Subgroups — C₁₉×#24424 #18030383

Order 4864.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₉	—	2	1	no	—
17	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	D₄²×C₁₉	—	2	4	no	—
24	D₄²×C₁₉	—	2	4	no	—
25	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	—	2	1	no	—
27	C₂×C₁₉×#121	—	2	1	no	—
28	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₉×#120	—	2	1	no	—
33	C₂×C₁₉×#120	—	2	1	no	—
34	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#466	—	2	4	no	—
38	C₁₉×#447	—	2	4	no	—
39	C₁₉×#447	—	2	4	no	—
40	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₉×#102	—	2	4	no	—
42	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#396	—	2	1	no	—
56	C₁₉×#394	—	2	1	no	—
57	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#389	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#386	—	2	1	no	—
60	C₁₉×#380	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₁₉	—	2	1	no	—
66	C₂⁵×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	—	2	2	no	—
68	C₂²×D₄×C₁₉	—	2	2	no	—
69	C₂²×D₄×C₁₉	—	2	8	no	—
70	C₂²×D₄×C₁₉	—	2	1	no	—
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	—	2	2	no	—
73	C₂²×D₄×C₁₉	—	2	2	no	—
74	C₂²×D₄×C₁₉	—	2	2	no	—
75	C₂²×D₄×C₁₉	—	2	2	no	—
76	C₂²×D₄×C₁₉	—	2	1	no	—
77	C₂²×D₄×C₁₉	—	2	1	no	—
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	—	2	1	no	—
81	C₂²×D₄×C₁₉	—	2	2	no	—
82	C₂²×D₄×C₁₉	—	2	1	no	—
83	C₂²×D₄×C₁₉	—	4	1	no	—
84	C₂²×D₄×C₁₉	—	4	1	no	—
85	C₂²×D₄×C₁₉	—	4	1	no	—
86	C₂²×D₄×C₁₉	—	4	1	no	—
87	C₂²×D₄×C₁₉	—	4	4	no	—
88	C₂²×D₄×C₁₉	—	4	4	no	—
89	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
91	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₉	—	2	1	no	—
96	C₂³×C₄×C₁₉	—	2	1	no	—
97	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×D₈×C₁₉	—	2	2	no	—
100	C₂×D₈×C₁₉	—	2	2	no	—
101	C₂×D₈×C₁₉	—	2	2	no	—
102	C₂×D₈×C₁₉	—	2	2	no	—
103	C₂×D₈×C₁₉	—	2	2	no	—
104	C₂×D₈×C₁₉	—	2	2	no	—
105	C₂×D₈×C₁₉	—	4	1	no	—
106	C₂×D₈×C₁₉	—	4	1	no	—
107	C₂×D₈×C₁₉	—	4	1	no	—
108	C₂²×C₈×C₁₉	—	2	2	no	—
109	C₂²×C₈×C₁₉	—	2	2	no	—
110	C₂²×C₈×C₁₉	—	4	1	no	—
111	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#127	—	2	2	no	—
116	C₁₉×#127	—	2	2	no	—
117	C₁₉×#121	—	2	8	no	—
118	C₁₉×#121	—	2	2	no	—
119	C₁₉×#121	—	2	2	no	—
120	C₁₉×#121	—	2	2	no	—
121	C₁₉×#121	—	2	2	no	—
122	C₁₉×#121	—	2	2	no	—
123	C₁₉×#121	—	2	2	no	—
124	C₁₉×#121	—	4	1	no	—
125	C₁₉×#121	—	4	4	no	—
126	C₁₉×#121	D₄	1	4	yes	complemented
127	C₁₉×#120	—	2	8	no	—
128	C₁₉×#120	—	2	8	no	—
129	C₄×D₄×C₁₉	—	2	2	no	—
130	C₄×D₄×C₁₉	—	2	2	no	—
131	C₄×D₄×C₁₉	—	2	2	no	—
132	C₄×D₄×C₁₉	—	2	2	no	—
133	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
137	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
152	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
153	C₁₉×#107	—	2	2	no	—
154	C₁₉×#102	—	2	2	no	—
155	C₁₉×#102	—	2	2	no	—
156	C₁₉×#102	—	2	2	no	—
157	C₁₉×#102	—	2	2	no	—
158	C₁₉×#102	—	2	2	no	—
159	C₁₉×#102	—	2	2	no	—
160	C₁₉×#102	—	2	2	no	—
161	C₁₉×#102	—	2	2	no	—
162	C₁₉×#102	—	4	1	no	—
163	C₁₉×#102	D₄	1	4	yes	complemented
164	C₁₉×C₂²⋊C₈	—	2	2	no	—
165	C₁₉×C₂²⋊C₈	—	2	2	no	—
166	C₁₉×C₂²⋊C₈	—	4	1	no	—
167	C₁₉×#95	—	2	1	no	—
168	C₁₉×#95	—	2	1	no	—
169	C₂⁴×C₁₉	—	2	1	no	—
170	C₂⁴×C₁₉	—	2	4	no	—
171	C₂⁴×C₁₉	—	2	1	no	—
172	C₂⁴×C₁₉	—	2	1	no	—
