Subgroups — C₁₉×#14726 #18020685

Order 4864.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#396	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#379	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#379	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1439	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	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
20	C₂²×C₂²⋊C₄×C₁₉	—	2	8	no	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#396	—	2	8	no	—
32	C₁₉×#385	—	2	4	no	—
33	C₁₉×#385	—	2	4	no	—
34	C₁₉×#380	—	2	4	no	—
35	C₁₉×#379	—	2	4	no	—
36	C₁₉×#379	—	2	4	no	—
37	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
38	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
39	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
42	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	4	no	—
44	C₂⁵×C₁₉	—	2	2	no	—
45	C₂⁵×C₁₉	—	2	4	no	—
46	C₂⁵×C₁₉	—	2	2	no	—
47	C₂⁵×C₁₉	—	2	2	no	—
48	C₂⁵×C₁₉	—	2	2	no	—
49	C₂⁵×C₁₉	—	2	2	no	—
50	C₂⁵×C₁₉	—	2	2	no	—
51	C₂⁵×C₁₉	—	4	2	no	—
52	C₂⁵×C₁₉	—	4	2	no	—
53	C₂⁵×C₁₉	Q₈	1	4	yes	—
54	C₂⁵×C₁₉	C₂³	1	2	yes	—
55	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	—	2	2	no	—
57	C₂³×C₄×C₁₉	—	2	2	no	—
58	C₂³×C₄×C₁₉	—	2	2	no	—
59	C₂³×C₄×C₁₉	—	2	4	no	—
60	C₂³×C₄×C₁₉	—	2	4	no	—
61	C₂³×C₄×C₁₉	—	2	2	no	—
62	C₂³×C₄×C₁₉	—	2	2	no	—
63	C₂³×C₄×C₁₉	—	4	2	no	—
64	C₂³×C₄×C₁₉	—	4	2	no	—
65	C₂³×C₄×C₁₉	D₄	1	4	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	32	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	4	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	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
113	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
116	C₁₉×#95	—	2	4	no	—
117	C₁₉×#95	—	2	4	no	—
118	C₁₉×#95	—	2	2	no	—
119	C₁₉×#95	—	2	2	no	—
120	C₁₉×#95	—	2	4	no	—
121	C₁₉×#95	—	4	2	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	8	no	—
127	C₂⁴×C₁₉	—	2	8	no	—
128	C₂⁴×C₁₉	—	2	16	no	—
129	C₂⁴×C₁₉	—	2	16	no	—
130	C₂⁴×C₁₉	—	2	8	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	—	2	2	no	—
137	C₂⁴×C₁₉	—	2	2	no	—
138	C₂⁴×C₁₉	—	2	2	no	—
139	C₂⁴×C₁₉	—	2	2	no	—
140	C₂⁴×C₁₉	—	2	2	no	—
141	C₂⁴×C₁₉	—	2	2	no	—
142	C₂⁴×C₁₉	—	2	2	no	—
143	C₂⁴×C₁₉	—	2	8	no	—
144	C₂⁴×C₁₉	—	2	8	no	—
145	C₂⁴×C₁₉	—	4	8	no	—
146	C₂⁴×C₁₉	—	4	8	no	—
147	C₂⁴×C₁₉	—	4	8	no	—
148	C₂⁴×C₁₉	—	4	8	no	—
149	C₂⁴×C₁₉	—	4	8	no	—
150	C₂⁴×C₁₉	—	4	8	no	—
151	C₂⁴×C₁₉	—	4	8	no	—
152	C₂⁴×C₁₉	—	4	8	no	—
153	C₂⁴×C₁₉	—	4	8	no	—
154	C₂⁴×C₁₉	—	4	4	no	—
155	C₂⁴×C₁₉	—	4	4	no	—
156	C₂⁴×C₁₉	—	4	8	no	—
157	C₂⁴×C₁₉	—	4	4	no	—
158	C₂⁴×C₁₉	—	4	4	no	—
159	C₂⁴×C₁₉	—	4	4	no	—
160	C₂⁴×C₁₉	—	4	4	no	—
161	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
162	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
163	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
164	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
165	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
166	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
167	C₂⁴×C₁₉	#41	1	4	yes	—
168	C₂⁴×C₁₉	#41	1	2	yes	—
169	C₂⁴×C₁₉	#41	1	2	yes	—
170	C₂⁴×C₁₉	#41	1	2	yes	—
