Subgroups — C₁₉×#14725 #18020684

Order 4864.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#120	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#394	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1440	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1438	C₂	1	2	yes	maximal, complemented
11	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#120	—	2	4	no	—
18	C₂×C₁₉×#120	—	2	4	no	—
19	C₂×C₁₉×#120	—	2	4	no	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
22	C₂²×C₂²⋊C₄×C₁₉	—	2	8	no	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#394	—	2	8	no	—
35	C₁₉×#386	—	2	4	no	—
36	C₁₉×#386	—	2	4	no	—
37	C₁₉×#380	—	2	4	no	—
38	C₁₉×#379	—	2	4	no	—
39	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
40	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
41	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
43	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₉	—	2	4	no	—
46	C₂⁵×C₁₉	—	2	2	no	—
47	C₂⁵×C₁₉	—	2	4	no	—
48	C₂⁵×C₁₉	—	2	2	no	—
49	C₂⁵×C₁₉	—	2	2	no	—
50	C₂⁵×C₁₉	—	2	2	no	—
51	C₂⁵×C₁₉	—	2	2	no	—
52	C₂⁵×C₁₉	—	2	2	no	—
53	C₂⁵×C₁₉	—	4	2	no	—
54	C₂⁵×C₁₉	—	4	2	no	—
55	C₂⁵×C₁₉	D₄	1	4	yes	—
56	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
57	C₂⁵×C₁₉	C₂³	1	2	yes	—
58	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	4	no	—
61	C₂²×D₄×C₁₉	—	2	4	no	—
62	C₂²×D₄×C₁₉	—	2	2	no	—
63	C₂²×D₄×C₁₉	—	2	2	no	—
64	C₂²×D₄×C₁₉	—	2	2	no	—
65	C₂²×D₄×C₁₉	—	2	2	no	—
66	C₂²×D₄×C₁₉	—	2	2	no	—
67	C₂²×D₄×C₁₉	—	2	4	no	—
68	C₂²×D₄×C₁₉	—	2	4	no	—
69	C₂²×D₄×C₁₉	—	2	4	no	—
70	C₂²×D₄×C₁₉	—	4	2	no	—
71	C₂²×D₄×C₁₉	—	4	2	no	—
72	C₂²×D₄×C₁₉	D₄	1	4	yes	—
73	C₂³×C₄×C₁₉	—	2	2	no	—
74	C₂³×C₄×C₁₉	—	2	2	no	—
75	C₂³×C₄×C₁₉	—	2	2	no	—
76	C₂³×C₄×C₁₉	—	2	4	no	—
77	C₂³×C₄×C₁₉	—	2	4	no	—
78	C₂³×C₄×C₁₉	—	2	2	no	—
79	C₂³×C₄×C₁₉	—	2	2	no	—
80	C₂³×C₄×C₁₉	—	4	2	no	—
81	C₂³×C₄×C₁₉	—	4	2	no	—
82	C₂³×C₄×C₁₉	D₄	1	4	yes	complemented
83	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#120	—	2	32	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
94	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	32	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	4	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	4	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
120	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
125	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	complemented
127	C₁₉×#95	—	2	4	no	—
128	C₁₉×#95	—	2	4	no	—
129	C₁₉×#95	—	2	2	no	—
130	C₁₉×#95	—	2	2	no	—
131	C₁₉×#95	—	2	4	no	—
132	C₁₉×#95	—	4	2	no	—
133	C₂⁴×C₁₉	—	2	2	no	—
134	C₂⁴×C₁₉	—	2	2	no	—
135	C₂⁴×C₁₉	—	2	2	no	—
136	C₂⁴×C₁₉	—	2	2	no	—
137	C₂⁴×C₁₉	—	2	8	no	—
138	C₂⁴×C₁₉	—	2	8	no	—
139	C₂⁴×C₁₉	—	2	16	no	—
140	C₂⁴×C₁₉	—	2	16	no	—
141	C₂⁴×C₁₉	—	2	8	no	—
142	C₂⁴×C₁₉	—	2	2	no	—
143	C₂⁴×C₁₉	—	2	2	no	—
144	C₂⁴×C₁₉	—	2	2	no	—
145	C₂⁴×C₁₉	—	2	2	no	—
146	C₂⁴×C₁₉	—	2	2	no	—
147	C₂⁴×C₁₉	—	2	2	no	—
148	C₂⁴×C₁₉	—	2	2	no	—
149	C₂⁴×C₁₉	—	2	2	no	—
150	C₂⁴×C₁₉	—	2	2	no	—
151	C₂⁴×C₁₉	—	2	2	no	—
152	C₂⁴×C₁₉	—	2	2	no	—
153	C₂⁴×C₁₉	—	2	2	no	—
154	C₂⁴×C₁₉	—	2	8	no	—
155	C₂⁴×C₁₉	—	2	8	no	—
156	C₂⁴×C₁₉	—	2	1	no	—
157	C₂⁴×C₁₉	—	2	2	no	—
158	C₂⁴×C₁₉	—	2	1	no	—
159	C₂⁴×C₁₉	—	2	1	no	—
160	C₂⁴×C₁₉	—	2	1	no	—
161	C₂⁴×C₁₉	—	2	1	no	—
162	C₂⁴×C₁₉	—	2	1	no	—
163	C₂⁴×C₁₉	—	2	2	no	—
164	C₂⁴×C₁₉	—	2	2	no	—
165	C₂⁴×C₁₉	—	2	2	no	—
166	C₂⁴×C₁₉	—	4	8	no	—
167	C₂⁴×C₁₉	—	4	8	no	—
168	C₂⁴×C₁₉	—	4	8	no	—
169	C₂⁴×C₁₉	—	4	8	no	—
170	C₂⁴×C₁₉	—	4	8	no	—
171	C₂⁴×C₁₉	—	4	8	no	—
172	C₂⁴×C₁₉	—	4	8	no	—
173	C₂⁴×C₁₉	—	4	8	no	—