173	C₂⁴×C₁₉	—	2	4	no	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	C₂⁴×C₁₉	—	4	2	no	—
176	C₂⁴×C₁₉	—	4	2	no	—
177	C₂⁴×C₁₉	—	4	2	no	—
178	C₂⁴×C₁₉	—	4	2	no	—
179	C₂⁴×C₁₉	—	4	2	no	—
180	C₂⁴×C₁₉	—	4	2	no	—
181	C₂⁴×C₁₉	—	4	2	no	—
182	C₂⁴×C₁₉	—	4	2	no	—
183	C₂⁴×C₁₉	—	8	1	no	—
184	C₂⁴×C₁₉	—	8	1	no	—
185	C₂⁴×C₁₉	—	8	1	no	—
186	C₂⁴×C₁₉	—	8	1	no	—
187	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₁₉	—	2	2	no	—
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	8	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	2	4	no	—
194	C₂×D₄×C₁₉	—	2	4	no	—
195	C₂×D₄×C₁₉	—	2	4	no	—
196	C₂×D₄×C₁₉	—	2	4	no	—
197	C₂×D₄×C₁₉	—	2	4	no	—
198	C₂×D₄×C₁₉	—	2	1	no	—
199	C₂×D₄×C₁₉	—	2	1	no	—
200	C₂×D₄×C₁₉	—	2	1	no	—
201	C₂×D₄×C₁₉	—	2	1	no	—
202	C₂×D₄×C₁₉	—	2	1	no	—
203	C₂×D₄×C₁₉	—	2	1	no	—
204	C₂×D₄×C₁₉	—	2	1	no	—
205	C₂×D₄×C₁₉	—	2	1	no	—
206	C₂×D₄×C₁₉	—	2	1	no	—
207	C₂×D₄×C₁₉	—	2	1	no	—
208	C₂×D₄×C₁₉	—	2	1	no	—
209	C₂×D₄×C₁₉	—	2	1	no	—
210	C₂×D₄×C₁₉	—	2	1	no	—
211	C₂×D₄×C₁₉	—	2	1	no	—
212	C₂×D₄×C₁₉	—	2	1	no	—
213	C₂×D₄×C₁₉	—	2	1	no	—
214	C₂×D₄×C₁₉	—	2	1	no	—
215	C₂×D₄×C₁₉	—	2	1	no	—
216	C₂×D₄×C₁₉	—	2	1	no	—
217	C₂×D₄×C₁₉	—	4	4	no	—
218	C₂×D₄×C₁₉	—	4	4	no	—
219	C₂×D₄×C₁₉	—	4	4	no	—
220	C₂×D₄×C₁₉	—	4	2	no	—
221	C₂×D₄×C₁₉	—	4	2	no	—
222	C₂×D₄×C₁₉	—	4	2	no	—
223	C₂×D₄×C₁₉	—	4	2	no	—
224	C₂×D₄×C₁₉	—	4	2	no	—
225	C₂×D₄×C₁₉	—	4	2	no	—
226	C₂×D₄×C₁₉	—	4	4	no	—
227	C₂×D₄×C₁₉	—	4	4	no	—
228	C₂×D₄×C₁₉	—	4	32	no	—
229	C₂×D₄×C₁₉	—	4	4	no	—
230	C₂×D₄×C₁₉	—	4	2	no	—
231	C₂×D₄×C₁₉	—	4	2	no	—
232	C₂×D₄×C₁₉	—	4	2	no	—
233	C₂×D₄×C₁₉	—	4	2	no	—
234	C₂×D₄×C₁₉	—	4	4	no	—
235	C₂×D₄×C₁₉	—	4	2	no	—
236	C₂×D₄×C₁₉	—	4	2	no	—
237	C₂×D₄×C₁₉	—	4	2	no	—
238	C₂×D₄×C₁₉	—	4	2	no	—
239	C₂×D₄×C₁₉	—	4	2	no	—
240	C₂×D₄×C₁₉	—	8	1	no	—
241	C₂×D₄×C₁₉	—	8	1	no	—
242	C₂×D₄×C₁₉	—	8	1	no	—
243	C₂×D₄×C₁₉	D₈	1	4	yes	complemented
244	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₁₉	#41	1	2	yes	—
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	—	2	1	no	—
253	C₂²×C₄×C₁₉	—	2	4	no	—
254	C₂²×C₄×C₁₉	—	2	1	no	—
255	C₂²×C₄×C₁₉	—	2	1	no	—
256	C₂²×C₄×C₁₉	—	2	1	no	—
257	C₂²×C₄×C₁₉	—	2	1	no	—
258	C₂²×C₄×C₁₉	—	2	1	no	—
259	C₂²×C₄×C₁₉	—	2	1	no	—
260	C₂²×C₄×C₁₉	—	2	1	no	—
261	C₂²×C₄×C₁₉	—	2	1	no	—
262	C₂²×C₄×C₁₉	—	2	1	no	—
263	C₂²×C₄×C₁₉	—	2	1	no	—
264	C₂²×C₄×C₁₉	—	4	2	no	—
265	C₂²×C₄×C₁₉	—	4	2	no	—
266	C₂²×C₄×C₁₉	—	4	2	no	—
267	C₂²×C₄×C₁₉	—	4	2	no	—
268	C₂²×C₄×C₁₉	—	8	1	no	—
269	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
276	D₈×C₁₉	—	4	4	no	—
277	D₈×C₁₉	—	4	4	no	—
278	D₈×C₁₉	—	4	4	no	—
279	C₂×C₈×C₁₉	—	2	1	no	—
280	C₂×C₈×C₁₉	—	2	1	no	—
281	C₂×C₈×C₁₉	—	2	1	no	—
282	C₂×C₈×C₁₉	—	2	1	no	—
283	C₂×C₈×C₁₉	—	2	1	no	—
284	C₂×C₈×C₁₉	—	2	1	no	—
285	C₂×C₈×C₁₉	—	2	1	no	—
286	C₂×C₈×C₁₉	—	2	1	no	—
287	C₂×C₈×C₁₉	—	2	1	no	—
288	C₂×C₈×C₁₉	—	2	1	no	—
289	C₂×C₈×C₁₉	—	2	1	no	—
290	C₂×C₈×C₁₉	—	4	4	no	—
291	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	complemented
292	C₄⋊C₄×C₁₉	—	2	2	no	—
293	C₄⋊C₄×C₁₉	—	2	1	no	—
294	C₄⋊C₄×C₁₉	—	2	1	no	—
295	C₄⋊C₄×C₁₉	—	2	1	no	—
296	C₄⋊C₄×C₁₉	—	2	1	no	—
297	C₄⋊C₄×C₁₉	—	2	1	no	—
298	C₄⋊C₄×C₁₉	—	2	1	no	—
299	C₄⋊C₄×C₁₉	—	4	2	no	—
300	C₄⋊C₄×C₁₉	—	4	2	no	—
301	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	complemented
303	C₂²⋊C₄×C₁₉	—	2	4	no	—
