Subgroups — C₁₉×#11066 #18017025

Order 4864.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
16	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#102	—	2	2	no	—
19	C₂×C₁₉×#102	—	2	2	no	—
20	C₂×C₁₉×#102	—	2	2	no	—
21	C₂×C₁₉×#102	—	2	2	no	—
22	C₂×C₁₉×#102	—	2	2	no	—
23	C₂×C₁₉×#102	C₄	1	4	yes	complemented
24	C₁₉×#390	—	2	2	no	—
25	C₁₉×#390	—	2	2	no	—
26	C₁₉×#389	—	2	2	no	—
27	C₁₉×#389	—	2	2	no	—
28	C₂×C₁₉×#95	—	2	1	no	—
29	C₁₉×#340	—	2	2	no	—
30	C₁₉×#340	—	2	2	no	—
31	C₁₉×#336	—	2	2	no	—
32	C₂⁵×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₉	D₄	1	2	yes	—
46	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₁₉	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	—	2	1	no	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₁₉×#102	—	2	8	no	—
101	C₁₉×#102	—	2	8	no	—
102	C₁₉×#95	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	2	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	2	2	no	—
106	C₂⁴×C₁₉	—	4	1	no	—
107	C₂⁴×C₁₉	—	4	1	no	—
108	C₂⁴×C₁₉	—	4	1	no	—
109	C₂⁴×C₁₉	—	4	1	no	—
110	C₂⁴×C₁₉	—	4	1	no	—
111	C₂⁴×C₁₉	—	4	1	no	—
112	C₂⁴×C₁₉	—	4	1	no	—
113	C₂⁴×C₁₉	—	4	1	no	—
114	C₂⁴×C₁₉	—	4	1	no	—
115	C₂⁴×C₁₉	—	4	1	no	—
116	C₂⁴×C₁₉	—	4	1	no	—
117	C₂⁴×C₁₉	—	4	1	no	—
118	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	1	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	4	1	no	—
146	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	complemented
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	C₂²×C₄×C₁₉	—	4	1	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	—	4	1	no	—
171	C₂²×C₄×C₁₉	—	4	1	no	—
172	C₂²×C₄×C₁₉	—	4	1	no	—
173	C₂²×C₄×C₁₉	—	4	1	no	—
174	C₂²×C₄×C₁₉	—	4	1	no	—
175	C₂²×C₄×C₁₉	—	4	1	no	—
176	C₂²×C₄×C₁₉	—	4	1	no	—
177	C₂²×C₄×C₁₉	—	4	1	no	—
178	C₂²×C₄×C₁₉	—	4	1	no	—
179	C₂²×C₄×C₁₉	—	4	1	no	—
180	C₂²×C₄×C₁₉	D₈	1	2	yes	—
181	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
191	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
193	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
196	C₂×C₈×C₁₉	—	2	2	no	—
197	C₂×C₈×C₁₉	—	2	2	no	—
198	C₂×C₈×C₁₉	—	2	2	no	—
199	C₂×C₈×C₁₉	—	2	2	no	—
200	C₂×C₈×C₁₉	—	2	2	no	—
201	C₂×C₈×C₁₉	—	2	2	no	—
202	C₂×C₈×C₁₉	—	4	1	no	—
203	C₂×C₈×C₁₉	—	4	1	no	—
204	C₂×C₈×C₁₉	—	4	1	no	—
205	C₂×C₈×C₁₉	—	4	1	no	—
206	C₂×C₈×C₁₉	—	4	1	no	—
207	C₂×C₈×C₁₉	—	4	1	no	—
208	C₂×C₈×C₁₉	—	4	1	no	—
209	C₂×C₈×C₁₉	—	4	1	no	—
210	C₄⋊C₄×C₁₉	—	2	2	no	—
211	C₄⋊C₄×C₁₉	—	2	2	no	—
212	C₄⋊C₄×C₁₉	—	2	2	no	—
213	C₄⋊C₄×C₁₉	—	2	2	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	2	no	—
217	C₄⋊C₄×C₁₉	—	4	8	no	—
218	C₄⋊C₄×C₁₉	—	4	1	no	—
219	C₄⋊C₄×C₁₉	—	4	1	no	—
220	C₄⋊C₄×C₁₉	—	4	1	no	—
221	C₄⋊C₄×C₁₉	—	4	1	no	—
222	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	complemented
223	C₂²⋊C₄×C₁₉	—	4	8	no	—
224	C₂²⋊C₄×C₁₉	—	4	8	no	—
225	C₄²×C₁₉	—	4	1	no	—
226	C₄²×C₁₉	—	4	1	no	—
227	C₄²×C₁₉	—	4	1	no	—
228	C₄²×C₁₉	—	4	1	no	—
229	#11066	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₁₉	—	2	4	no	—
231	C₂³×C₁₉	—	4	2	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	2	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	—	4	2	no	—
238	C₂³×C₁₉	—	4	2	no	—
239	C₂³×C₁₉	—	4	2	no	—
240	C₂³×C₁₉	—	4	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	4	2	no	—
244	C₂³×C₁₉	—	4	2	no	—
245	C₂³×C₁₉	—	4	2	no	—
246	C₂³×C₁₉	—	4	2	no	—
247	C₂³×C₁₉	—	4	2	no	—
248	C₂³×C₁₉	—	4	2	no	—