174	C₂⁴×C₁₉	—	4	8	no	—
175	C₂⁴×C₁₉	—	4	4	no	—
176	C₂⁴×C₁₉	—	4	4	no	—
177	C₂⁴×C₁₉	—	4	8	no	—
178	C₂⁴×C₁₉	—	4	4	no	—
179	C₂⁴×C₁₉	—	4	4	no	—
180	C₂⁴×C₁₉	—	4	4	no	—
181	C₂⁴×C₁₉	—	4	4	no	—
182	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
183	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
184	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
185	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
186	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
187	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
188	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
189	C₂⁴×C₁₉	#41	1	4	yes	—
190	C₂⁴×C₁₉	#41	1	2	yes	—
191	C₂⁴×C₁₉	#41	1	2	yes	—
192	C₂⁴×C₁₉	#41	1	2	yes	—
193	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
194	C₂×D₄×C₁₉	—	2	16	no	—
195	C₂×D₄×C₁₉	—	2	8	no	—
196	C₂×D₄×C₁₉	—	2	8	no	—
197	C₂×D₄×C₁₉	—	2	8	no	—
198	C₂×D₄×C₁₉	—	4	8	no	—
199	C₂×D₄×C₁₉	—	4	8	no	—
200	C₂×D₄×C₁₉	—	4	8	no	—
201	C₂×D₄×C₁₉	—	4	8	no	—
202	C₂×D₄×C₁₉	—	4	8	no	—
203	C₂×D₄×C₁₉	—	4	8	no	—
204	C₂×D₄×C₁₉	—	4	4	no	—
205	C₂×D₄×C₁₉	—	4	4	no	—
206	C₂×D₄×C₁₉	—	4	4	no	—
207	C₂×D₄×C₁₉	—	4	4	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
210	C₂²×C₄×C₁₉	—	2	2	no	—
211	C₂²×C₄×C₁₉	—	2	8	no	—
212	C₂²×C₄×C₁₉	—	2	8	no	—
213	C₂²×C₄×C₁₉	—	2	2	no	—
214	C₂²×C₄×C₁₉	—	2	2	no	—
215	C₂²×C₄×C₁₉	—	2	2	no	—
216	C₂²×C₄×C₁₉	—	2	1	no	—
217	C₂²×C₄×C₁₉	—	2	1	no	—
218	C₂²×C₄×C₁₉	—	2	2	no	—
219	C₂²×C₄×C₁₉	—	2	2	no	—
220	C₂²×C₄×C₁₉	—	2	2	no	—
221	C₂²×C₄×C₁₉	—	2	2	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	2	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	2	no	—
230	C₂²×C₄×C₁₉	—	2	2	no	—
231	C₂²×C₄×C₁₉	—	2	2	no	—
232	C₂²×C₄×C₁₉	—	2	2	no	—
233	C₂²×C₄×C₁₉	—	2	2	no	—
234	C₂²×C₄×C₁₉	—	2	2	no	—
235	C₂²×C₄×C₁₉	—	2	8	no	—
236	C₂²×C₄×C₁₉	—	2	2	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	2	1	no	—
239	C₂²×C₄×C₁₉	—	2	2	no	—
240	C₂²×C₄×C₁₉	—	2	1	no	—
241	C₂²×C₄×C₁₉	—	2	2	no	—
242	C₂²×C₄×C₁₉	—	2	2	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	2	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	2	no	—
247	C₂²×C₄×C₁₉	—	2	1	no	—
248	C₂²×C₄×C₁₉	—	2	2	no	—
249	C₂²×C₄×C₁₉	—	2	2	no	—
250	C₂²×C₄×C₁₉	—	2	2	no	—
251	C₂²×C₄×C₁₉	—	2	2	no	—
252	C₂²×C₄×C₁₉	—	2	2	no	—
253	C₂²×C₄×C₁₉	—	4	4	no	—
254	C₂²×C₄×C₁₉	—	4	8	no	—
255	C₂²×C₄×C₁₉	—	4	8	no	—
256	C₂²×C₄×C₁₉	—	4	8	no	—
257	C₂²×C₄×C₁₉	—	4	8	no	—
258	C₂²×C₄×C₁₉	—	4	4	no	—
259	C₂²×C₄×C₁₉	—	4	4	no	—
260	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
262	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
264	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
266	C₄⋊C₄×C₁₉	—	4	8	no	—
267	C₂²⋊C₄×C₁₉	—	2	16	no	—
268	C₂²⋊C₄×C₁₉	—	2	16	no	—
269	C₂²⋊C₄×C₁₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₉	—	2	16	no	—
271	C₂²⋊C₄×C₁₉	—	4	8	no	—
272	C₂²⋊C₄×C₁₉	—	4	4	no	—
273	C₂²⋊C₄×C₁₉	—	4	8	no	—
274	C₂²⋊C₄×C₁₉	—	4	4	no	—
275	C₂²⋊C₄×C₁₉	—	4	8	no	—
276	C₂²⋊C₄×C₁₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₉	—	4	4	no	—
278	#14725	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂³×C₁₉	—	2	2	no	—
280	C₂³×C₁₉	—	2	4	no	—
281	C₂³×C₁₉	—	2	2	no	—
282	C₂³×C₁₉	—	2	4	no	—
283	C₂³×C₁₉	—	2	2	no	—
284	C₂³×C₁₉	—	2	4	no	—
285	C₂³×C₁₉	—	2	2	no	—
286	C₂³×C₁₉	—	2	4	no	—
287	C₂³×C₁₉	—	2	4	no	—
288	C₂³×C₁₉	—	2	4	no	—
289	C₂³×C₁₉	—	2	4	no	—
290	C₂³×C₁₉	—	2	4	no	—
291	C₂³×C₁₉	—	2	4	no	—
292	C₂³×C₁₉	—	2	4	no	—
293	C₂³×C₁₉	—	2	4	no	—
294	C₂³×C₁₉	—	2	4	no	—
295	C₂³×C₁₉	—	2	32	no	—
296	C₂³×C₁₉	—	2	4	no	—
297	C₂³×C₁₉	—	2	4	no	—