171	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	8	no	—
176	C₂²×C₄×C₁₉	—	2	8	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	1	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	1	no	—
193	C₂²×C₄×C₁₉	—	2	2	no	—
194	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	8	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	2	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	2	no	—
207	C₂²×C₄×C₁₉	—	2	2	no	—
208	C₂²×C₄×C₁₉	—	2	2	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
210	C₂²×C₄×C₁₉	—	2	2	no	—
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	2	1	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	2	no	—
217	C₂²×C₄×C₁₉	—	2	2	no	—
218	C₂²×C₄×C₁₉	—	2	2	no	—
219	C₂²×C₄×C₁₉	—	4	4	no	—
220	C₂²×C₄×C₁₉	—	4	8	no	—
221	C₂²×C₄×C₁₉	—	4	8	no	—
222	C₂²×C₄×C₁₉	—	4	8	no	—
223	C₂²×C₄×C₁₉	—	4	8	no	—
224	C₂²×C₄×C₁₉	—	4	4	no	—
225	C₂²×C₄×C₁₉	—	4	4	no	—
226	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
228	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₁₉	—	4	8	no	—
234	C₄⋊C₄×C₁₉	—	4	8	no	—
235	C₄⋊C₄×C₁₉	—	4	4	no	—
236	C₄⋊C₄×C₁₉	—	4	4	no	—
237	C₂²⋊C₄×C₁₉	—	2	16	no	—
238	C₂²⋊C₄×C₁₉	—	2	8	no	—
239	C₂²⋊C₄×C₁₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₉	—	2	16	no	—
241	C₂²⋊C₄×C₁₉	—	4	8	no	—
242	C₂²⋊C₄×C₁₉	—	4	8	no	—
243	C₂²⋊C₄×C₁₉	—	4	8	no	—
244	C₂²⋊C₄×C₁₉	—	4	8	no	—
245	C₂²⋊C₄×C₁₉	—	4	4	no	—
246	C₂²⋊C₄×C₁₉	—	4	4	no	—
247	#14726	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂³×C₁₉	—	2	2	no	—
249	C₂³×C₁₉	—	2	4	no	—
250	C₂³×C₁₉	—	2	2	no	—
251	C₂³×C₁₉	—	2	4	no	—
252	C₂³×C₁₉	—	2	2	no	—
253	C₂³×C₁₉	—	2	2	no	—
254	C₂³×C₁₉	—	2	4	no	—
255	C₂³×C₁₉	—	2	4	no	—
256	C₂³×C₁₉	—	2	4	no	—
257	C₂³×C₁₉	—	2	4	no	—
258	C₂³×C₁₉	—	2	4	no	—
259	C₂³×C₁₉	—	2	4	no	—
260	C₂³×C₁₉	—	2	4	no	—
261	C₂³×C₁₉	—	2	4	no	—
262	C₂³×C₁₉	—	2	4	no	—
263	C₂³×C₁₉	—	2	4	no	—
264	C₂³×C₁₉	—	2	32	no	—
265	C₂³×C₁₉	—	2	4	no	—
266	C₂³×C₁₉	—	2	4	no	—
267	C₂³×C₁₉	—	2	4	no	—
268	C₂³×C₁₉	—	2	4	no	—
269	C₂³×C₁₉	—	2	4	no	—
270	C₂³×C₁₉	—	2	4	no	—
271	C₂³×C₁₉	—	2	4	no	—
272	C₂³×C₁₉	—	2	4	no	—
273	C₂³×C₁₉	—	2	4	no	—
274	C₂³×C₁₉	—	2	4	no	—
275	C₂³×C₁₉	—	2	4	no	—
276	C₂³×C₁₉	—	2	4	no	—
277	C₂³×C₁₉	—	2	4	no	—
278	C₂³×C₁₉	—	2	4	no	—
279	C₂³×C₁₉	—	2	4	no	—
280	C₂³×C₁₉	—	2	4	no	—
281	C₂³×C₁₉	—	2	4	no	—
282	C₂³×C₁₉	—	2	4	no	—
283	C₂³×C₁₉	—	4	32	no	—
284	C₂³×C₁₉	—	4	32	no	—
285	C₂³×C₁₉	—	4	16	no	—
286	C₂³×C₁₉	—	4	16	no	—
287	C₂³×C₁₉	—	4	16	no	—
288	C₂³×C₁₉	—	4	16	no	—
289	C₂³×C₁₉	—	4	32	no	—
290	C₂³×C₁₉	—	4	32	no	—
291	C₂³×C₁₉	—	4	16	no	—
292	C₂³×C₁₉	—	4	2	no	—
293	C₂³×C₁₉	—	4	2	no	—
294	C₂³×C₁₉	—	4	2	no	—
295	C₂³×C₁₉	—	4	2	no	—
296	C₂³×C₁₉	—	4	2	no	—
297	C₂³×C₁₉	—	4	2	no	—
298	C₂³×C₁₉	—	4	2	no	—
299	C₂³×C₁₉	—	4	2	no	—
300	C₂³×C₁₉	—	4	2	no	—
301	C₂³×C₁₉	—	4	2	no	—
302	C₂³×C₁₉	—	4	2	no	—
303	C₂³×C₁₉	—	4	2	no	—
304	C₂³×C₁₉	—	4	2	no	—
305	C₂³×C₁₉	—	4	2	no	—
306	C₂³×C₁₉	—	4	2	no	—
307	C₂³×C₁₉	—	4	2	no	—
308	C₂³×C₁₉	—	4	16	no	—
309	C₂³×C₁₉	#121	1	4	yes	—
310	C₂³×C₁₉	#121	1	4	yes	—
311	C₂³×C₁₉	#121	1	4	yes	—
312	C₂³×C₁₉	C₂²⋊Q₈	1	8	yes	—