249	C₂³×C₁₉	—	8	1	no	—
250	C₂³×C₁₉	—	8	1	no	—
251	C₂³×C₁₉	—	8	1	no	—
252	C₂³×C₁₉	—	8	1	no	—
253	C₂³×C₁₉	—	8	1	no	—
254	C₂³×C₁₉	—	8	1	no	—
255	C₂³×C₁₉	—	8	1	no	—
256	C₂³×C₁₉	—	8	1	no	—
257	C₂³×C₁₉	—	8	1	no	—
258	C₂³×C₁₉	—	8	1	no	—
259	C₂³×C₁₉	—	8	1	no	—
260	C₂³×C₁₉	—	8	1	no	—
261	C₂³×C₁₉	—	8	1	no	—
262	C₂³×C₁₉	—	8	1	no	—
263	C₂³×C₁₉	—	8	1	no	—
264	C₂³×C₁₉	—	8	1	no	—
265	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
266	C₂³×C₁₉	#120	1	1	yes	characteristic
267	C₂³×C₁₉	#120	1	1	yes	characteristic
268	C₂³×C₁₉	#121	1	1	yes	characteristic
269	C₂³×C₁₉	#121	1	1	yes	characteristic
270	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂³×C₁₉	#124	1	1	yes	characteristic
272	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
273	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
274	C₂³×C₁₉	#135	1	1	yes	characteristic
275	C₂³×C₁₉	#135	1	1	yes	characteristic
276	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₂³×C₁₉	#137	1	1	yes	characteristic
280	D₄×C₁₉	—	2	4	no	—
281	D₄×C₁₉	—	2	4	no	—
282	D₄×C₁₉	—	4	2	no	—
283	D₄×C₁₉	—	4	2	no	—
284	D₄×C₁₉	—	4	2	no	—
285	D₄×C₁₉	—	4	2	no	—
286	D₄×C₁₉	—	4	2	no	—
287	D₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	2	4	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	2	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	4	1	no	—
296	C₂×C₄×C₁₉	—	4	1	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	—	4	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	1	no	—
301	C₂×C₄×C₁₉	—	4	1	no	—
302	C₂×C₄×C₁₉	—	4	1	no	—
303	C₂×C₄×C₁₉	—	4	2	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	2	no	—
310	C₂×C₄×C₁₉	—	4	2	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	4	2	no	—
313	C₂×C₄×C₁₉	—	4	2	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	8	1	no	—
316	C₂×C₄×C₁₉	—	8	1	no	—
317	C₂×C₄×C₁₉	—	8	1	no	—
318	C₂×C₄×C₁₉	—	8	1	no	—
319	C₂×C₄×C₁₉	—	8	1	no	—
320	C₂×C₄×C₁₉	—	8	1	no	—
321	C₂×C₄×C₁₉	—	8	1	no	—
322	C₂×C₄×C₁₉	—	8	1	no	—
323	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
326	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
330	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
332	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
333	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
334	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
335	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
336	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
337	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
339	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
340	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
341	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
342	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
343	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
344	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
345	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
346	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
347	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
348	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
349	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
350	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
351	C₈×C₁₉	—	4	2	no	—
352	C₈×C₁₉	—	4	2	no	—
353	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
354	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
