Subgroups — C₁₉×#16261 #18022220

Order 4864.

2402 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#396	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#394	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1444	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1441	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1438	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1438	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	4	no	—
16	C₂×C₁₉×#121	—	2	8	no	—
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	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
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	2	yes	—
30	C₁₉×#396	—	2	8	no	—
31	C₁₉×#394	—	2	4	no	—
32	C₁₉×#394	—	2	8	no	—
33	C₁₉×#385	—	2	4	no	—
34	C₁₉×#380	—	2	4	no	—
35	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#95	C₂²	1	2	yes	—
37	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#95	C₂²	1	2	yes	—
40	C₂×C₁₉×#95	C₂²	1	2	yes	—
41	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₂⁵×C₁₉	C₂³	1	2	yes	—
43	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	4	2	no	—
54	C₂²×D₄×C₁₉	—	4	2	no	—
55	C₂²×D₄×C₁₉	—	4	2	no	—
56	C₂³×C₄×C₁₉	—	2	2	no	—
57	C₂³×C₄×C₁₉	—	2	4	no	—
58	C₂³×C₄×C₁₉	—	2	2	no	—
59	C₂³×C₄×C₁₉	—	4	2	no	—
60	C₂³×C₄×C₁₉	D₄	1	4	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
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	C₁₉×#121	—	2	32	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
106	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	complemented
107	C₁₉×#95	—	2	2	no	—
108	C₁₉×#95	—	2	2	no	—
109	C₁₉×#95	—	2	2	no	—
110	C₁₉×#95	—	2	4	no	—
111	C₁₉×#95	—	2	4	no	—
112	C₁₉×#95	—	4	2	no	—
113	C₁₉×#95	D₄	1	4	yes	complemented
114	C₂⁴×C₁₉	—	2	1	no	—
115	C₂⁴×C₁₉	—	2	2	no	—
116	C₂⁴×C₁₉	—	2	1	no	—
117	C₂⁴×C₁₉	—	2	1	no	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	—	2	2	no	—
120	C₂⁴×C₁₉	—	2	2	no	—
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂⁴×C₁₉	—	2	2	no	—
123	C₂⁴×C₁₉	—	2	2	no	—
124	C₂⁴×C₁₉	—	2	2	no	—
125	C₂⁴×C₁₉	—	2	2	no	—
126	C₂⁴×C₁₉	—	2	2	no	—
127	C₂⁴×C₁₉	—	2	2	no	—
128	C₂⁴×C₁₉	—	2	2	no	—
129	C₂⁴×C₁₉	—	2	2	no	—
130	C₂⁴×C₁₉	—	2	2	no	—
131	C₂⁴×C₁₉	—	2	2	no	—
132	C₂⁴×C₁₉	—	2	2	no	—
133	C₂⁴×C₁₉	—	2	2	no	—
134	C₂⁴×C₁₉	—	2	2	no	—
135	C₂⁴×C₁₉	—	2	2	no	—
136	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
137	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
138	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
139	C₂⁴×C₁₉	#41	1	2	yes	—
140	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂×D₄×C₁₉	—	2	8	no	—
142	C₂×D₄×C₁₉	—	2	16	no	—
143	C₂×D₄×C₁₉	—	4	8	no	—
144	C₂×D₄×C₁₉	—	4	8	no	—
145	C₂×D₄×C₁₉	—	4	8	no	—
146	C₂×D₄×C₁₉	—	4	8	no	—
147	C₂×D₄×C₁₉	—	4	4	no	—
148	C₂×D₄×C₁₉	—	4	8	no	—
149	C₂×D₄×C₁₉	—	4	8	no	—
150	C₂×D₄×C₁₉	—	4	8	no	—
151	C₂×D₄×C₁₉	—	4	8	no	—
152	C₂×D₄×C₁₉	—	4	4	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	8	no	—
