Subgroups — C₄×C₁₉×#449 #18027409

Order 4864.

1564 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₄×#41×C₁₉	—	2	4	no	—
21	C₄×#41×C₁₉	—	2	4	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	—	2	1	no	—
25	C₂×C₄×D₄×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	—	2	1	no	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	—	2	1	no	—
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₉	—	2	1	no	—
33	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#449	C₄	1	8	yes	direct product factor
35	C₄×SD₁₆×C₁₉	—	2	4	no	—
36	C₄×D₈×C₁₉	—	2	4	no	—
37	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
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
46	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
51	C₁₉×#390	C₂²	1	1	yes	characteristic
52	C₁₉×#389	C₂²	1	1	yes	characteristic
53	C₁₉×#388	—	2	1	no	—
54	C₁₉×#386	—	2	1	no	—
55	C₁₉×#380	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₁₉×#336	C₂²	1	1	yes	characteristic
63	C₁₉×#336	C₂²	1	1	yes	characteristic
64	C₂×#41×C₁₉	—	2	2	no	—
65	C₂×#41×C₁₉	—	2	2	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	—	2	2	no	—
68	C₂×#41×C₁₉	—	2	2	no	—
69	C₂×#41×C₁₉	C₂×C₄	1	4	yes	complemented
70	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₉	—	2	1	no	—
72	C₂²×D₄×C₁₉	—	2	1	no	—
73	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	—	2	1	no	—
76	C₂³×C₄×C₁₉	—	2	1	no	—
77	C₂³×C₄×C₁₉	—	2	1	no	—
78	C₂³×C₄×C₁₉	—	2	1	no	—
79	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×SD₁₆×C₁₉	—	2	2	no	—
83	C₂×SD₁₆×C₁₉	—	2	2	no	—
84	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
85	C₂×D₈×C₁₉	—	2	2	no	—
86	C₂×D₈×C₁₉	—	2	2	no	—
87	C₂×D₈×C₁₉	C₂×C₄	1	4	yes	complemented
88	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₁₉×#121	—	2	2	no	—
93	C₁₉×#121	C₂×C₄	1	4	yes	complemented
94	C₄×Q₈×C₁₉	—	2	2	no	—
95	C₄×Q₈×C₁₉	—	2	2	no	—
96	C₄×Q₈×C₁₉	—	2	2	no	—
97	C₄×Q₈×C₁₉	D₄	1	4	yes	complemented
98	C₄×D₄×C₁₉	—	2	8	no	—
99	C₄×D₄×C₁₉	—	2	8	no	—
100	C₄×D₄×C₁₉	—	2	2	no	—
101	C₄×D₄×C₁₉	—	2	2	no	—
102	C₄×D₄×C₁₉	—	2	2	no	—
103	C₄×D₄×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	4	4	no	—
106	C₄×D₄×C₁₉	D₄	1	4	yes	complemented
107	C₁₉×#117	—	2	8	no	—
108	C₁₉×#117	—	2	2	no	—
109	C₁₉×#117	—	2	2	no	—
110	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄²×C₁₉	—	2	8	no	—
127	C₂×C₄²×C₁₉	—	2	1	no	—
128	C₂×C₄²×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	—	2	1	no	—
130	C₂×C₄²×C₁₉	—	2	2	no	—
131	C₂×C₄²×C₁₉	—	2	2	no	—
132	C₂×C₄²×C₁₉	—	2	1	no	—
133	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
135	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
137	C₁₉×#107	—	2	2	no	—
138	C₁₉×#106	—	2	2	no	—
139	C₁₉×#103	—	2	2	no	—
140	C₁₉×#103	—	2	2	no	—
141	C₁₉×#103	C₂×C₄	1	4	yes	complemented
142	C₁₉×#102	—	2	2	no	—
143	C₁₉×#102	—	2	2	no	—
144	C₁₉×#102	—	2	2	no	—
145	C₁₉×#102	—	2	2	no	—
146	C₁₉×#102	C₂×C₄	1	4	yes	complemented
147	C₁₉×C₂²⋊C₈	—	2	2	no	—
148	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
149	C₄×C₈×C₁₉	—	2	2	no	—
150	C₄×C₈×C₁₉	—	2	2	no	—
151	C₁₉×#95	—	2	1	no	—
152	C₁₉×#95	—	2	1	no	—
153	C₁₉×#95	—	2	1	no	—
154	C₂⁴×C₁₉	—	2	1	no	—
155	C₂⁴×C₁₉	—	2	1	no	—
156	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
157	#41×C₁₉	—	2	8	no	—
158	#41×C₁₉	—	2	8	no	—
159	#41×C₁₉	—	2	8	no	—
160	#41×C₁₉	—	2	8	no	—