355	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
356	C₂×#389	C₂×C₁₉	1	1	yes	characteristic, complemented
357	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
358	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
359	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
360	C₂²×C₁₉	—	4	4	no	—
361	C₂²×C₁₉	—	4	4	no	—
362	C₂²×C₁₉	—	4	4	no	—
363	C₂²×C₁₉	—	8	2	no	—
364	C₂²×C₁₉	—	8	2	no	—
365	C₂²×C₁₉	—	8	2	no	—
366	C₂²×C₁₉	—	8	2	no	—
367	C₂²×C₁₉	—	8	2	no	—
368	C₂²×C₁₉	—	8	2	no	—
369	C₂²×C₁₉	—	8	2	no	—
370	C₂²×C₁₉	—	8	2	no	—
371	C₂²×C₁₉	—	8	2	no	—
372	C₂²×C₁₉	—	8	2	no	—
373	C₂²×C₁₉	—	8	2	no	—
374	C₂²×C₁₉	—	8	2	no	—
375	C₂²×C₁₉	#385	1	1	yes	characteristic
376	C₂²×C₁₉	#386	1	1	yes	characteristic
377	C₂²×C₁₉	#388	1	1	yes	characteristic
378	C₂²×C₁₉	#392	1	1	yes	characteristic
379	C₂²×C₁₉	#393	1	1	yes	characteristic
380	C₂²×C₁₉	#394	1	1	yes	characteristic
381	C₂²×C₁₉	#396	1	1	yes	characteristic
382	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
383	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
384	C₂²×C₁₉	#440	1	1	yes	characteristic
385	C₂²×C₁₉	#442	1	1	yes	characteristic
386	C₂²×C₁₉	#447	1	1	yes	characteristic
387	C₂²×C₁₉	#447	1	1	yes	characteristic
388	C₂²×C₁₉	#448	1	1	yes	characteristic
389	C₂²×C₁₉	#449	1	1	yes	characteristic
390	C₂²×C₁₉	#449	1	1	yes	characteristic
391	C₂²×C₁₉	#449	1	1	yes	characteristic
392	C₂²×C₁₉	#450	1	1	yes	characteristic
393	C₂²×C₁₉	#452	1	1	yes	characteristic
394	C₂²×C₁₉	#459	1	1	yes	characteristic
395	C₂²×C₁₉	#460	1	1	yes	characteristic
396	C₂²×C₁₉	#463	1	1	yes	characteristic
397	C₂²×C₁₉	#464	1	1	yes	characteristic
398	C₂²×C₁₉	#465	1	1	yes	characteristic
399	C₂²×C₁₉	#466	1	1	yes	characteristic
400	C₂²×C₁₉	#468	1	1	yes	characteristic
401	C₂²×C₁₉	#469	1	1	yes	characteristic
402	C₂²×C₁₉	#474	1	1	yes	characteristic
403	C₂²×C₁₉	#476	1	1	yes	characteristic
404	C₂²×C₁₉	#478	1	1	yes	characteristic
405	C₂²×C₁₉	#478	1	1	yes	characteristic
406	C₂²×C₁₉	#486	1	1	yes	characteristic
407	C₂²×C₁₉	#488	1	1	yes	characteristic
408	C₂²×C₁₉	#489	1	1	yes	characteristic
409	C₂²×C₁₉	#490	1	1	yes	characteristic
410	C₄×C₁₉	—	4	4	no	—
411	C₄×C₁₉	—	4	2	no	—
412	C₄×C₁₉	—	4	2	no	—
413	C₄×C₁₉	—	8	2	no	—
414	C₄×C₁₉	—	8	2	no	—
415	C₄×C₁₉	#380	1	1	yes	characteristic
416	C₄×C₁₉	#385	1	1	yes	characteristic
417	C₄×C₁₉	#388	1	1	yes	characteristic
418	C₄×C₁₉	#390	1	1	yes	characteristic
419	C₄×C₁₉	#394	1	1	yes	characteristic
420	C₄×C₁₉	#396	1	1	yes	characteristic
421	C₄×C₁₉	#397	1	1	yes	characteristic
422	C₄×C₁₉	#399	1	1	yes	characteristic
423	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
424	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
425	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	—	2	1	no	—
427	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
429	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	—	2	1	no	—
431	C₂²×C₂²⋊C₄	—	2	1	no	—
432	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×#102	—	2	2	no	—
434	C₂×#102	—	2	2	no	—
435	C₂×#102	—	2	2	no	—
436	C₂×#102	—	2	2	no	—
437	C₂×#102	—	2	2	no	—
438	C₂×#102	C₄×C₁₉	1	4	yes	complemented
439	#390	—	2	2	no	—
440	#390	—	2	2	no	—
441	#389	—	2	2	no	—
442	#389	—	2	2	no	—
443	C₂×#95	—	2	1	no	—
444	#340	—	2	2	no	—
445	#340	—	2	2	no	—
446	#336	—	2	2	no	—
447	C₂×C₁₉	—	8	4	no	—
448	C₂×C₁₉	#1439	1	1	yes	characteristic
