	yes	characteristic
982	C₂²	C₁₉×#547	1	1	yes	characteristic
983	C₂²	C₁₉×#548	1	1	yes	characteristic
984	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
985	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
986	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
987	C₂²	C₁₉×#554	1	1	yes	characteristic
988	C₂²	C₁₉×#556	1	1	yes	characteristic
989	C₂²	C₁₉×#562	1	1	yes	characteristic
990	C₂²	C₁₉×#562	1	1	yes	characteristic
991	C₂²	C₁₉×#563	1	1	yes	characteristic
992	C₂²	C₁₉×#563	1	1	yes	characteristic
993	C₄	—	2	4	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	8	1	no	—
1006	C₄	—	8	1	no	—
1007	C₂	—	8	2	no	—
1008	C₂	C₁₉×#2424	1	1	yes	characteristic
1009	C₂	C₁₉×#2429	1	1	yes	characteristic
1010	C₂	C₁₉×#2465	1	1	yes	characteristic
1011	C₂	C₁₉×#2620	1	1	yes	characteristic
1012	C₂	C₁₉×#2637	1	1	yes	characteristic
1013	C₂	C₁₉×#2665	1	1	yes	characteristic
1014	C₂	C₁₉×#2672	1	1	yes	characteristic
1015	C₂	C₁₉×#2676	1	1	yes	characteristic
1016	C₂	C₁₉×#2677	1	1	yes	characteristic
1017	C₂	C₁₉×#2683	1	1	yes	characteristic
1018	C₂	C₁₉×#2692	1	1	yes	characteristic
1019	C₂	C₁₉×#2704	1	1	yes	characteristic
1020	C₂	C₁₉×#2715	1	1	yes	characteristic
1021	C₂	C₁₉×#2716	1	1	yes	characteristic
1022	C₂	C₁₉×#2831	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#395	C₂	semidirect
5. C₂×C₁₉×#391	C₂	semidirect
6. C₂×C₁₉×#387	C₂	semidirect
7. C₁₉×#1444	C₂	semidirect
8. C₁₉×#1442	C₂	semidirect
9. C₁₉×#1441	C₂	semidirect
10. C₁₉×#1441	C₂	semidirect
11. C₁₉×#1441	C₂	semidirect
123. C₂×C₂²⋊C₄×C₁₉	Q₈	semidirect
282. #16296	C₁₉	direct (N × H)
434. C₂×#395	C₂×C₁₉	semidirect
436. C₂×#391	C₂×C₁₉	semidirect
437. C₂×#387	C₂×C₁₉	semidirect
438. #1444	C₂×C₁₉	semidirect
439. #1442	C₂×C₁₉	semidirect
440. #1441	C₂×C₁₉	semidirect
441. #1441	C₂×C₁₉	semidirect
442. #1441	C₂×C₁₉	semidirect
634. C₂×C₂²⋊C₄	Q₈×C₁₉	semidirect
656. C₁₉	#16296	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×#396	2
C₂×C₁₉×#395	2
C₂×C₁₉×#393	2
C₂×C₁₉×#391	2
C₂×C₁₉×#387	2
C₁₉×#1444	2
C₁₉×#1442	2
C₁₉×#1441	2
C₁₉×#1440	2
C₁₉×#1439	2
C₁₉×#1437	2
#16296	19

Subgroups — C19×#16296 #18022255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16296 #18022255