313	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
314	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
315	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
316	C₂³×C₁₉	#126	1	4	yes	—
317	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
318	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
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	C₂×#41	1	2	yes	—
326	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
327	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	2	no	—
330	C₂×C₄×C₁₉	—	2	4	no	—
331	C₂×C₄×C₁₉	—	2	4	no	—
332	C₂×C₄×C₁₉	—	2	4	no	—
333	C₂×C₄×C₁₉	—	2	2	no	—
334	C₂×C₄×C₁₉	—	2	2	no	—
335	C₂×C₄×C₁₉	—	2	4	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	4	no	—
340	C₂×C₄×C₁₉	—	2	4	no	—
341	C₂×C₄×C₁₉	—	2	4	no	—
342	C₂×C₄×C₁₉	—	2	4	no	—
343	C₂×C₄×C₁₉	—	2	4	no	—
344	C₂×C₄×C₁₉	—	2	4	no	—
345	C₂×C₄×C₁₉	—	4	16	no	—
346	C₂×C₄×C₁₉	—	4	16	no	—
347	C₂×C₄×C₁₉	—	4	1	no	—
348	C₂×C₄×C₁₉	—	4	2	no	—
349	C₂×C₄×C₁₉	—	4	2	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	2	no	—
354	C₂×C₄×C₁₉	—	4	2	no	—
355	C₂×C₄×C₁₉	—	4	2	no	—
356	C₂×C₄×C₁₉	—	4	2	no	—
357	C₂×C₄×C₁₉	—	4	2	no	—
358	C₂×C₄×C₁₉	—	4	2	no	—
359	C₂×C₄×C₁₉	—	4	2	no	—
360	C₂×C₄×C₁₉	—	4	2	no	—
361	C₂×C₄×C₁₉	—	4	2	no	—
362	C₂×C₄×C₁₉	—	4	2	no	—
363	C₂×C₄×C₁₉	—	4	1	no	—
364	C₂×C₄×C₁₉	—	4	1	no	—
365	C₂×C₄×C₁₉	—	4	1	no	—
366	C₂×C₄×C₁₉	—	4	2	no	—
367	C₂×C₄×C₁₉	—	4	1	no	—
368	C₂×C₄×C₁₉	—	4	2	no	—
369	C₂×C₄×C₁₉	—	4	1	no	—
370	C₂×C₄×C₁₉	—	4	1	no	—
371	C₂×C₄×C₁₉	—	4	2	no	—
372	C₂×C₄×C₁₉	—	4	2	no	—
373	C₂×C₄×C₁₉	—	4	2	no	—
374	C₂×C₄×C₁₉	—	4	2	no	—
375	C₂×C₄×C₁₉	—	4	2	no	—
376	C₂×C₄×C₁₉	—	4	2	no	—
377	C₂×C₄×C₁₉	—	4	2	no	—
378	C₂×C₄×C₁₉	—	4	2	no	—
379	C₂×C₄×C₁₉	—	4	2	no	—
380	C₂×C₄×C₁₉	#120	1	4	yes	—
381	C₂³×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
382	C₂×#396	C₂×C₁₉	1	2	yes	complemented
383	C₂×#385	C₂×C₁₉	1	1	yes	characteristic, complemented
384	C₂×#385	C₂×C₁₉	1	1	yes	characteristic, complemented
385	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
386	C₂×#379	C₂×C₁₉	1	1	yes	characteristic
387	C₂×#379	C₂×C₁₉	1	1	yes	characteristic
388	#1439	C₂×C₁₉	1	2	yes	complemented
389	#1439	C₂×C₁₉	1	2	yes	complemented
390	#1439	C₂×C₁₉	1	2	yes	complemented
391	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
392	C₂²×C₁₉	—	2	4	no	—
393	C₂²×C₁₉	—	2	4	no	—
394	C₂²×C₁₉	—	2	4	no	—
395	C₂²×C₁₉	—	2	4	no	—
396	C₂²×C₁₉	—	2	4	no	—
397	C₂²×C₁₉	—	2	8	no	—
398	C₂²×C₁₉	—	2	8	no	—
399	C₂²×C₁₉	—	2	8	no	—
400	C₂²×C₁₉	—	2	8	no	—
401	C₂²×C₁₉	—	2	4	no	—
402	C₂²×C₁₉	—	2	8	no	—
403	C₂²×C₁₉	—	2	8	no	—
404	C₂²×C₁₉	—	2	8	no	—
405	C₂²×C₁₉	—	4	64	no	—
406	C₂²×C₁₉	—	4	4	no	—
407	C₂²×C₁₉	—	4	4	no	—
408	C₂²×C₁₉	—	4	4	no	—
409	C₂²×C₁₉	—	4	4	no	—
410	C₂²×C₁₉	—	4	4	no	—
411	C₂²×C₁₉	—	4	4	no	—
412	C₂²×C₁₉	—	4	4	no	—
413	C₂²×C₁₉	—	4	4	no	—
414	C₂²×C₁₉	—	4	4	no	—
415	C₂²×C₁₉	—	4	4	no	—
416	C₂²×C₁₉	—	4	4	no	—
417	C₂²×C₁₉	—	4	4	no	—
418	C₂²×C₁₉	#396	1	8	yes	complemented
419	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
420	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