304	C₂²⋊C₄×C₁₉	—	2	4	no	—
305	C₂²⋊C₄×C₁₉	—	2	2	no	—
306	C₂²⋊C₄×C₁₉	—	2	4	no	—
307	C₂²⋊C₄×C₁₉	—	2	2	no	—
308	C₂²⋊C₄×C₁₉	—	4	2	no	—
309	C₂²⋊C₄×C₁₉	—	4	2	no	—
310	C₂²⋊C₄×C₁₉	—	4	2	no	—
311	C₂²⋊C₄×C₁₉	—	4	2	no	—
312	C₂²⋊C₄×C₁₉	—	8	1	no	—
313	C₄²×C₁₉	—	2	1	no	—
314	C₄²×C₁₉	—	2	1	no	—
315	#24424	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂³×C₁₉	—	2	1	no	—
317	C₂³×C₁₉	—	2	1	no	—
318	C₂³×C₁₉	—	2	1	no	—
319	C₂³×C₁₉	—	2	1	no	—
320	C₂³×C₁₉	—	2	1	no	—
321	C₂³×C₁₉	—	2	2	no	—
322	C₂³×C₁₉	—	2	1	no	—
323	C₂³×C₁₉	—	2	2	no	—
324	C₂³×C₁₉	—	2	1	no	—
325	C₂³×C₁₉	—	2	2	no	—
326	C₂³×C₁₉	—	2	1	no	—
327	C₂³×C₁₉	—	2	1	no	—
328	C₂³×C₁₉	—	2	1	no	—
329	C₂³×C₁₉	—	2	2	no	—
330	C₂³×C₁₉	—	2	2	no	—
331	C₂³×C₁₉	—	4	8	no	—
332	C₂³×C₁₉	—	4	8	no	—
333	C₂³×C₁₉	—	4	8	no	—
334	C₂³×C₁₉	—	4	1	no	—
335	C₂³×C₁₉	—	4	1	no	—
336	C₂³×C₁₉	—	4	1	no	—
337	C₂³×C₁₉	—	4	1	no	—
338	C₂³×C₁₉	—	4	1	no	—
339	C₂³×C₁₉	—	4	1	no	—
340	C₂³×C₁₉	—	4	1	no	—
341	C₂³×C₁₉	—	4	1	no	—
342	C₂³×C₁₉	—	4	1	no	—
343	C₂³×C₁₉	—	4	1	no	—
344	C₂³×C₁₉	—	4	1	no	—
345	C₂³×C₁₉	—	4	1	no	—
346	C₂³×C₁₉	—	4	1	no	—
347	C₂³×C₁₉	—	4	1	no	—
348	C₂³×C₁₉	—	4	1	no	—
349	C₂³×C₁₉	—	4	1	no	—
350	C₂³×C₁₉	—	4	8	no	—
351	C₂³×C₁₉	—	4	1	no	—
352	C₂³×C₁₉	—	4	1	no	—
353	C₂³×C₁₉	—	4	1	no	—
354	C₂³×C₁₉	—	4	1	no	—
355	C₂³×C₁₉	—	4	1	no	—
356	C₂³×C₁₉	—	4	1	no	—
357	C₂³×C₁₉	—	4	1	no	—
358	C₂³×C₁₉	—	8	4	no	—
359	C₂³×C₁₉	—	8	4	no	—
360	C₂³×C₁₉	—	8	4	no	—
361	C₂³×C₁₉	—	8	4	no	—
362	C₂³×C₁₉	—	8	4	no	—
363	C₂³×C₁₉	—	8	4	no	—
364	C₂³×C₁₉	—	8	4	no	—
365	C₂³×C₁₉	—	8	4	no	—
366	C₂³×C₁₉	—	8	4	no	—
367	C₂³×C₁₉	—	8	4	no	—
368	C₂³×C₁₉	#120	1	2	yes	—
369	C₂³×C₁₉	C₂×D₈	1	2	yes	—
370	C₂³×C₁₉	C₂×D₈	1	2	yes	—
371	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
372	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
373	D₄×C₁₉	—	2	8	no	—
374	D₄×C₁₉	—	2	2	no	—
375	D₄×C₁₉	—	2	2	no	—
376	D₄×C₁₉	—	2	2	no	—
377	D₄×C₁₉	—	2	2	no	—
378	D₄×C₁₉	—	2	2	no	—
379	D₄×C₁₉	—	2	2	no	—
380	D₄×C₁₉	—	2	2	no	—
381	D₄×C₁₉	—	4	8	no	—
382	D₄×C₁₉	—	4	8	no	—
383	D₄×C₁₉	—	4	8	no	—
384	D₄×C₁₉	—	4	8	no	—
385	D₄×C₁₉	—	4	8	no	—
386	D₄×C₁₉	—	4	1	no	—
387	D₄×C₁₉	—	4	1	no	—
388	D₄×C₁₉	—	4	1	no	—
389	D₄×C₁₉	—	4	1	no	—
390	D₄×C₁₉	—	4	1	no	—
391	D₄×C₁₉	—	4	1	no	—
392	D₄×C₁₉	—	4	1	no	—
393	D₄×C₁₉	—	4	1	no	—
394	D₄×C₁₉	—	8	4	no	—
395	D₄×C₁₉	—	8	4	no	—
396	D₄×C₁₉	—	8	4	no	—
397	D₄×C₁₉	#121	1	4	yes	complemented
398	C₂×C₄×C₁₉	—	2	1	no	—
399	C₂×C₄×C₁₉	—	2	1	no	—
400	C₂×C₄×C₁₉	—	2	1	no	—
401	C₂×C₄×C₁₉	—	2	1	no	—
402	C₂×C₄×C₁₉	—	2	2	no	—
403	C₂×C₄×C₁₉	—	2	2	no	—
404	C₂×C₄×C₁₉	—	2	2	no	—
405	C₂×C₄×C₁₉	—	2	2	no	—
406	C₂×C₄×C₁₉	—	2	1	no	—
407	C₂×C₄×C₁₉	—	2	1	no	—
408	C₂×C₄×C₁₉	—	2	2	no	—
409	C₂×C₄×C₁₉	—	2	1	no	—
410	C₂×C₄×C₁₉	—	2	2	no	—
411	C₂×C₄×C₁₉	—	2	1	no	—
412	C₂×C₄×C₁₉	—	2	1	no	—
413	C₂×C₄×C₁₉	—	2	1	no	—
414	C₂×C₄×C₁₉	—	4	8	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	—	8	4	no	—
430	C₂×C₄×C₁₉	#120	1	2	yes	—
431	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
432	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
436	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
438	C₈×C₁₉	—	2	2	no	—
439	C₈×C₁₉	—	4	1	no	—
440	C₈×C₁₉	—	4	1	no	—
441	C₈×C₁₉	—	4	1	no	—
442	C₂×D₄²	C₂×C₁₉	1	1	yes	characteristic, complemented
443	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