449	C₂×C₁₉	#1862	1	1	yes	characteristic
450	C₂×C₁₉	#1864	1	1	yes	characteristic
451	C₂×C₁₉	#1879	1	1	yes	characteristic
452	C₂×C₁₉	#1880	1	1	yes	characteristic
453	C₂×C₁₉	#1934	1	1	yes	characteristic
454	C₂×C₁₉	#1936	1	1	yes	characteristic
455	C₂×C₁₉	#1999	1	1	yes	characteristic
456	C₂×C₁₉	#2000	1	1	yes	characteristic
457	C₂×C₁₉	#2023	1	1	yes	characteristic
458	C₂×C₁₉	#2025	1	1	yes	characteristic
459	C₂×C₁₉	#2041	1	1	yes	characteristic
460	C₂×C₁₉	#2042	1	1	yes	characteristic
461	C₂×C₁₉	#2065	1	1	yes	characteristic
462	C₂×C₁₉	#2067	1	1	yes	characteristic
463	C₂⁵	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
476	C₂²×D₄	D₄×C₁₉	1	2	yes	—
477	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
482	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
484	C₂²×C₈	—	2	1	no	—
485	C₂²×C₈	—	2	1	no	—
486	C₂²×C₈	—	2	1	no	—
487	C₂²×C₈	—	2	1	no	—
488	C₂²×C₈	—	2	1	no	—
489	C₂²×C₈	—	2	1	no	—
490	C₂²×C₈	—	2	1	no	—
491	C₂²×C₈	—	2	1	no	—
492	C₂²×C₈	—	2	1	no	—
493	C₂²×C₈	—	2	1	no	—
494	C₂²×C₈	—	2	1	no	—
495	C₂²×C₈	—	2	1	no	—
496	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
497	C₂²×C₈	D₄×C₁₉	1	2	yes	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	4	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	4	2	no	—
513	C₂×C₄⋊C₄	—	4	2	no	—
514	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
515	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
516	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
517	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
518	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
519	C₂×C₂²⋊C₄	—	2	4	no	—
520	C₂×C₂²⋊C₄	—	2	4	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×C₄²	—	2	1	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	#102	—	2	8	no	—
532	#102	—	2	8	no	—
533	#95	—	2	4	no	—
534	C₁₉	#11066	1	1	yes	characteristic, direct product factor, Sylow
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	4	1	no	—
539	C₂⁴	—	4	1	no	—
540	C₂⁴	—	4	1	no	—
541	C₂⁴	—	4	1	no	—
542	C₂⁴	—	4	1	no	—
543	C₂⁴	—	4	1	no	—
544	C₂⁴	—	4	1	no	—
545	C₂⁴	—	4	1	no	—
546	C₂⁴	—	4	1	no	—
547	C₂⁴	—	4	1	no	—
548	C₂⁴	—	4	1	no	—
549	C₂⁴	—	4	1	no	—
550	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂×D₄	—	4	1	no	—
571	C₂×D₄	—	4	1	no	—
572	C₂×D₄	—	4	1	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	complemented
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	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	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	1	no	—
599	C₂²×C₄	—	4	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	1	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	D₈×C₁₉	1	2	yes	—
613	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
614	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
622	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
623	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
624	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
625	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
626	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	4	1	no	—
635	C₂×C₈	—	4	1	no	—
636	C₂×C₈	—	4	1	no	—
637	C₂×C₈	—	4	1	no	—
638	C₂×C₈	—	4	1	no	—
639	C₂×C₈	—	4	1	no	—
640	C₂×C₈	—	4	1	no	—
641	C₂×C₈	—	4	1	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	4	8	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	complemented