181	C₂²×C₄×C₁₉	—	2	8	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	2	no	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	2	2	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	—	2	2	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	2	no	—
196	C₂²×C₄×C₁₉	—	2	2	no	—
197	C₂²×C₄×C₁₉	—	2	2	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	4	4	no	—
200	C₂²×C₄×C₁₉	—	4	8	no	—
201	C₂²×C₄×C₁₉	—	4	8	no	—
202	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₉	#41	1	2	yes	—
211	C₄⋊C₄×C₁₉	—	2	8	no	—
212	C₄⋊C₄×C₁₉	—	4	8	no	—
213	C₄⋊C₄×C₁₉	—	4	8	no	—
214	C₄⋊C₄×C₁₉	—	4	4	no	—
215	C₄⋊C₄×C₁₉	—	4	4	no	—
216	C₂²⋊C₄×C₁₉	—	2	8	no	—
217	C₂²⋊C₄×C₁₉	—	2	16	no	—
218	C₂²⋊C₄×C₁₉	—	4	8	no	—
219	C₂²⋊C₄×C₁₉	—	4	8	no	—
220	C₂²⋊C₄×C₁₉	—	4	8	no	—
221	C₂²⋊C₄×C₁₉	—	4	8	no	—
222	C₂²⋊C₄×C₁₉	—	4	4	no	—
223	C₂²⋊C₄×C₁₉	—	4	8	no	—
224	#16261	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂³×C₁₉	—	2	2	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	2	2	no	—
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	—	2	2	no	—
230	C₂³×C₁₉	—	2	4	no	—
231	C₂³×C₁₉	—	2	2	no	—
232	C₂³×C₁₉	—	2	4	no	—
233	C₂³×C₁₉	—	2	2	no	—
234	C₂³×C₁₉	—	2	4	no	—
235	C₂³×C₁₉	—	2	4	no	—
236	C₂³×C₁₉	—	2	2	no	—
237	C₂³×C₁₉	—	2	2	no	—
238	C₂³×C₁₉	—	2	2	no	—
239	C₂³×C₁₉	—	2	4	no	—
240	C₂³×C₁₉	—	2	4	no	—
241	C₂³×C₁₉	—	2	4	no	—
242	C₂³×C₁₉	—	2	4	no	—
243	C₂³×C₁₉	—	2	4	no	—
244	C₂³×C₁₉	—	2	4	no	—
245	C₂³×C₁₉	—	2	4	no	—
246	C₂³×C₁₉	—	4	2	no	—
247	C₂³×C₁₉	—	4	2	no	—
248	C₂³×C₁₉	—	4	2	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	4	2	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	4	2	no	—
255	C₂³×C₁₉	—	4	2	no	—
256	C₂³×C₁₉	—	4	2	no	—
257	C₂³×C₁₉	—	4	2	no	—
258	C₂³×C₁₉	—	4	2	no	—
259	C₂³×C₁₉	—	4	2	no	—
260	C₂³×C₁₉	—	4	2	no	—
261	C₂³×C₁₉	—	4	2	no	—
262	C₂³×C₁₉	—	4	2	no	—
263	C₂³×C₁₉	—	4	2	no	—
264	C₂³×C₁₉	—	4	2	no	—
265	C₂³×C₁₉	—	4	2	no	—
266	C₂³×C₁₉	—	4	2	no	—
267	C₂³×C₁₉	—	4	2	no	—
268	C₂³×C₁₉	—	4	2	no	—
269	C₂³×C₁₉	—	4	2	no	—
270	C₂³×C₁₉	—	4	2	no	—
271	C₂³×C₁₉	—	4	2	no	—
272	C₂³×C₁₉	—	4	2	no	—
273	C₂³×C₁₉	—	4	2	no	—
274	C₂³×C₁₉	—	4	2	no	—
275	C₂³×C₁₉	—	4	2	no	—
276	C₂³×C₁₉	—	4	2	no	—
277	C₂³×C₁₉	—	4	2	no	—
278	C₂³×C₁₉	—	4	2	no	—
279	C₂³×C₁₉	—	4	2	no	—
280	C₂³×C₁₉	—	4	2	no	—
281	C₂³×C₁₉	—	4	2	no	—
282	C₂³×C₁₉	#121	1	4	yes	—
283	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
285	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
286	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
287	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
288	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
289	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
290	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
291	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
293	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
294	D₄×C₁₉	—	4	16	no	—
295	D₄×C₁₉	—	4	32	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	4	no	—
301	C₂×C₄×C₁₉	—	2	4	no	—
302	C₂×C₄×C₁₉	—	2	4	no	—