444	C₂×#447	C₂×C₁₉	1	1	yes	characteristic, complemented
445	C₂×#447	C₂×C₁₉	1	1	yes	characteristic, complemented
446	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
447	#2416	C₂×C₁₉	1	1	yes	characteristic, complemented
448	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
449	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
450	#2011	C₂×C₁₉	1	1	yes	characteristic, complemented
451	#1999	C₂×C₁₉	1	1	yes	characteristic, complemented
452	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
453	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
454	#1869	C₂×C₁₉	1	1	yes	characteristic, complemented
455	#1862	C₂×C₁₉	1	1	yes	characteristic, complemented
456	#1786	C₂×C₁₉	1	1	yes	characteristic, complemented
457	C₂²×C₁₉	—	2	2	no	—
458	C₂²×C₁₉	—	2	2	no	—
459	C₂²×C₁₉	—	2	2	no	—
460	C₂²×C₁₉	—	2	2	no	—
461	C₂²×C₁₉	—	2	2	no	—
462	C₂²×C₁₉	—	2	2	no	—
463	C₂²×C₁₉	—	2	4	no	—
464	C₂²×C₁₉	—	2	2	no	—
465	C₂²×C₁₉	—	2	2	no	—
466	C₂²×C₁₉	—	2	2	no	—
467	C₂²×C₁₉	—	4	1	no	—
468	C₂²×C₁₉	—	4	2	no	—
469	C₂²×C₁₉	—	4	1	no	—
470	C₂²×C₁₉	—	4	2	no	—
471	C₂²×C₁₉	—	4	1	no	—
472	C₂²×C₁₉	—	4	2	no	—
473	C₂²×C₁₉	—	4	2	no	—
474	C₂²×C₁₉	—	4	2	no	—
475	C₂²×C₁₉	—	4	1	no	—
476	C₂²×C₁₉	—	4	2	no	—
477	C₂²×C₁₉	—	4	2	no	—
478	C₂²×C₁₉	—	4	2	no	—
479	C₂²×C₁₉	—	4	2	no	—
480	C₂²×C₁₉	—	4	2	no	—
481	C₂²×C₁₉	—	4	2	no	—
482	C₂²×C₁₉	—	4	2	no	—
483	C₂²×C₁₉	—	8	16	no	—
484	C₂²×C₁₉	—	8	16	no	—
485	C₂²×C₁₉	—	8	1	no	—
486	C₂²×C₁₉	—	8	1	no	—
487	C₂²×C₁₉	—	8	1	no	—
488	C₂²×C₁₉	—	8	1	no	—
489	C₂²×C₁₉	—	8	1	no	—
490	C₂²×C₁₉	—	8	1	no	—
491	C₂²×C₁₉	—	8	1	no	—
492	C₂²×C₁₉	—	8	1	no	—
493	C₂²×C₁₉	—	8	1	no	—
494	C₂²×C₁₉	—	8	1	no	—
495	C₂²×C₁₉	—	8	1	no	—
496	C₂²×C₁₉	—	8	1	no	—
497	C₂²×C₁₉	—	8	1	no	—
498	C₂²×C₁₉	—	8	1	no	—
499	C₂²×C₁₉	—	8	1	no	—
500	C₂²×C₁₉	#447	1	4	yes	complemented
501	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
502	C₂²×C₁₉	D₄²	1	1	yes	characteristic
503	C₂²×C₁₉	#546	1	1	yes	characteristic
504	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
505	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₂²×C₁₉	#576	1	1	yes	characteristic
507	C₂²×C₁₉	#577	1	1	yes	characteristic
508	C₄×C₁₉	—	2	2	no	—
509	C₄×C₁₉	—	2	2	no	—
510	C₄×C₁₉	—	4	1	no	—
511	C₄×C₁₉	—	4	2	no	—
512	C₄×C₁₉	—	4	1	no	—
513	C₄×C₁₉	—	4	2	no	—
514	C₄×C₁₉	—	8	1	no	—
515	C₄×C₁₉	—	8	1	no	—
516	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
517	C₄×C₁₉	#534	1	1	yes	characteristic
518	C₄×C₁₉	D₄²	1	1	yes	characteristic
519	C₄×C₁₉	#546	1	1	yes	characteristic
520	C₂³×D₄	—	2	1	no	—
521	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
522	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
523	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
524	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
525	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
526	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
527	D₄²	—	2	4	no	—
528	D₄²	—	2	4	no	—
529	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
530	C₂×#121	—	2	1	no	—
531	C₂×#121	—	2	1	no	—
532	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
533	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
534	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
535	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