421	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
422	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
423	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
424	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
425	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
426	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
427	C₂²×C₁₉	#525	1	1	yes	characteristic
428	C₂²×C₁₉	#525	1	2	yes	—
429	C₂²×C₁₉	C₂×#126	1	1	yes	characteristic
430	C₂²×C₁₉	#534	1	1	yes	characteristic
431	C₂²×C₁₉	#535	1	1	yes	characteristic
432	C₂²×C₁₉	#538	1	2	yes	—
433	C₂²×C₁₉	#543	1	2	yes	—
434	C₂²×C₁₉	D₄²	1	2	yes	—
435	C₂²×C₁₉	D₄²	1	2	yes	—
436	C₂²×C₁₉	#546	1	2	yes	—
437	C₂²×C₁₉	#546	1	2	yes	—
438	C₂²×C₁₉	#546	1	2	yes	—
439	C₂²×C₁₉	#546	1	2	yes	—
440	C₂²×C₁₉	#551	1	2	yes	—
441	C₂²×C₁₉	#551	1	2	yes	—
442	C₄×C₁₉	—	2	4	no	—
443	C₄×C₁₉	—	4	2	no	—
444	C₄×C₁₉	—	4	4	no	—
445	C₄×C₁₉	—	4	2	no	—
446	C₄×C₁₉	—	4	4	no	—
447	C₄×C₁₉	—	4	2	no	—
448	C₄×C₁₉	—	8	1	no	—
449	C₄×C₁₉	—	8	1	no	—
450	C₄×C₁₉	—	8	2	no	—
451	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
452	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
453	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
454	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
455	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
456	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
457	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
458	C₂²×C₂²⋊C₄	—	2	4	no	—
459	C₂²×C₂²⋊C₄	—	2	8	no	—
460	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
461	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
462	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
463	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
464	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
465	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
466	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
467	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
468	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
469	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
470	#396	—	2	8	no	—
471	#385	—	2	4	no	—
472	#385	—	2	4	no	—
473	#380	—	2	4	no	—
474	#379	—	2	4	no	—
475	#379	—	2	4	no	—
476	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
477	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
478	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
479	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
480	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
481	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
482	C₂×C₁₉	—	2	8	no	—
483	C₂×C₁₉	—	4	8	no	—
484	C₂×C₁₉	C₂×#396	1	1	yes	characteristic
485	C₂×C₁₉	#2408	1	1	yes	characteristic
486	C₂×C₁₉	#2410	1	1	yes	characteristic
487	C₂×C₁₉	#2411	1	1	yes	characteristic
488	C₂×C₁₉	#2424	1	2	yes	—
489	C₂×C₁₉	#2437	1	2	yes	—
490	C₂×C₁₉	#2437	1	2	yes	—
491	C₂×C₁₉	#2480	1	2	yes	—
492	C₂×C₁₉	#2534	1	1	yes	characteristic
493	C₂×C₁₉	#2626	1	1	yes	characteristic
494	C₂×C₁₉	#2848	1	1	yes	characteristic
495	C₂⁵	—	2	4	no	—
496	C₂⁵	—	2	2	no	—
497	C₂⁵	—	2	4	no	—
498	C₂⁵	—	2	2	no	—