303	C₂×C₄×C₁₉	—	2	4	no	—
304	C₂×C₄×C₁₉	—	2	4	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	2	no	—
307	C₂×C₄×C₁₉	—	2	4	no	—
308	C₂×C₄×C₁₉	—	2	2	no	—
309	C₂×C₄×C₁₉	—	2	4	no	—
310	C₂×C₄×C₁₉	—	2	4	no	—
311	C₂×C₄×C₁₉	—	2	4	no	—
312	C₂×C₄×C₁₉	—	2	4	no	—
313	C₂×C₄×C₁₉	—	2	4	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	4	16	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	2	no	—
323	C₂×C₄×C₁₉	—	4	2	no	—
324	C₂×C₄×C₁₉	—	4	2	no	—
325	C₂×C₄×C₁₉	—	4	2	no	—
326	C₂×C₄×C₁₉	—	4	2	no	—
327	C₂×C₄×C₁₉	—	4	2	no	—
328	C₂×C₄×C₁₉	—	4	1	no	—
329	C₂×C₄×C₁₉	—	4	1	no	—
330	C₂×C₄×C₁₉	—	4	2	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	2	no	—
337	C₂×C₄×C₁₉	—	4	2	no	—
338	C₂×C₄×C₁₉	—	4	2	no	—
339	C₂×C₄×C₁₉	—	4	1	no	—
340	C₂×C₄×C₁₉	—	4	2	no	—
341	C₂×C₄×C₁₉	—	4	2	no	—
342	C₂×C₄×C₁₉	—	4	2	no	—
343	C₂×C₄×C₁₉	—	4	2	no	—
344	C₂×C₄×C₁₉	—	4	2	no	—
345	C₂×C₄×C₁₉	—	4	2	no	—
346	C₂×C₄×C₁₉	—	4	2	no	—
347	C₂×C₄×C₁₉	—	4	2	no	—
348	C₂×C₄×C₁₉	#120	1	4	yes	—
349	C₂×C₄×C₁₉	#121	1	4	yes	—
350	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
351	C₂×#396	C₂×C₁₉	1	2	yes	complemented
352	C₂×#394	C₂×C₁₉	1	1	yes	characteristic, complemented
353	C₂×#394	C₂×C₁₉	1	2	yes	complemented
354	C₂×#385	C₂×C₁₉	1	1	yes	characteristic, complemented
355	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
356	#1444	C₂×C₁₉	1	1	yes	characteristic, complemented
357	#1441	C₂×C₁₉	1	1	yes	characteristic, complemented
358	#1439	C₂×C₁₉	1	2	yes	complemented
359	#1438	C₂×C₁₉	1	1	yes	characteristic, complemented
360	#1438	C₂×C₁₉	1	2	yes	complemented
361	C₂²×C₁₉	—	2	4	no	—
362	C₂²×C₁₉	—	2	4	no	—
363	C₂²×C₁₉	—	2	4	no	—
364	C₂²×C₁₉	—	4	2	no	—
365	C₂²×C₁₉	—	4	2	no	—
366	C₂²×C₁₉	—	4	2	no	—
367	C₂²×C₁₉	—	4	4	no	—
368	C₂²×C₁₉	—	4	4	no	—
369	C₂²×C₁₉	—	4	4	no	—
370	C₂²×C₁₉	—	4	4	no	—
371	C₂²×C₁₉	—	4	2	no	—
372	C₂²×C₁₉	—	4	4	no	—
373	C₂²×C₁₉	—	4	4	no	—
374	C₂²×C₁₉	—	4	4	no	—
375	C₂²×C₁₉	—	4	4	no	—
376	C₂²×C₁₉	—	4	4	no	—
377	C₂²×C₁₉	—	4	4	no	—
378	C₂²×C₁₉	—	4	4	no	—
379	C₂²×C₁₉	—	8	2	no	—
380	C₂²×C₁₉	—	8	2	no	—
381	C₂²×C₁₉	—	8	2	no	—
382	C₂²×C₁₉	—	8	2	no	—
383	C₂²×C₁₉	—	8	2	no	—
384	C₂²×C₁₉	—	8	2	no	—
385	C₂²×C₁₉	—	8	2	no	—
386	C₂²×C₁₉	—	8	2	no	—
387	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
388	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
389	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
390	C₂²×C₁₉	#534	1	1	yes	characteristic
391	C₂²×C₁₉	#535	1	1	yes	characteristic
392	C₂²×C₁₉	#536	1	1	yes	characteristic
393	C₂²×C₁₉	#536	1	2	yes	—
394	C₂²×C₁₉	#537	1	1	yes	characteristic
395	C₂²×C₁₉	#537	1	2	yes	—
396	C₂²×C₁₉	#537	1	2	yes	—
397	C₂²×C₁₉	#537	1	2	yes	—
398	C₂²×C₁₉	#539	1	2	yes	—
399	C₂²×C₁₉	#542	1	2	yes	—
400	C₂²×C₁₉	D₄²	1	2	yes	—
401	C₂²×C₁₉	D₄²	1	2	yes	—
402	C₂²×C₁₉	D₄²	1	1	yes	characteristic
403	C₂²×C₁₉	#546	1	2	yes	—
404	C₂²×C₁₉	#546	1	2	yes	—
405	C₂²×C₁₉	#547	1	1	yes	characteristic
406	C₂²×C₁₉	#548	1	1	yes	characteristic