536	C₂×#120	—	2	1	no	—
537	C₂×#120	—	2	1	no	—
538	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
539	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
540	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
541	#466	—	2	4	no	—
542	#447	—	2	4	no	—
543	#447	—	2	4	no	—
544	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
545	C₂×#102	—	2	4	no	—
546	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
547	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
548	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
549	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
550	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
551	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
552	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
553	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
554	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
555	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
556	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
557	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
558	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
559	#396	—	2	1	no	—
560	#394	—	2	1	no	—
561	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
562	#389	C₂²×C₁₉	1	1	yes	characteristic, complemented
563	#386	—	2	1	no	—
564	#380	C₂²×C₁₉	1	1	yes	characteristic, complemented
565	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
566	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
567	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
568	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
569	C₂×C₁₉	—	2	4	no	—
570	C₂×C₁₉	—	4	2	no	—
571	C₂×C₁₉	—	4	4	no	—
572	C₂×C₁₉	—	8	2	no	—
573	C₂×C₁₉	—	8	2	no	—
574	C₂×C₁₉	—	16	1	no	—
575	C₂×C₁₉	#2410	1	1	yes	characteristic
576	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
577	C₂×C₁₉	#3012	1	1	yes	characteristic
578	C₂×C₁₉	#3265	1	1	yes	characteristic
579	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
580	C₂×C₁₉	#3294	1	1	yes	characteristic
581	C₂×C₁₉	#3318	1	1	yes	characteristic
582	C₂⁵	—	2	1	no	—
583	C₂⁵	—	2	1	no	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	2	no	—
586	C₂²×D₄	—	2	8	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	—	2	1	no	—
589	C₂²×D₄	—	2	2	no	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	2	2	no	—
592	C₂²×D₄	—	2	2	no	—
593	C₂²×D₄	—	2	1	no	—
594	C₂²×D₄	—	2	1	no	—
595	C₂²×D₄	—	2	1	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	2	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	—	4	1	no	—
601	C₂²×D₄	—	4	1	no	—
602	C₂²×D₄	—	4	1	no	—
603	C₂²×D₄	—	4	1	no	—
604	C₂²×D₄	—	4	4	no	—
605	C₂²×D₄	—	4	4	no	—
606	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
607	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
608	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
612	C₂³×C₄	—	2	1	no	—
613	C₂³×C₄	—	2	1	no	—
614	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
616	C₂×D₈	—	2	2	no	—
617	C₂×D₈	—	2	2	no	—
618	C₂×D₈	—	2	2	no	—
619	C₂×D₈	—	2	2	no	—
620	C₂×D₈	—	2	2	no	—
621	C₂×D₈	—	2	2	no	—
622	C₂×D₈	—	4	1	no	—
623	C₂×D₈	—	4	1	no	—
624	C₂×D₈	—	4	1	no	—
625	C₂²×C₈	—	2	2	no	—
626	C₂²×C₈	—	2	2	no	—
627	C₂²×C₈	—	4	1	no	—
628	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