161	C₂×Q₈×C₁₉	—	2	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
165	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
166	C₂×Q₈×C₁₉	#41	1	2	yes	—
167	C₂×D₄×C₁₉	—	2	4	no	—
168	C₂×D₄×C₁₉	—	2	4	no	—
169	C₂×D₄×C₁₉	—	2	4	no	—
170	C₂×D₄×C₁₉	—	2	4	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	—	2	1	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	4	2	no	—
180	C₂×D₄×C₁₉	—	4	2	no	—
181	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
182	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
183	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
184	C₂×D₄×C₁₉	#41	1	2	yes	—
185	C₂²×C₄×C₁₉	—	2	4	no	—
186	C₂²×C₄×C₁₉	—	2	4	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	4	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	4	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	2	no	—
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	4	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	2	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	—	4	2	no	—
207	C₂²×C₄×C₁₉	—	4	2	no	—
208	C₂²×C₄×C₁₉	—	4	2	no	—
209	C₂²×C₄×C₁₉	—	4	2	no	—
210	C₂²×C₄×C₁₉	—	4	2	no	—
211	C₂²×C₄×C₁₉	—	4	2	no	—
212	C₂²×C₄×C₁₉	—	4	2	no	—
213	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
214	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	#41	1	2	yes	—
220	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	SD₁₆×C₁₉	—	2	8	no	—
222	D₈×C₁₉	—	2	8	no	—
223	C₂×C₈×C₁₉	—	2	1	no	—
224	C₂×C₈×C₁₉	—	2	1	no	—
225	C₂×C₈×C₁₉	—	2	1	no	—
226	C₂×C₈×C₁₉	—	2	1	no	—
227	C₂×C₈×C₁₉	—	2	1	no	—
228	C₂×C₈×C₁₉	—	2	1	no	—
229	C₂×C₈×C₁₉	—	2	1	no	—
230	C₂×C₈×C₁₉	—	2	1	no	—
231	C₂×C₈×C₁₉	—	2	1	no	—
232	C₂×C₈×C₁₉	—	2	1	no	—
233	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
234	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
235	C₄⋊C₄×C₁₉	—	2	4	no	—
236	C₄⋊C₄×C₁₉	—	2	4	no	—
237	C₄⋊C₄×C₁₉	—	2	1	no	—
238	C₄⋊C₄×C₁₉	—	2	1	no	—
239	C₄⋊C₄×C₁₉	—	2	1	no	—
240	C₄⋊C₄×C₁₉	—	2	1	no	—
241	C₄⋊C₄×C₁₉	—	2	1	no	—
242	C₄⋊C₄×C₁₉	—	2	1	no	—
243	C₄⋊C₄×C₁₉	—	2	1	no	—
244	C₄⋊C₄×C₁₉	—	4	2	no	—
245	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
246	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₁₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₉	—	4	2	no	—
253	C₂²⋊C₄×C₁₉	—	4	2	no	—
254	C₂²⋊C₄×C₁₉	—	4	2	no	—
255	C₂²⋊C₄×C₁₉	—	4	2	no	—
256	C₄²×C₁₉	—	2	4	no	—
257	C₄²×C₁₉	—	2	4	no	—
258	C₄²×C₁₉	—	2	2	no	—
259	C₄²×C₁₉	—	2	4	no	—
260	C₄²×C₁₉	—	2	2	no	—
261	C₄²×C₁₉	—	2	1	no	—
262	C₄²×C₁₉	—	2	1	no	—
263	C₄²×C₁₉	—	4	2	no	—
264	C₄²×C₁₉	C₂×D₄	1	2	yes	—
265	C₄²×C₁₉	C₂×D₄	1	2	yes	—
266	C₄×#449	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₁₉	—	2	2	no	—
268	C₂³×C₁₉	—	2	1	no	—
269	C₂³×C₁₉	—	2	2	no	—
270	C₂³×C₁₉	—	2	1	no	—
271	C₂³×C₁₉	—	2	2	no	—
272	C₂³×C₁₉	—	2	1	no	—
273	C₂³×C₁₉	—	2	1	no	—
274	C₂³×C₁₉	—	2	1	no	—
275	C₂³×C₁₉	—	2	1	no	—
276	C₂³×C₁₉	—	2	2	no	—
277	C₂³×C₁₉	—	4	1	no	—
278	C₂³×C₁₉	—	4	1	no	—
279	C₂³×C₁₉	—	4	1	no	—
280	C₂³×C₁₉	—	4	1	no	—
281	C₂³×C₁₉	—	4	1	no	—
282	C₂³×C₁₉	—	4	1	no	—
283	C₂³×C₁₉	—	4	1	no	—
284	C₂³×C₁₉	—	4	1	no	—
285	C₂³×C₁₉	—	4	1	no	—
286	C₂³×C₁₉	—	4	1	no	—
287	C₂³×C₁₉	C₄×D₄	1	2	yes	—
288	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₁₉	—	2	2	no	—
290	Q₈×C₁₉	—	2	2	no	—
291	Q₈×C₁₉	—	2	2	no	—
292	Q₈×C₁₉	C₄×D₄	1	4	yes	complemented
293	D₄×C₁₉	—	2	16	no	—
294	D₄×C₁₉	—	2	2	no	—
295	D₄×C₁₉	—	2	2	no	—