298	C₂³×C₁₉	—	2	4	no	—
299	C₂³×C₁₉	—	2	4	no	—
300	C₂³×C₁₉	—	2	4	no	—
301	C₂³×C₁₉	—	2	4	no	—
302	C₂³×C₁₉	—	2	4	no	—
303	C₂³×C₁₉	—	2	4	no	—
304	C₂³×C₁₉	—	2	4	no	—
305	C₂³×C₁₉	—	2	4	no	—
306	C₂³×C₁₉	—	2	4	no	—
307	C₂³×C₁₉	—	2	4	no	—
308	C₂³×C₁₉	—	2	4	no	—
309	C₂³×C₁₉	—	2	4	no	—
310	C₂³×C₁₉	—	2	4	no	—
311	C₂³×C₁₉	—	2	4	no	—
312	C₂³×C₁₉	—	2	4	no	—
313	C₂³×C₁₉	—	2	4	no	—
314	C₂³×C₁₉	—	2	2	no	—
315	C₂³×C₁₉	—	2	2	no	—
316	C₂³×C₁₉	—	2	2	no	—
317	C₂³×C₁₉	—	2	4	no	—
318	C₂³×C₁₉	—	2	4	no	—
319	C₂³×C₁₉	—	4	32	no	—
320	C₂³×C₁₉	—	4	32	no	—
321	C₂³×C₁₉	—	4	16	no	—
322	C₂³×C₁₉	—	4	16	no	—
323	C₂³×C₁₉	—	4	16	no	—
324	C₂³×C₁₉	—	4	16	no	—
325	C₂³×C₁₉	—	4	32	no	—
326	C₂³×C₁₉	—	4	32	no	—
327	C₂³×C₁₉	—	4	16	no	—
328	C₂³×C₁₉	—	4	2	no	—
329	C₂³×C₁₉	—	4	2	no	—
330	C₂³×C₁₉	—	4	2	no	—
331	C₂³×C₁₉	—	4	2	no	—
332	C₂³×C₁₉	—	4	2	no	—
333	C₂³×C₁₉	—	4	2	no	—
334	C₂³×C₁₉	—	4	2	no	—
335	C₂³×C₁₉	—	4	2	no	—
336	C₂³×C₁₉	—	4	2	no	—
337	C₂³×C₁₉	—	4	2	no	—
338	C₂³×C₁₉	—	4	2	no	—
339	C₂³×C₁₉	—	4	2	no	—
340	C₂³×C₁₉	—	4	2	no	—
341	C₂³×C₁₉	—	4	2	no	—
342	C₂³×C₁₉	—	4	2	no	—
343	C₂³×C₁₉	—	4	2	no	—
344	C₂³×C₁₉	—	4	16	no	—
345	C₂³×C₁₉	—	4	1	no	—
346	C₂³×C₁₉	—	4	1	no	—
347	C₂³×C₁₉	—	4	1	no	—
348	C₂³×C₁₉	—	4	2	no	—
349	C₂³×C₁₉	—	4	1	no	—
350	C₂³×C₁₉	—	4	2	no	—
351	C₂³×C₁₉	—	4	1	no	—
352	C₂³×C₁₉	—	4	1	no	—
353	C₂³×C₁₉	—	4	1	no	—
354	C₂³×C₁₉	—	4	2	no	—
355	C₂³×C₁₉	—	4	1	no	—
356	C₂³×C₁₉	—	4	2	no	—
357	C₂³×C₁₉	—	4	2	no	—
358	C₂³×C₁₉	—	4	2	no	—
359	C₂³×C₁₉	—	4	2	no	—
360	C₂³×C₁₉	—	4	2	no	—
361	C₂³×C₁₉	—	4	2	no	—
362	C₂³×C₁₉	—	4	2	no	—
363	C₂³×C₁₉	#120	1	4	yes	—
364	C₂³×C₁₉	#121	1	8	yes	—
365	C₂³×C₁₉	#121	1	4	yes	—
366	C₂³×C₁₉	#121	1	4	yes	—
367	C₂³×C₁₉	#121	1	4	yes	—
368	C₂³×C₁₉	#123	1	4	yes	—
369	C₂³×C₁₉	#123	1	4	yes	—
370	C₂³×C₁₉	#124	1	4	yes	—
371	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
373	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
374	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
375	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
376	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
377	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
378	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
379	C₂³×C₁₉	C₂×#41	1	2	yes	—
380	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
381	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
382	D₄×C₁₉	—	4	32	no	—
383	D₄×C₁₉	—	4	16	no	—
384	C₂×C₄×C₁₉	—	2	2	no	—
385	C₂×C₄×C₁₉	—	2	2	no	—
386	C₂×C₄×C₁₉	—	2	4	no	—
387	C₂×C₄×C₁₉	—	2	4	no	—
388	C₂×C₄×C₁₉	—	2	4	no	—
389	C₂×C₄×C₁₉	—	2	2	no	—
390	C₂×C₄×C₁₉	—	2	2	no	—
391	C₂×C₄×C₁₉	—	2	4	no	—
392	C₂×C₄×C₁₉	—	2	2	no	—
393	C₂×C₄×C₁₉	—	2	2	no	—
394	C₂×C₄×C₁₉	—	2	2	no	—
395	C₂×C₄×C₁₉	—	2	2	no	—
396	C₂×C₄×C₁₉	—	2	4	no	—
397	C₂×C₄×C₁₉	—	2	4	no	—
398	C₂×C₄×C₁₉	—	2	4	no	—
399	C₂×C₄×C₁₉	—	2	4	no	—
400	C₂×C₄×C₁₉	—	4	16	no	—
401	C₂×C₄×C₁₉	—	4	16	no	—
402	C₂×C₄×C₁₉	—	4	2	no	—
403	C₂×C₄×C₁₉	—	4	1	no	—
404	C₂×C₄×C₁₉	—	4	1	no	—
405	C₂×C₄×C₁₉	—	4	2	no	—
406	C₂×C₄×C₁₉	—	4	1	no	—
407	C₂×C₄×C₁₉	—	4	1	no	—
408	C₂×C₄×C₁₉	—	4	2	no	—
409	C₂×C₄×C₁₉	—	4	2	no	—
410	C₂×C₄×C₁₉	—	4	2	no	—
411	C₂×C₄×C₁₉	—	4	2	no	—
412	C₂×C₄×C₁₉	—	4	2	no	—
413	C₂×C₄×C₁₉	—	4	2	no	—
414	C₂×C₄×C₁₉	—	4	2	no	—
415	C₂×C₄×C₁₉	—	4	2	no	—
416	C₂×C₄×C₁₉	—	4	1	no	—
417	C₂×C₄×C₁₉	—	4	2	no	—
418	C₂×C₄×C₁₉	—	4	1	no	—
419	C₂×C₄×C₁₉	—	4	2	no	—
420	C₂×C₄×C₁₉	—	4	1	no	—
421	C₂×C₄×C₁₉	—	4	2	no	—
422	C₂×C₄×C₁₉	—	4	1	no	—
423	C₂×C₄×C₁₉	—	4	2	no	—
424	C₂×C₄×C₁₉	—	4	2	no	—
425	C₂×C₄×C₁₉	—	4	1	no	—
426	C₂×C₄×C₁₉	—	4	2	no	—