407	C₂²×C₁₉	#553	1	1	yes	characteristic
408	C₂²×C₁₉	#560	1	2	yes	—
409	C₂²×C₁₉	#562	1	2	yes	—
410	C₄×C₁₉	—	2	4	no	—
411	C₄×C₁₉	—	2	4	no	—
412	C₄×C₁₉	—	4	2	no	—
413	C₄×C₁₉	—	4	4	no	—
414	C₄×C₁₉	—	4	2	no	—
415	C₄×C₁₉	—	4	4	no	—
416	C₄×C₁₉	—	8	1	no	—
417	C₄×C₁₉	—	8	2	no	—
418	C₄×C₁₉	—	8	1	no	—
419	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
420	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×#121	—	2	4	no	—
423	C₂×#121	—	2	8	no	—
424	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
428	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
429	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
430	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
431	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
433	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
434	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
437	#396	—	2	8	no	—
438	#394	—	2	8	no	—
439	#394	—	2	4	no	—
440	#385	—	2	4	no	—
441	#380	—	2	4	no	—
442	C₂×#95	C₂²×C₁₉	1	2	yes	—
443	C₂×#95	C₂²×C₁₉	1	2	yes	—
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	2	yes	—
448	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
449	C₂×C₁₉	—	4	4	no	—
450	C₂×C₁₉	—	8	4	no	—
451	C₂×C₁₉	#2408	1	1	yes	characteristic
452	C₂×C₁₉	#2410	1	1	yes	characteristic
453	C₂×C₁₉	#2416	1	1	yes	characteristic
454	C₂×C₁₉	#2616	1	1	yes	characteristic
455	C₂×C₁₉	#2618	1	1	yes	characteristic
456	C₂×C₁₉	#2620	1	1	yes	characteristic
457	C₂×C₁₉	#2672	1	2	yes	—
458	C₂×C₁₉	#2675	1	2	yes	—
459	C₂×C₁₉	#2681	1	2	yes	—
460	C₂×C₁₉	#2691	1	2	yes	—
461	C₂×C₁₉	#2813	1	1	yes	characteristic
462	C₂⁵	C₂³×C₁₉	1	2	yes	—
463	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
464	C₂²×D₄	—	2	4	no	—
465	C₂²×D₄	—	2	4	no	—
466	C₂²×D₄	—	2	4	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	2	4	no	—
469	C₂²×D₄	—	2	4	no	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	—	2	2	no	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	—	4	2	no	—
474	C₂²×D₄	—	4	2	no	—
475	C₂²×D₄	—	4	2	no	—
476	C₂³×C₄	—	2	4	no	—
477	C₂³×C₄	—	2	2	no	—
478	C₂³×C₄	—	2	2	no	—
479	C₂³×C₄	—	4	2	no	—
480	C₂³×C₄	D₄×C₁₉	1	4	yes	—
481	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
486	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
490	#121	—	2	32	no	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	—	2	2	no	—
495	C₂×C₄⋊C₄	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	4	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	4	no	—
499	C₂×C₄⋊C₄	—	2	4	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	4	2	no	—
503	C₂×C₄⋊C₄	—	4	2	no	—
504	C₂×C₂²⋊C₄	—	2	2	no	—
505	C₂×C₂²⋊C₄	—	2	2	no	—
506	C₂×C₂²⋊C₄	—	2	4	no	—
507	C₂×C₂²⋊C₄	—	2	4	no	—
508	C₂×C₂²⋊C₄	—	2	2	no	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₂²⋊C₄	—	4	2	no	—
518	C₂×C₂²⋊C₄	—	4	2	no	—
519	C₂×C₂²⋊C₄	—	4	2	no	—
520	C₂×C₂²⋊C₄	—	4	2	no	—
521	C₂×C₂²⋊C₄	—	4	2	no	—
522	C₂×C₂²⋊C₄	—	4	2	no	—
523	C₂×C₂²⋊C₄	—	4	2	no	—
524	C₂×C₂²⋊C₄	—	4	2	no	—