655	C₂²⋊C₄	—	4	8	no	—
656	C₂²⋊C₄	—	4	8	no	—
657	C₄²	—	4	1	no	—
658	C₄²	—	4	1	no	—
659	C₄²	—	4	1	no	—
660	C₄²	—	4	1	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	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	—	8	1	no	—
681	C₂³	—	8	1	no	—
682	C₂³	—	8	1	no	—
683	C₂³	—	8	1	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	—	8	1	no	—
687	C₂³	—	8	1	no	—
688	C₂³	—	8	1	no	—
689	C₂³	—	8	1	no	—
690	C₂³	—	8	1	no	—
691	C₂³	—	8	1	no	—
692	C₂³	—	8	1	no	—
693	C₂³	—	8	1	no	—
694	C₂³	—	8	1	no	—
695	C₂³	—	8	1	no	—
696	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
697	C₂³	C₁₉×#120	1	1	yes	characteristic
698	C₂³	C₁₉×#120	1	1	yes	characteristic
699	C₂³	C₁₉×#121	1	1	yes	characteristic
700	C₂³	C₁₉×#121	1	1	yes	characteristic
701	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
702	C₂³	C₁₉×#124	1	1	yes	characteristic
703	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
704	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
705	C₂³	C₁₉×#135	1	1	yes	characteristic
706	C₂³	C₁₉×#135	1	1	yes	characteristic
707	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
708	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
709	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
710	C₂³	C₁₉×#137	1	1	yes	characteristic
711	D₄	—	2	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	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	—	8	1	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	—	8	1	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	1	no	—
751	C₂×C₄	—	8	1	no	—
752	C₂×C₄	—	8	1	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
755	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
756	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
757	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
758	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
759	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
760	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
761	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
762	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
763	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
764	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
765	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
766	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
767	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
768	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
769	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
770	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
771	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
772	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
773	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
774	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
775	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
776	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
777	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
778	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
779	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
780	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
781	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
782	C₈	—	4	2	no	—
783	C₈	—	4	2	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	8	2	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	—	8	2	no	—