427	C₂×C₄×C₁₉	—	4	1	no	—
428	C₂×C₄×C₁₉	—	4	2	no	—
429	C₂×C₄×C₁₉	—	4	2	no	—
430	C₂×C₄×C₁₉	—	4	2	no	—
431	C₂×C₄×C₁₉	—	4	2	no	—
432	C₂×C₄×C₁₉	—	4	2	no	—
433	C₂×C₄×C₁₉	#120	1	4	yes	complemented
434	C₂²×#120	C₂×C₁₉	1	1	yes	characteristic
435	C₂³×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
436	C₂×#394	C₂×C₁₉	1	2	yes	complemented
437	C₂×#386	C₂×C₁₉	1	1	yes	characteristic, complemented
438	C₂×#386	C₂×C₁₉	1	1	yes	characteristic, complemented
439	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
440	C₂×#379	C₂×C₁₉	1	1	yes	characteristic, complemented
441	#1440	C₂×C₁₉	1	2	yes	complemented
442	#1439	C₂×C₁₉	1	2	yes	complemented
443	#1438	C₂×C₁₉	1	2	yes	complemented
444	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
445	C₂²×C₁₉	—	2	4	no	—
446	C₂²×C₁₉	—	2	4	no	—
447	C₂²×C₁₉	—	2	4	no	—
448	C₂²×C₁₉	—	2	4	no	—
449	C₂²×C₁₉	—	2	8	no	—
450	C₂²×C₁₉	—	2	4	no	—
451	C₂²×C₁₉	—	2	8	no	—
452	C₂²×C₁₉	—	2	8	no	—
453	C₂²×C₁₉	—	2	8	no	—
454	C₂²×C₁₉	—	2	4	no	—
455	C₂²×C₁₉	—	2	8	no	—
456	C₂²×C₁₉	—	2	8	no	—
457	C₂²×C₁₉	—	2	8	no	—
458	C₂²×C₁₉	—	4	64	no	—
459	C₂²×C₁₉	—	4	4	no	—
460	C₂²×C₁₉	—	4	4	no	—
461	C₂²×C₁₉	—	4	4	no	—
462	C₂²×C₁₉	—	4	4	no	—
463	C₂²×C₁₉	—	4	4	no	—
464	C₂²×C₁₉	—	4	4	no	—
465	C₂²×C₁₉	—	4	4	no	—
466	C₂²×C₁₉	—	4	4	no	—
467	C₂²×C₁₉	—	4	4	no	—
468	C₂²×C₁₉	—	4	4	no	—
469	C₂²×C₁₉	—	4	4	no	—
470	C₂²×C₁₉	—	4	4	no	—
471	C₂²×C₁₉	—	4	2	no	—
472	C₂²×C₁₉	—	4	2	no	—
473	C₂²×C₁₉	—	4	4	no	—
474	C₂²×C₁₉	—	4	4	no	—
475	C₂²×C₁₉	—	4	2	no	—
476	C₂²×C₁₉	—	8	1	no	—
477	C₂²×C₁₉	—	8	1	no	—
478	C₂²×C₁₉	—	8	1	no	—
479	C₂²×C₁₉	—	8	1	no	—
480	C₂²×C₁₉	—	8	2	no	—
481	C₂²×C₁₉	—	8	2	no	—
482	C₂²×C₁₉	#394	1	8	yes	complemented
483	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
484	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
485	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
486	C₂²×C₁₉	C₂×#121	1	2	yes	—
487	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
488	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
489	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
490	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
491	C₂²×C₁₉	#525	1	1	yes	characteristic
492	C₂²×C₁₉	#525	1	2	yes	—
493	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
494	C₂²×C₁₉	#534	1	2	yes	—
495	C₂²×C₁₉	#534	1	1	yes	characteristic
496	C₂²×C₁₉	#535	1	1	yes	characteristic
497	C₂²×C₁₉	#538	1	2	yes	—
498	C₂²×C₁₉	D₄²	1	2	yes	—
499	C₂²×C₁₉	D₄²	1	2	yes	—
500	C₂²×C₁₉	#546	1	2	yes	—
501	C₂²×C₁₉	#546	1	2	yes	—
502	C₂²×C₁₉	#546	1	2	yes	—
503	C₂²×C₁₉	#546	1	2	yes	—
504	C₂²×C₁₉	#551	1	2	yes	—
505	C₂²×C₁₉	#551	1	2	yes	—
506	C₄×C₁₉	—	2	4	no	—
507	C₄×C₁₉	—	4	2	no	—
508	C₄×C₁₉	—	4	4	no	—
509	C₄×C₁₉	—	4	2	no	—
510	C₄×C₁₉	—	4	4	no	—
511	C₄×C₁₉	—	8	1	no	—
512	C₄×C₁₉	—	8	1	no	—
513	C₄×C₁₉	—	8	2	no	—
514	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
515	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
516	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
517	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
518	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
519	C₂×#120	—	2	4	no	—
520	C₂×#120	—	2	4	no	—
521	C₂×#120	—	2	4	no	—
522	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
523	C₂²×C₂²⋊C₄	—	2	4	no	—
524	C₂²×C₂²⋊C₄	—	2	8	no	—
525	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
526	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
527	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
528	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