629	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
630	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
631	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
632	#127	—	2	2	no	—
633	#127	—	2	2	no	—
634	#121	—	2	8	no	—
635	#121	—	2	2	no	—
636	#121	—	2	2	no	—
637	#121	—	2	2	no	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	4	1	no	—
642	#121	—	4	4	no	—
643	#121	D₄×C₁₉	1	4	yes	complemented
644	#120	—	2	8	no	—
645	#120	—	2	8	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₂×C₄⋊C₄	—	2	2	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	4	1	no	—
654	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
670	#107	—	2	2	no	—
671	#102	—	2	2	no	—
672	#102	—	2	2	no	—
673	#102	—	2	2	no	—
674	#102	—	2	2	no	—
675	#102	—	2	2	no	—
676	#102	—	2	2	no	—
677	#102	—	2	2	no	—
678	#102	—	2	2	no	—
679	#102	—	4	1	no	—
680	#102	D₄×C₁₉	1	4	yes	complemented
681	C₂²⋊C₈	—	2	2	no	—
682	C₂²⋊C₈	—	2	2	no	—
683	C₂²⋊C₈	—	4	1	no	—
684	#95	—	2	1	no	—
685	#95	—	2	1	no	—
686	C₁₉	#24424	1	1	yes	characteristic, direct product factor, Sylow
687	C₂⁴	—	2	1	no	—
688	C₂⁴	—	2	4	no	—
689	C₂⁴	—	2	1	no	—
690	C₂⁴	—	2	1	no	—
691	C₂⁴	—	2	4	no	—
692	C₂⁴	—	2	1	no	—
693	C₂⁴	—	4	2	no	—
694	C₂⁴	—	4	2	no	—
695	C₂⁴	—	4	2	no	—
696	C₂⁴	—	4	2	no	—
697	C₂⁴	—	4	2	no	—
698	C₂⁴	—	4	2	no	—
699	C₂⁴	—	4	2	no	—
700	C₂⁴	—	4	2	no	—
701	C₂⁴	—	8	1	no	—
702	C₂⁴	—	8	1	no	—
703	C₂⁴	—	8	1	no	—
704	C₂⁴	—	8	1	no	—
705	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
706	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	8	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	4	4	no	—
746	C₂×D₄	—	4	32	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	4	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	8	1	no	—
759	C₂×D₄	—	8	1	no	—
760	C₂×D₄	—	8	1	no	—
761	C₂×D₄	D₈×C₁₉	1	4	yes	complemented
762	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
763	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
764	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
765	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
766	C₂×D₄	#41×C₁₉	1	2	yes	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	8	1	no	—
787	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
791	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
794	D₈	—	4	4	no	—
795	D₈	—	4	4	no	—
796	D₈	—	4	4	no	—
797	C₂×C₈	—	2	1	no	—
798	C₂×C₈	—	2	1	no	—
799	C₂×C₈	—	2	1	no	—
800	C₂×C₈	—	2	1	no	—
801	C₂×C₈	—	2	1	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	2	1	no	—
806	C₂×C₈	—	2	1	no	—
807	C₂×C₈	—	2	1	no	—
808	C₂×C₈	—	4	4	no	—
809	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	complemented
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	complemented
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	8	1	no	—
831	C₄²	—	2	1	no	—
832	C₄²	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	8	no	—
849	C₂³	—	4	8	no	—
850	C₂³	—	4	8	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	1	no	—
853	C₂³	—	4	1	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	8	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	1	no	—
862	C₂³	—	4	1	no	—
863	C₂³	—	4	1	no	—
864	C₂³	—	4	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	1	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	4	1	no	—