797	C₂²	—	8	2	no	—
798	C₂²	—	8	2	no	—
799	C₂²	C₁₉×#385	1	1	yes	characteristic
800	C₂²	C₁₉×#386	1	1	yes	characteristic
801	C₂²	C₁₉×#388	1	1	yes	characteristic
802	C₂²	C₁₉×#392	1	1	yes	characteristic
803	C₂²	C₁₉×#393	1	1	yes	characteristic
804	C₂²	C₁₉×#394	1	1	yes	characteristic
805	C₂²	C₁₉×#396	1	1	yes	characteristic
806	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
807	C₂²	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
808	C₂²	C₁₉×#440	1	1	yes	characteristic
809	C₂²	C₁₉×#442	1	1	yes	characteristic
810	C₂²	C₁₉×#447	1	1	yes	characteristic
811	C₂²	C₁₉×#447	1	1	yes	characteristic
812	C₂²	C₁₉×#448	1	1	yes	characteristic
813	C₂²	C₁₉×#449	1	1	yes	characteristic
814	C₂²	C₁₉×#449	1	1	yes	characteristic
815	C₂²	C₁₉×#449	1	1	yes	characteristic
816	C₂²	C₁₉×#450	1	1	yes	characteristic
817	C₂²	C₁₉×#452	1	1	yes	characteristic
818	C₂²	C₁₉×#459	1	1	yes	characteristic
819	C₂²	C₁₉×#460	1	1	yes	characteristic
820	C₂²	C₁₉×#463	1	1	yes	characteristic
821	C₂²	C₁₉×#464	1	1	yes	characteristic
822	C₂²	C₁₉×#465	1	1	yes	characteristic
823	C₂²	C₁₉×#466	1	1	yes	characteristic
824	C₂²	C₁₉×#468	1	1	yes	characteristic
825	C₂²	C₁₉×#469	1	1	yes	characteristic
826	C₂²	C₁₉×#474	1	1	yes	characteristic
827	C₂²	C₁₉×#476	1	1	yes	characteristic
828	C₂²	C₁₉×#478	1	1	yes	characteristic
829	C₂²	C₁₉×#478	1	1	yes	characteristic
830	C₂²	C₁₉×#486	1	1	yes	characteristic
831	C₂²	C₁₉×#488	1	1	yes	characteristic
832	C₂²	C₁₉×#489	1	1	yes	characteristic
833	C₂²	C₁₉×#490	1	1	yes	characteristic
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	4	no	—
837	C₄	—	8	2	no	—
838	C₄	—	8	2	no	—
839	C₄	C₁₉×#380	1	1	yes	characteristic
840	C₄	C₁₉×#385	1	1	yes	characteristic
841	C₄	C₁₉×#388	1	1	yes	characteristic
842	C₄	C₁₉×#390	1	1	yes	characteristic
843	C₄	C₁₉×#394	1	1	yes	characteristic
844	C₄	C₁₉×#396	1	1	yes	characteristic
845	C₄	C₁₉×#397	1	1	yes	characteristic
846	C₄	C₁₉×#399	1	1	yes	characteristic
847	C₂	—	8	4	no	—
848	C₂	C₁₉×#1439	1	1	yes	characteristic
849	C₂	C₁₉×#1862	1	1	yes	characteristic
850	C₂	C₁₉×#1864	1	1	yes	characteristic
851	C₂	C₁₉×#1879	1	1	yes	characteristic
852	C₂	C₁₉×#1880	1	1	yes	characteristic
853	C₂	C₁₉×#1934	1	1	yes	characteristic
854	C₂	C₁₉×#1936	1	1	yes	characteristic
855	C₂	C₁₉×#1999	1	1	yes	characteristic
856	C₂	C₁₉×#2000	1	1	yes	characteristic
857	C₂	C₁₉×#2023	1	1	yes	characteristic
858	C₂	C₁₉×#2025	1	1	yes	characteristic
859	C₂	C₁₉×#2041	1	1	yes	characteristic
860	C₂	C₁₉×#2042	1	1	yes	characteristic
861	C₂	C₁₉×#2065	1	1	yes	characteristic
862	C₂	C₁₉×#2067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#389	C₂	semidirect
5. C₂×C₁₉×#340	C₂	semidirect
6. C₂×C₁₉×#340	C₂	semidirect
7. C₂×C₁₉×#336	C₂	semidirect
23. C₂×C₁₉×#102	C₄	semidirect
146. C₂×D₄×C₁₉	C₄⋊C₄	semidirect
222. C₄⋊C₄×C₁₉	C₂²⋊C₄	semidirect
229. #11066	C₁₉	direct (N × H)
356. C₂×#389	C₂×C₁₉	semidirect
357. C₂×#340	C₂×C₁₉	semidirect
358. C₂×#340	C₂×C₁₉	semidirect
359. C₂×#336	C₂×C₁₉	semidirect
438. C₂×#102	C₄×C₁₉	semidirect
534. C₁₉	#11066	direct (N × H)
578. C₂×D₄	C₄⋊C₄×C₁₉	semidirect
654. C₄⋊C₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₂×C₁₉×#389	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
#11066	19

Subgroups — C19×#11066 #18017025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11066 #18017025