529	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
530	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
531	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
532	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
533	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
534	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	complemented
535	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
536	#394	—	2	8	no	—
537	#386	—	2	4	no	—
538	#386	—	2	4	no	—
539	#380	—	2	4	no	—
540	#379	—	2	4	no	—
541	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
542	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
543	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
544	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
545	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
546	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
547	C₂×C₁₉	—	2	8	no	—
548	C₂×C₁₉	—	4	8	no	—
549	C₂×C₁₉	—	8	2	no	—
550	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
551	C₂×C₁₉	#2408	1	1	yes	characteristic
552	C₂×C₁₉	#2410	1	1	yes	characteristic
553	C₂×C₁₉	#2410	1	2	yes	—
554	C₂×C₁₉	#2411	1	1	yes	characteristic
555	C₂×C₁₉	#2412	1	2	yes	—
556	C₂×C₁₉	#2418	1	2	yes	—
557	C₂×C₁₉	#2472	1	2	yes	—
558	C₂×C₁₉	#2534	1	1	yes	characteristic
559	C₂×C₁₉	#2617	1	1	yes	characteristic
560	C₂×C₁₉	#2847	1	1	yes	characteristic
561	C₂⁵	—	2	4	no	—
562	C₂⁵	—	2	2	no	—
563	C₂⁵	—	2	4	no	—
564	C₂⁵	—	2	2	no	—
565	C₂⁵	—	2	2	no	—
566	C₂⁵	—	2	2	no	—
567	C₂⁵	—	2	2	no	—
568	C₂⁵	—	2	2	no	—
569	C₂⁵	—	4	2	no	—
570	C₂⁵	—	4	2	no	—
571	C₂⁵	D₄×C₁₉	1	4	yes	—
572	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
573	C₂⁵	C₂³×C₁₉	1	2	yes	—
574	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
575	C₂²×D₄	—	2	4	no	—
576	C₂²×D₄	—	2	4	no	—
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	—	2	2	no	—
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	4	no	—
584	C₂²×D₄	—	2	4	no	—
585	C₂²×D₄	—	2	4	no	—
586	C₂²×D₄	—	4	2	no	—
587	C₂²×D₄	—	4	2	no	—
588	C₂²×D₄	D₄×C₁₉	1	4	yes	—
589	C₂³×C₄	—	2	2	no	—
590	C₂³×C₄	—	2	2	no	—
591	C₂³×C₄	—	2	2	no	—
592	C₂³×C₄	—	2	4	no	—
593	C₂³×C₄	—	2	4	no	—
594	C₂³×C₄	—	2	2	no	—
595	C₂³×C₄	—	2	2	no	—
596	C₂³×C₄	—	4	2	no	—
597	C₂³×C₄	—	4	2	no	—
598	C₂³×C₄	D₄×C₁₉	1	4	yes	complemented
599	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
600	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
604	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
605	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
607	#120	—	2	32	no	—
608	C₂×C₄⋊C₄	—	2	4	no	—
609	C₂×C₄⋊C₄	—	2	4	no	—
610	C₂×C₄⋊C₄	—	4	2	no	—
611	C₂×C₂²⋊C₄	—	2	32	no	—
612	C₂×C₂²⋊C₄	—	2	4	no	—
613	C₂×C₂²⋊C₄	—	2	4	no	—
614	C₂×C₂²⋊C₄	—	2	2	no	—
615	C₂×C₂²⋊C₄	—	2	2	no	—
616	C₂×C₂²⋊C₄	—	2	4	no	—
617	C₂×C₂²⋊C₄	—	2	4	no	—
618	C₂×C₂²⋊C₄	—	2	4	no	—
619	C₂×C₂²⋊C₄	—	2	4	no	—
620	C₂×C₂²⋊C₄	—	2	4	no	—
621	C₂×C₂²⋊C₄	—	2	4	no	—
622	C₂×C₂²⋊C₄	—	2	4	no	—
623	C₂×C₂²⋊C₄	—	2	2	no	—
624	C₂×C₂²⋊C₄	—	2	4	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	4	no	—
630	C₂×C₂²⋊C₄	—	2	4	no	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	4	no	—
636	C₂×C₂²⋊C₄	—	2	4	no	—
637	C₂×C₂²⋊C₄	—	4	2	no	—
638	C₂×C₂²⋊C₄	—	4	2	no	—
639	C₂×C₂²⋊C₄	—	4	2	no	—
640	C₂×C₂²⋊C₄	—	4	2	no	—
641	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
642	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	complemented
643	#95	—	2	4	no	—
644	#95	—	2	2	no	—
645	#95	—	2	2	no	—
646	#95	—	2	4	no	—
647	#95	—	2	4	no	—
648	#95	—	4	2	no	—