499	C₂⁵	—	2	2	no	—
500	C₂⁵	—	2	2	no	—
501	C₂⁵	—	2	2	no	—
502	C₂⁵	—	2	2	no	—
503	C₂⁵	—	4	2	no	—
504	C₂⁵	—	4	2	no	—
505	C₂⁵	Q₈×C₁₉	1	4	yes	—
506	C₂⁵	C₂³×C₁₉	1	2	yes	—
507	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
508	C₂³×C₄	—	2	2	no	—
509	C₂³×C₄	—	2	2	no	—
510	C₂³×C₄	—	2	2	no	—
511	C₂³×C₄	—	2	4	no	—
512	C₂³×C₄	—	2	4	no	—
513	C₂³×C₄	—	2	2	no	—
514	C₂³×C₄	—	2	2	no	—
515	C₂³×C₄	—	4	2	no	—
516	C₂³×C₄	—	4	2	no	—
517	C₂³×C₄	D₄×C₁₉	1	4	yes	—
518	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
520	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
526	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	—	2	4	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	—	2	4	no	—
532	C₂×C₄⋊C₄	—	2	4	no	—
533	C₂×C₄⋊C₄	—	2	4	no	—
534	C₂×C₄⋊C₄	—	4	2	no	—
535	C₂×C₄⋊C₄	—	4	2	no	—
536	C₂×C₄⋊C₄	—	4	2	no	—
537	C₂×C₂²⋊C₄	—	2	32	no	—
538	C₂×C₂²⋊C₄	—	2	4	no	—
539	C₂×C₂²⋊C₄	—	2	2	no	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₂²⋊C₄	—	2	2	no	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	2	4	no	—
545	C₂×C₂²⋊C₄	—	2	4	no	—
546	C₂×C₂²⋊C₄	—	2	4	no	—
547	C₂×C₂²⋊C₄	—	2	2	no	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₂²⋊C₄	—	2	2	no	—
551	C₂×C₂²⋊C₄	—	2	4	no	—
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	—	2	4	no	—
555	C₂×C₂²⋊C₄	—	2	2	no	—
556	C₂×C₂²⋊C₄	—	2	2	no	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	4	no	—
561	C₂×C₂²⋊C₄	—	4	2	no	—
562	C₂×C₂²⋊C₄	—	4	2	no	—
563	C₂×C₂²⋊C₄	—	4	2	no	—
564	C₂×C₂²⋊C₄	—	4	2	no	—
565	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
566	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
567	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
568	#95	—	2	4	no	—
569	#95	—	2	4	no	—
570	#95	—	2	2	no	—
571	#95	—	2	2	no	—
572	#95	—	2	4	no	—
573	#95	—	4	2	no	—
574	C₁₉	#14726	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	2	2	no	—
577	C₂⁴	—	2	2	no	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	—	2	8	no	—
580	C₂⁴	—	2	8	no	—
581	C₂⁴	—	2	16	no	—
582	C₂⁴	—	2	16	no	—
583	C₂⁴	—	2	8	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	2	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	8	no	—
597	C₂⁴	—	2	8	no	—
598	C₂⁴	—	4	8	no	—
599	C₂⁴	—	4	8	no	—
600	C₂⁴	—	4	8	no	—
601	C₂⁴	—	4	8	no	—
602	C₂⁴	—	4	8	no	—
603	C₂⁴	—	4	8	no	—
604	C₂⁴	—	4	8	no	—
605	C₂⁴	—	4	8	no	—
606	C₂⁴	—	4	8	no	—
607	C₂⁴	—	4	4	no	—
608	C₂⁴	—	4	4	no	—
609	C₂⁴	—	4	8	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	4	4	no	—
612	C₂⁴	—	4	4	no	—
613	C₂⁴	—	4	4	no	—
614	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
615	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
616	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
617	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
618	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
619	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
620	C₂⁴	#41×C₁₉	1	4	yes	—
621	C₂⁴	#41×C₁₉	1	2	yes	—
622	C₂⁴	#41×C₁₉	1	2	yes	—
623	C₂⁴	#41×C₁₉	1	2	yes	—
624	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	8	no	—