525	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
526	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	complemented
527	#95	—	2	2	no	—
528	#95	—	2	2	no	—
529	#95	—	2	2	no	—
530	#95	—	2	4	no	—
531	#95	—	2	4	no	—
532	#95	—	4	2	no	—
533	#95	D₄×C₁₉	1	4	yes	complemented
534	C₁₉	#16261	1	1	yes	characteristic, direct product factor, Sylow
535	C₂⁴	—	2	1	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	1	no	—
538	C₂⁴	—	2	1	no	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	2	1	no	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	2	no	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	—	2	2	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
558	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
559	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
560	C₂⁴	#41×C₁₉	1	2	yes	—
561	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	2	16	no	—
564	C₂×D₄	—	4	8	no	—
565	C₂×D₄	—	4	8	no	—
566	C₂×D₄	—	4	8	no	—
567	C₂×D₄	—	4	8	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	8	no	—
570	C₂×D₄	—	4	8	no	—
571	C₂×D₄	—	4	8	no	—
572	C₂×D₄	—	4	8	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	8	no	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	—	4	8	no	—
622	C₂²×C₄	—	4	8	no	—
623	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
624	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
630	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
631	C₂²×C₄	#41×C₁₉	1	2	yes	—
632	C₄⋊C₄	—	2	8	no	—
633	C₄⋊C₄	—	4	8	no	—
634	C₄⋊C₄	—	4	8	no	—
635	C₄⋊C₄	—	4	4	no	—
636	C₄⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	16	no	—
639	C₂²⋊C₄	—	4	8	no	—
640	C₂²⋊C₄	—	4	8	no	—
641	C₂²⋊C₄	—	4	8	no	—
642	C₂²⋊C₄	—	4	8	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	8	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	4	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	4	2	no	—
676	C₂³	—	4	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	2	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	C₁₉×#121	1	4	yes	—
703	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
704	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
705	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
706	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
707	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
708	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
709	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
710	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
711	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
712	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
713	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
714	D₄	—	4	16	no	—
715	D₄	—	4	32	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	4	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	16	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	2	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	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	C₁₉×#120	1	4	yes	—