649	C₁₉	#14725	1	1	yes	characteristic, direct product factor, Sylow
650	C₂⁴	—	2	2	no	—
651	C₂⁴	—	2	2	no	—
652	C₂⁴	—	2	2	no	—
653	C₂⁴	—	2	2	no	—
654	C₂⁴	—	2	8	no	—
655	C₂⁴	—	2	8	no	—
656	C₂⁴	—	2	16	no	—
657	C₂⁴	—	2	16	no	—
658	C₂⁴	—	2	8	no	—
659	C₂⁴	—	2	2	no	—
660	C₂⁴	—	2	2	no	—
661	C₂⁴	—	2	2	no	—
662	C₂⁴	—	2	2	no	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	2	no	—
668	C₂⁴	—	2	2	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	2	2	no	—
671	C₂⁴	—	2	8	no	—
672	C₂⁴	—	2	8	no	—
673	C₂⁴	—	2	1	no	—
674	C₂⁴	—	2	2	no	—
675	C₂⁴	—	2	1	no	—
676	C₂⁴	—	2	1	no	—
677	C₂⁴	—	2	1	no	—
678	C₂⁴	—	2	1	no	—
679	C₂⁴	—	2	1	no	—
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	2	no	—
683	C₂⁴	—	4	8	no	—
684	C₂⁴	—	4	8	no	—
685	C₂⁴	—	4	8	no	—
686	C₂⁴	—	4	8	no	—
687	C₂⁴	—	4	8	no	—
688	C₂⁴	—	4	8	no	—
689	C₂⁴	—	4	8	no	—
690	C₂⁴	—	4	8	no	—
691	C₂⁴	—	4	8	no	—
692	C₂⁴	—	4	4	no	—
693	C₂⁴	—	4	4	no	—
694	C₂⁴	—	4	8	no	—
695	C₂⁴	—	4	4	no	—
696	C₂⁴	—	4	4	no	—
697	C₂⁴	—	4	4	no	—
698	C₂⁴	—	4	4	no	—
699	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
700	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
701	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
702	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
703	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
704	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
705	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
706	C₂⁴	#41×C₁₉	1	4	yes	—
707	C₂⁴	#41×C₁₉	1	2	yes	—
708	C₂⁴	#41×C₁₉	1	2	yes	—
709	C₂⁴	#41×C₁₉	1	2	yes	—
710	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
711	C₂×D₄	—	2	16	no	—
712	C₂×D₄	—	2	8	no	—
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	4	8	no	—
716	C₂×D₄	—	4	8	no	—
717	C₂×D₄	—	4	8	no	—
718	C₂×D₄	—	4	8	no	—
719	C₂×D₄	—	4	8	no	—
720	C₂×D₄	—	4	8	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	4	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	8	no	—
729	C₂²×C₄	—	2	8	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	8	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	4	4	no	—
771	C₂²×C₄	—	4	8	no	—
772	C₂²×C₄	—	4	8	no	—
773	C₂²×C₄	—	4	8	no	—
774	C₂²×C₄	—	4	8	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	—	4	4	no	—
777	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
778	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
779	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
780	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
781	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
783	C₄⋊C₄	—	4	8	no	—
784	C₂²⋊C₄	—	2	16	no	—
785	C₂²⋊C₄	—	2	16	no	—
786	C₂²⋊C₄	—	2	8	no	—
787	C₂²⋊C₄	—	2	16	no	—
788	C₂²⋊C₄	—	4	8	no	—
789	C₂²⋊C₄	—	4	4	no	—
790	C₂²⋊C₄	—	4	8	no	—
791	C₂²⋊C₄	—	4	4	no	—
792	C₂²⋊C₄	—	4	8	no	—
793	C₂²⋊C₄	—	4	4	no	—
794	C₂²⋊C₄	—	4	4	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	4	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	4	no	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	2	32	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	2	4	no	—
820	C₂³	—	2	4	no	—
821	C₂³	—	2	4	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	4	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	4	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	2	4	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	4	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	4	no	—
834	C₂³	—	2	4	no	—
835	C₂³	—	4	32	no	—
836	C₂³	—	4	32	no	—
837	C₂³	—	4	16	no	—
838	C₂³	—	4	16	no	—
839	C₂³	—	4	16	no	—
840	C₂³	—	4	32	no	—