629	C₂²×C₄	—	2	8	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	8	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	—	4	8	no	—
674	C₂²×C₄	—	4	8	no	—
675	C₂²×C₄	—	4	8	no	—
676	C₂²×C₄	—	4	8	no	—
677	C₂²×C₄	—	4	4	no	—
678	C₂²×C₄	—	4	4	no	—
679	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
680	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
681	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
683	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
684	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
686	C₄⋊C₄	—	4	8	no	—
687	C₄⋊C₄	—	4	8	no	—
688	C₄⋊C₄	—	4	4	no	—
689	C₄⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	2	16	no	—
691	C₂²⋊C₄	—	2	8	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	16	no	—
694	C₂²⋊C₄	—	4	8	no	—
695	C₂²⋊C₄	—	4	8	no	—
696	C₂²⋊C₄	—	4	8	no	—
697	C₂²⋊C₄	—	4	8	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	—	4	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	4	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	2	32	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	4	no	—
719	C₂³	—	2	4	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	4	no	—
735	C₂³	—	4	32	no	—
736	C₂³	—	4	32	no	—
737	C₂³	—	4	16	no	—
738	C₂³	—	4	16	no	—
739	C₂³	—	4	16	no	—
740	C₂³	—	4	32	no	—
741	C₂³	—	4	32	no	—
742	C₂³	—	4	16	no	—
743	C₂³	—	4	16	no	—
744	C₂³	—	4	16	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	4	2	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	2	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	C₁₉×#121	1	4	yes	—
762	C₂³	C₁₉×#121	1	4	yes	—
763	C₂³	C₁₉×#121	1	4	yes	—
764	C₂³	C₁₉×C₂²⋊Q₈	1	8	yes	—
765	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
766	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
767	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
768	C₂³	C₁₉×#126	1	4	yes	—
769	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
770	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
771	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
773	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
774	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
775	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
776	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
777	C₂³	C₂×#41×C₁₉	1	2	yes	—
778	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
779	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	4	16	no	—
798	C₂×C₄	—	4	16	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	C₁₉×#120	1	4	yes	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	8	no	—
837	C₂²	—	2	8	no	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	8	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	8	no	—
844	C₂²	—	2	8	no	—
845	C₂²	—	2	8	no	—
846	C₂²	—	4	64	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	4	no	—
852	C₂²	—	4	4	no	—
853	C₂²	—	4	4	no	—
854	C₂²	—	4	4	no	—
855	C₂²	—	4	4	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	4	no	—
859	C₂²	C₁₉×#396	1	8	yes	complemented
860	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