871	C₂³	—	4	1	no	—
872	C₂³	—	4	1	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	1	no	—
875	C₂³	—	8	4	no	—
876	C₂³	—	8	4	no	—
877	C₂³	—	8	4	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	4	no	—
880	C₂³	—	8	4	no	—
881	C₂³	—	8	4	no	—
882	C₂³	—	8	4	no	—
883	C₂³	—	8	4	no	—
884	C₂³	—	8	4	no	—
885	C₂³	C₁₉×#120	1	2	yes	—
886	C₂³	C₂×D₈×C₁₉	1	2	yes	—
887	C₂³	C₂×D₈×C₁₉	1	2	yes	—
888	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
889	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
890	D₄	—	2	8	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	4	8	no	—
899	D₄	—	4	8	no	—
900	D₄	—	4	8	no	—
901	D₄	—	4	8	no	—
902	D₄	—	4	8	no	—
903	D₄	—	4	1	no	—
904	D₄	—	4	1	no	—
905	D₄	—	4	1	no	—
906	D₄	—	4	1	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	1	no	—
910	D₄	—	4	1	no	—
911	D₄	—	8	4	no	—
912	D₄	—	8	4	no	—
913	D₄	—	8	4	no	—
914	D₄	C₁₉×#121	1	4	yes	complemented
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	4	8	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	—	4	1	no	—
943	C₂×C₄	—	4	1	no	—
944	C₂×C₄	—	4	1	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	8	4	no	—
947	C₂×C₄	C₁₉×#120	1	2	yes	—
948	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
949	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
952	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
953	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	4	1	no	—
957	C₈	—	4	1	no	—
958	C₈	—	4	1	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	4	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	8	16	no	—
986	C₂²	—	8	16	no	—
987	C₂²	—	8	1	no	—
988	C₂²	—	8	1	no	—
989	C₂²	—	8	1	no	—
990	C₂²	—	8	1	no	—
991	C₂²	—	8	1	no	—
992	C₂²	—	8	1	no	—
993	C₂²	—	8	1	no	—
994	C₂²	—	8	1	no	—
995	C₂²	—	8	1	no	—
996	C₂²	—	8	1	no	—
997	C₂²	—	8	1	no	—
998	C₂²	—	8	1	no	—
999	C₂²	—	8	1	no	—
1000	C₂²	—	8	1	no	—
1001	C₂²	—	8	1	no	—
1002	C₂²	C₁₉×#447	1	4	yes	complemented
1003	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1004	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1005	C₂²	C₁₉×#546	1	1	yes	characteristic
1006	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
1007	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
1008	C₂²	C₁₉×#576	1	1	yes	characteristic
1009	C₂²	C₁₉×#577	1	1	yes	characteristic
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	8	1	no	—
1017	C₄	—	8	1	no	—
1018	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
1019	C₄	C₁₉×#534	1	1	yes	characteristic
1020	C₄	D₄²×C₁₉	1	1	yes	characteristic
1021	C₄	C₁₉×#546	1	1	yes	characteristic
1022	C₂	—	2	4	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	4	no	—
1025	C₂	—	8	2	no	—
1026	C₂	—	8	2	no	—
1027	C₂	—	16	1	no	—
1028	C₂	C₁₉×#2410	1	1	yes	characteristic
1029	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
1030	C₂	C₁₉×#3012	1	1	yes	characteristic
1031	C₂	C₁₉×#3265	1	1	yes	characteristic
1032	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
1033	C₂	C₁₉×#3294	1	1	yes	characteristic
1034	C₂	C₁₉×#3318	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄²×C₁₉	C₂	semidirect
2. C₂×C₁₉×#466	C₂	semidirect
3. C₂×C₁₉×#447	C₂	semidirect
4. C₂×C₁₉×#447	C₂	semidirect
5. C₂²×C₁₉×#102	C₂	semidirect
6. C₁₉×#2416	C₂	semidirect