841	C₂³	—	4	32	no	—
842	C₂³	—	4	16	no	—
843	C₂³	—	4	16	no	—
844	C₂³	—	4	16	no	—
845	C₂³	—	4	2	no	—
846	C₂³	—	4	2	no	—
847	C₂³	—	4	2	no	—
848	C₂³	—	4	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	—	4	2	no	—
851	C₂³	—	4	2	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	2	no	—
858	C₂³	—	4	2	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	4	2	no	—
861	C₂³	—	4	1	no	—
862	C₂³	—	4	2	no	—
863	C₂³	—	4	1	no	—
864	C₂³	—	4	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	4	2	no	—
871	C₂³	—	4	1	no	—
872	C₂³	—	4	2	no	—
873	C₂³	—	4	2	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	2	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	4	2	no	—
878	C₂³	—	4	2	no	—
879	C₂³	C₁₉×#120	1	4	yes	—
880	C₂³	C₁₉×#121	1	8	yes	—
881	C₂³	C₁₉×#121	1	4	yes	—
882	C₂³	C₁₉×#121	1	4	yes	—
883	C₂³	C₁₉×#121	1	4	yes	—
884	C₂³	C₁₉×#123	1	4	yes	—
885	C₂³	C₁₉×#123	1	4	yes	—
886	C₂³	C₁₉×#124	1	4	yes	—
887	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
888	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
889	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
890	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
891	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
892	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
893	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
894	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
895	C₂³	C₂×#41×C₁₉	1	2	yes	—
896	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
897	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
898	D₄	—	4	32	no	—
899	D₄	—	4	16	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	4	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	4	no	—
913	C₂×C₄	—	2	4	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	4	no	—
916	C₂×C₄	—	4	16	no	—
917	C₂×C₄	—	4	16	no	—
918	C₂×C₄	—	4	2	no	—
919	C₂×C₄	—	4	2	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	2	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	4	2	no	—
928	C₂×C₄	—	4	2	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	4	2	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	1	no	—
944	C₂×C₄	—	4	2	no	—
945	C₂×C₄	—	4	2	no	—
946	C₂×C₄	—	4	2	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	C₁₉×#120	1	4	yes	complemented
950	C₂²	—	2	4	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	2	8	no	—
953	C₂²	—	2	4	no	—
954	C₂²	—	2	8	no	—
955	C₂²	—	2	8	no	—
956	C₂²	—	2	8	no	—
957	C₂²	—	2	4	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	2	4	no	—
960	C₂²	—	2	8	no	—
961	C₂²	—	2	8	no	—
962	C₂²	—	2	8	no	—
963	C₂²	—	4	64	no	—
964	C₂²	—	4	4	no	—
965	C₂²	—	4	4	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	4	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	4	4	no	—
971	C₂²	—	4	4	no	—
972	C₂²	—	4	4	no	—
973	C₂²	—	4	4	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	4	4	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	4	no	—
978	C₂²	—	4	4	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	8	1	no	—
982	C₂²	—	8	1	no	—
983	C₂²	—	8	2	no	—
984	C₂²	—	8	2	no	—
985	C₂²	—	8	1	no	—
986	C₂²	—	8	1	no	—
987	C₂²	C₁₉×#394	1	8	yes	complemented
988	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
989	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
990	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
991	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
992	C₂²	C₂×C₁₉×#121	1	2	yes	—
993	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
994	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