769	C₂×C₄	C₁₉×#121	1	4	yes	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	8	2	no	—
789	C₂²	—	8	2	no	—
790	C₂²	—	8	2	no	—
791	C₂²	—	8	2	no	—
792	C₂²	—	8	2	no	—
793	C₂²	—	8	2	no	—
794	C₂²	—	8	2	no	—
795	C₂²	—	8	2	no	—
796	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
797	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
798	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
799	C₂²	C₁₉×#534	1	1	yes	characteristic
800	C₂²	C₁₉×#535	1	1	yes	characteristic
801	C₂²	C₁₉×#536	1	2	yes	—
802	C₂²	C₁₉×#536	1	1	yes	characteristic
803	C₂²	C₁₉×#537	1	1	yes	characteristic
804	C₂²	C₁₉×#537	1	2	yes	—
805	C₂²	C₁₉×#537	1	2	yes	—
806	C₂²	C₁₉×#537	1	2	yes	—
807	C₂²	C₁₉×#539	1	2	yes	—
808	C₂²	C₁₉×#542	1	2	yes	—
809	C₂²	D₄²×C₁₉	1	2	yes	—
810	C₂²	D₄²×C₁₉	1	2	yes	—
811	C₂²	D₄²×C₁₉	1	1	yes	characteristic
812	C₂²	C₁₉×#546	1	2	yes	—
813	C₂²	C₁₉×#546	1	2	yes	—
814	C₂²	C₁₉×#547	1	1	yes	characteristic
815	C₂²	C₁₉×#548	1	1	yes	characteristic
816	C₂²	C₁₉×#553	1	1	yes	characteristic
817	C₂²	C₁₉×#560	1	2	yes	—
818	C₂²	C₁₉×#562	1	2	yes	—
819	C₄	—	2	4	no	—
820	C₄	—	2	4	no	—
821	C₄	—	4	4	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	4	no	—
825	C₄	—	8	1	no	—
826	C₄	—	8	2	no	—
827	C₄	—	8	1	no	—
828	C₂	—	4	4	no	—
829	C₂	—	8	4	no	—
830	C₂	C₁₉×#2408	1	1	yes	characteristic
831	C₂	C₁₉×#2410	1	1	yes	characteristic
832	C₂	C₁₉×#2416	1	1	yes	characteristic
833	C₂	C₁₉×#2616	1	1	yes	characteristic
834	C₂	C₁₉×#2618	1	1	yes	characteristic
835	C₂	C₁₉×#2620	1	1	yes	characteristic
836	C₂	C₁₉×#2672	1	2	yes	—
837	C₂	C₁₉×#2675	1	2	yes	—
838	C₂	C₁₉×#2681	1	2	yes	—
839	C₂	C₁₉×#2691	1	2	yes	—
840	C₂	C₁₉×#2813	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#121	C₂
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
2. C₂×C₁₉×#396	C₂	semidirect
3. C₂×C₁₉×#394	C₂	semidirect
4. C₂×C₁₉×#394	C₂	semidirect
5. C₂×C₁₉×#385	C₂	semidirect
6. C₂×C₁₉×#380	C₂	semidirect
7. C₁₉×#1444	C₂	semidirect
8. C₁₉×#1441	C₂	semidirect
9. C₁₉×#1439	C₂	semidirect
10. C₁₉×#1438	C₂	semidirect
11. C₁₉×#1438	C₂	semidirect
106. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
113. C₁₉×#95	D₄	semidirect
224. #16261	C₁₉	direct (N × H)
351. C₂×#396	C₂×C₁₉	semidirect
352. C₂×#394	C₂×C₁₉	semidirect
353. C₂×#394	C₂×C₁₉	semidirect
354. C₂×#385	C₂×C₁₉	semidirect
355. C₂×#380	C₂×C₁₉	semidirect
356. #1444	C₂×C₁₉	semidirect
357. #1441	C₂×C₁₉	semidirect
358. #1439	C₂×C₁₉	semidirect
359. #1438	C₂×C₁₉	semidirect
360. #1438	C₂×C₁₉	semidirect
526. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
533. #95	D₄×C₁₉	semidirect
534. C₁₉	#16261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#121	2
C₂×C₁₉×#396	2
C₂×C₁₉×#394	2
C₂×C₁₉×#385	2
C₂×C₁₉×#380	2
C₁₉×#1444	2
C₁₉×#1441	2
C₁₉×#1439	2
C₁₉×#1438	2
#16261	19

Subgroups — C19×#16261 #18022220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16261 #18022220