861	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
862	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
863	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
864	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
865	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
866	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
867	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
868	C₂²	C₁₉×#525	1	1	yes	characteristic
869	C₂²	C₁₉×#525	1	2	yes	—
870	C₂²	C₂×C₁₉×#126	1	1	yes	characteristic
871	C₂²	C₁₉×#534	1	1	yes	characteristic
872	C₂²	C₁₉×#535	1	1	yes	characteristic
873	C₂²	C₁₉×#538	1	2	yes	—
874	C₂²	C₁₉×#543	1	2	yes	—
875	C₂²	D₄²×C₁₉	1	2	yes	—
876	C₂²	D₄²×C₁₉	1	2	yes	—
877	C₂²	C₁₉×#546	1	2	yes	—
878	C₂²	C₁₉×#546	1	2	yes	—
879	C₂²	C₁₉×#546	1	2	yes	—
880	C₂²	C₁₉×#546	1	2	yes	—
881	C₂²	C₁₉×#551	1	2	yes	—
882	C₂²	C₁₉×#551	1	2	yes	—
883	C₄	—	2	4	no	—
884	C₄	—	4	4	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	4	no	—
888	C₄	—	4	2	no	—
889	C₄	—	8	1	no	—
890	C₄	—	8	1	no	—
891	C₄	—	8	2	no	—
892	C₂	—	2	8	no	—
893	C₂	—	4	8	no	—
894	C₂	C₂×C₁₉×#396	1	1	yes	characteristic
895	C₂	C₁₉×#2408	1	1	yes	characteristic
896	C₂	C₁₉×#2410	1	1	yes	characteristic
897	C₂	C₁₉×#2411	1	1	yes	characteristic
898	C₂	C₁₉×#2424	1	2	yes	—
899	C₂	C₁₉×#2437	1	2	yes	—
900	C₂	C₁₉×#2437	1	2	yes	—
901	C₂	C₁₉×#2480	1	2	yes	—
902	C₂	C₁₉×#2534	1	1	yes	characteristic
903	C₂	C₁₉×#2626	1	1	yes	characteristic
904	C₂	C₁₉×#2848	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
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×#385	C₂	semidirect
4. C₂×C₁₉×#385	C₂	semidirect
5. C₂×C₁₉×#380	C₂	semidirect
8. C₁₉×#1439	C₂	semidirect
9. C₁₉×#1439	C₂	semidirect
10. C₁₉×#1439	C₂	semidirect
11. C₁₉×C₂²⋊#95	C₂	semidirect
15. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
16. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
17. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
37. C₂×C₁₉×#95	C₂²	semidirect
38. C₂×C₁₉×#95	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
247. #14726	C₁₉	direct (N × H)
382. C₂×#396	C₂×C₁₉	semidirect
383. C₂×#385	C₂×C₁₉	semidirect
384. C₂×#385	C₂×C₁₉	semidirect
385. C₂×#380	C₂×C₁₉	semidirect
388. #1439	C₂×C₁₉	semidirect
389. #1439	C₂×C₁₉	semidirect
390. #1439	C₂×C₁₉	semidirect
391. C₂²⋊#95	C₂×C₁₉	semidirect
418. C₂²×C₁₉	#396	semidirect
454. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
455. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
456. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
457. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
476. C₂×#95	C₂²×C₁₉	semidirect
477. C₂×#95	C₂²×C₁₉	semidirect
478. C₂×#95	C₂²×C₁₉	semidirect
479. C₂×#95	C₂²×C₁₉	semidirect
480. C₂×#95	C₂²×C₁₉	semidirect
481. C₂×#95	C₂²×C₁₉	semidirect
574. C₁₉	#14726	direct (N × H)
859. C₂²	C₁₉×#396	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#396	2
C₂×C₁₉×#385	2
C₂×C₁₉×#380	2
C₂×C₁₉×#379	2
C₁₉×#1439	2
C₁₉×C₂²⋊#95	2
#14726	19

Subgroups — C19×#14726 #18020685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14726 #18020685