995	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
996	C₂²	C₁₉×#525	1	1	yes	characteristic
997	C₂²	C₁₉×#525	1	2	yes	—
998	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
999	C₂²	C₁₉×#534	1	2	yes	—
1000	C₂²	C₁₉×#534	1	1	yes	characteristic
1001	C₂²	C₁₉×#535	1	1	yes	characteristic
1002	C₂²	C₁₉×#538	1	2	yes	—
1003	C₂²	D₄²×C₁₉	1	2	yes	—
1004	C₂²	D₄²×C₁₉	1	2	yes	—
1005	C₂²	C₁₉×#546	1	2	yes	—
1006	C₂²	C₁₉×#546	1	2	yes	—
1007	C₂²	C₁₉×#546	1	2	yes	—
1008	C₂²	C₁₉×#546	1	2	yes	—
1009	C₂²	C₁₉×#551	1	2	yes	—
1010	C₂²	C₁₉×#551	1	2	yes	—
1011	C₄	—	2	4	no	—
1012	C₄	—	4	4	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	4	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	8	2	no	—
1017	C₄	—	8	1	no	—
1018	C₄	—	8	1	no	—
1019	C₂	—	2	8	no	—
1020	C₂	—	4	8	no	—
1021	C₂	—	8	2	no	—
1022	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
1023	C₂	C₁₉×#2408	1	1	yes	characteristic
1024	C₂	C₁₉×#2410	1	1	yes	characteristic
1025	C₂	C₁₉×#2410	1	2	yes	—
1026	C₂	C₁₉×#2411	1	1	yes	characteristic
1027	C₂	C₁₉×#2412	1	2	yes	—
1028	C₂	C₁₉×#2418	1	2	yes	—
1029	C₂	C₁₉×#2472	1	2	yes	—
1030	C₂	C₁₉×#2534	1	1	yes	characteristic
1031	C₂	C₁₉×#2617	1	1	yes	characteristic
1032	C₂	C₁₉×#2847	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#120	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. C₂³×C₂²⋊C₄×C₁₉	C₂	semidirect
3. C₂×C₁₉×#394	C₂	semidirect
4. C₂×C₁₉×#386	C₂	semidirect
5. C₂×C₁₉×#386	C₂	semidirect
6. C₂×C₁₉×#380	C₂	semidirect
7. C₂×C₁₉×#379	C₂	semidirect
8. C₁₉×#1440	C₂	semidirect
9. C₁₉×#1439	C₂	semidirect
10. C₁₉×#1438	C₂	semidirect
11. C₁₉×C₂²⋊#95	C₂	semidirect
20. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
31. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
32. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
33. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
39. C₂×C₁₉×#95	C₂²	semidirect
40. C₂×C₁₉×#95	C₂²	semidirect
41. C₂×C₁₉×#95	C₂²	semidirect
42. C₂×C₁₉×#95	C₂²	semidirect
43. C₂×C₁₉×#95	C₂²	semidirect
44. C₂×C₁₉×#95	C₂²	semidirect
82. C₂³×C₄×C₁₉	D₄	semidirect
126. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
278. #14725	C₁₉	direct (N × H)
433. C₂×C₄×C₁₉	#120	semidirect
435. C₂³×C₂²⋊C₄	C₂×C₁₉	semidirect
436. C₂×#394	C₂×C₁₉	semidirect
437. C₂×#386	C₂×C₁₉	semidirect
438. C₂×#386	C₂×C₁₉	semidirect
439. C₂×#380	C₂×C₁₉	semidirect
440. C₂×#379	C₂×C₁₉	semidirect
441. #1440	C₂×C₁₉	semidirect
442. #1439	C₂×C₁₉	semidirect
443. #1438	C₂×C₁₉	semidirect
444. C₂²⋊#95	C₂×C₁₉	semidirect
482. C₂²×C₁₉	#394	semidirect
522. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
533. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
534. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
535. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
541. C₂×#95	C₂²×C₁₉	semidirect
542. C₂×#95	C₂²×C₁₉	semidirect
543. C₂×#95	C₂²×C₁₉	semidirect
544. C₂×#95	C₂²×C₁₉	semidirect
545. C₂×#95	C₂²×C₁₉	semidirect
546. C₂×#95	C₂²×C₁₉	semidirect
598. C₂³×C₄	D₄×C₁₉	semidirect
642. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
649. C₁₉	#14725	direct (N × H)
949. C₂×C₄	C₁₉×#120	semidirect
987. C₂²	C₁₉×#394	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#120	2
C₂³×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#394	2
C₂×C₁₉×#386	2
C₂×C₁₉×#380	2
C₂×C₁₉×#379	2
C₁₉×#1440	2
C₁₉×#1439	2
C₁₉×#1438	2
C₁₉×C₂²⋊#95	2
#14725	19

Subgroups — C19×#14725 #18020684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14725 #18020684