7. C₁₉×#2041	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#2011	C₂	semidirect
10. C₁₉×#1999	C₂	semidirect
11. C₁₉×#1879	C₂	semidirect
12. C₁₉×#1874	C₂	semidirect
13. C₁₉×#1869	C₂	semidirect
14. C₁₉×#1862	C₂	semidirect
15. C₁₉×#1786	C₂	semidirect
20. C₂²×D₈×C₁₉	C₂²	semidirect
21. C₂²×D₈×C₁₉	C₂²	semidirect
22. C₂³×C₈×C₁₉	C₂²	semidirect
30. C₂×C₁₉×#121	C₂²	semidirect
31. C₂×C₁₉×#121	C₂²	semidirect
36. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
40. C₂×C₁₉×#107	C₂²	semidirect
45. C₂×C₁₉×#102	C₂²	semidirect
46. C₂×C₁₉×#102	C₂²	semidirect
47. C₂×C₁₉×#102	C₂²	semidirect
48. C₂×C₁₉×#102	C₂²	semidirect
49. C₂×C₁₉×#102	C₂²	semidirect
50. C₂×C₁₉×#102	C₂²	semidirect
51. C₂×C₁₉×#102	C₂²	semidirect
52. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
53. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
57. C₁₉×#390	C₂²	semidirect
58. C₁₉×#389	C₂²	semidirect
60. C₁₉×#380	C₂²	semidirect
61. C₁₉×#340	C₂²	semidirect
62. C₁₉×#340	C₂²	semidirect
63. C₁₉×#336	C₂²	semidirect
64. C₁₉×#336	C₂²	semidirect
90. C₂²×D₄×C₁₉	D₄	semidirect
126. C₁₉×#121	D₄	semidirect
163. C₁₉×#102	D₄	semidirect
243. C₂×D₄×C₁₉	D₈	semidirect
291. C₂×C₈×C₁₉	C₂×D₄	semidirect
302. C₄⋊C₄×C₁₉	C₂×D₄	semidirect
315. #24424	C₁₉	direct (N × H)
397. D₄×C₁₉	#121	semidirect
442. C₂×D₄²	C₂×C₁₉	semidirect
443. C₂×#466	C₂×C₁₉	semidirect
444. C₂×#447	C₂×C₁₉	semidirect
445. C₂×#447	C₂×C₁₉	semidirect
446. C₂²×#102	C₂×C₁₉	semidirect
447. #2416	C₂×C₁₉	semidirect
448. #2041	C₂×C₁₉	semidirect
449. #2033	C₂×C₁₉	semidirect
450. #2011	C₂×C₁₉	semidirect
451. #1999	C₂×C₁₉	semidirect
452. #1879	C₂×C₁₉	semidirect
453. #1874	C₂×C₁₉	semidirect
454. #1869	C₂×C₁₉	semidirect
455. #1862	C₂×C₁₉	semidirect
456. #1786	C₂×C₁₉	semidirect
500. C₂²×C₁₉	#447	semidirect
524. C₂²×D₈	C₂²×C₁₉	semidirect
525. C₂²×D₈	C₂²×C₁₉	semidirect
526. C₂³×C₈	C₂²×C₁₉	semidirect
534. C₂×#121	C₂²×C₁₉	semidirect
535. C₂×#121	C₂²×C₁₉	semidirect
540. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
544. C₂×#107	C₂²×C₁₉	semidirect
549. C₂×#102	C₂²×C₁₉	semidirect
550. C₂×#102	C₂²×C₁₉	semidirect
551. C₂×#102	C₂²×C₁₉	semidirect
552. C₂×#102	C₂²×C₁₉	semidirect
553. C₂×#102	C₂²×C₁₉	semidirect
554. C₂×#102	C₂²×C₁₉	semidirect
555. C₂×#102	C₂²×C₁₉	semidirect
556. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
557. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
558. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
561. #390	C₂²×C₁₉	semidirect
562. #389	C₂²×C₁₉	semidirect
564. #380	C₂²×C₁₉	semidirect
565. #340	C₂²×C₁₉	semidirect
566. #340	C₂²×C₁₉	semidirect
567. #336	C₂²×C₁₉	semidirect
568. #336	C₂²×C₁₉	semidirect
607. C₂²×D₄	D₄×C₁₉	semidirect
643. #121	D₄×C₁₉	semidirect
680. #102	D₄×C₁₉	semidirect
686. C₁₉	#24424	direct (N × H)
761. C₂×D₄	D₈×C₁₉	semidirect
809. C₂×C₈	C₂×D₄×C₁₉	semidirect
820. C₄⋊C₄	C₂×D₄×C₁₉	semidirect
914. D₄	C₁₉×#121	semidirect
1002. C₂²	C₁₉×#447	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₉	2
C₂×C₁₉×#466	2
C₂×C₁₉×#447	2
C₂²×C₁₉×#102	2
C₁₉×#2416	2
C₁₉×#2041	2
C₁₉×#2033	2
C₁₉×#2011	2
C₁₉×#1999	2
C₁₉×#1879	2
C₁₉×#1874	2
C₁₉×#1869	2
C₁₉×#1862	2
C₁₉×#1786	2
#24424	19

Subgroups — C19×#24424 #18030383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24424 #18030383