296	D₄×C₁₉	—	2	2	no	—
297	D₄×C₁₉	—	2	2	no	—
298	D₄×C₁₉	—	2	2	no	—
299	D₄×C₁₉	—	4	8	no	—
300	D₄×C₁₉	—	4	1	no	—
301	D₄×C₁₉	—	4	1	no	—
302	D₄×C₁₉	C₄×D₄	1	4	yes	complemented
303	C₂×C₄×C₁₉	—	2	16	no	—
304	C₂×C₄×C₁₉	—	2	2	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	2	1	no	—
313	C₂×C₄×C₁₉	—	2	2	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	2	no	—
316	C₂×C₄×C₁₉	—	2	2	no	—
317	C₂×C₄×C₁₉	—	2	2	no	—
318	C₂×C₄×C₁₉	—	2	1	no	—
319	C₂×C₄×C₁₉	—	2	2	no	—
320	C₂×C₄×C₁₉	—	2	2	no	—
321	C₂×C₄×C₁₉	—	2	1	no	—
322	C₂×C₄×C₁₉	—	2	1	no	—
323	C₂×C₄×C₁₉	—	4	4	no	—
324	C₂×C₄×C₁₉	—	4	8	no	—
325	C₂×C₄×C₁₉	—	4	1	no	—
326	C₂×C₄×C₁₉	—	4	1	no	—
327	C₂×C₄×C₁₉	—	4	1	no	—
328	C₂×C₄×C₁₉	—	4	1	no	—
329	C₂×C₄×C₁₉	—	4	1	no	—
330	C₂×C₄×C₁₉	—	4	1	no	—
331	C₂×C₄×C₁₉	—	4	4	no	—
332	C₂×C₄×C₁₉	—	4	8	no	—
333	C₂×C₄×C₁₉	—	4	1	no	—
334	C₂×C₄×C₁₉	—	4	1	no	—
335	C₂×C₄×C₁₉	—	4	1	no	—
336	C₂×C₄×C₁₉	—	4	1	no	—
337	C₂×C₄×C₁₉	—	4	1	no	—
338	C₂×C₄×C₁₉	—	4	1	no	—
339	C₂×C₄×C₁₉	—	8	4	no	—
340	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
341	C₂×C₄×C₁₉	#120	1	2	yes	—
342	C₂×C₄×C₁₉	#120	1	2	yes	—
343	C₂×C₄×C₁₉	#135	1	2	yes	—
344	C₂×C₄×C₁₉	#135	1	2	yes	—
345	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
346	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
352	C₈×C₁₉	—	2	2	no	—
353	C₈×C₁₉	—	2	2	no	—
354	C₈×C₁₉	—	4	1	no	—
355	C₈×C₁₉	—	4	1	no	—
356	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
357	C₂×#449	C₂×C₁₉	1	1	yes	characteristic
358	C₂×C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
359	C₂×C₄×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
360	C₄×#121	C₂×C₁₉	1	1	yes	characteristic, complemented
361	#1880	C₂×C₁₉	1	1	yes	characteristic, complemented
362	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
363	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
364	#1864	C₂×C₁₉	1	1	yes	characteristic, complemented
365	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
366	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
367	#1788	C₂×C₁₉	1	1	yes	characteristic, complemented
368	C₄×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
369	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
370	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
371	C₂²×C₁₉	—	2	2	no	—
372	C₂²×C₁₉	—	2	2	no	—
373	C₂²×C₁₉	—	2	2	no	—
374	C₂²×C₁₉	—	2	4	no	—
375	C₂²×C₁₉	—	4	1	no	—
376	C₂²×C₁₉	—	4	2	no	—
377	C₂²×C₁₉	—	4	1	no	—
378	C₂²×C₁₉	—	4	2	no	—
379	C₂²×C₁₉	—	4	2	no	—
380	C₂²×C₁₉	—	4	2	no	—
381	C₂²×C₁₉	—	4	1	no	—
382	C₂²×C₁₉	—	4	2	no	—
383	C₂²×C₁₉	—	4	1	no	—
384	C₂²×C₁₉	—	4	2	no	—
385	C₂²×C₁₉	—	4	2	no	—
386	C₂²×C₁₉	—	4	2	no	—
387	C₂²×C₁₉	—	4	2	no	—
388	C₂²×C₁₉	—	8	1	no	—
389	C₂²×C₁₉	—	8	1	no	—
390	C₂²×C₁₉	—	8	1	no	—
391	C₂²×C₁₉	—	8	1	no	—
392	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
393	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
394	C₂²×C₁₉	#525	1	1	yes	characteristic
395	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
396	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
397	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₂²×C₁₉	#575	1	1	yes	characteristic
399	C₄×C₁₉	—	2	2	no	—
400	C₄×C₁₉	—	2	2	no	—
401	C₄×C₁₉	—	2	2	no	—
402	C₄×C₁₉	—	2	4	no	—
403	C₄×C₁₉	—	4	2	no	—
404	C₄×C₁₉	—	4	1	no	—
405	C₄×C₁₉	—	4	2	no	—
406	C₄×C₁₉	—	4	2	no	—
407	C₄×C₁₉	—	8	1	no	—
408	C₄×C₁₉	—	8	1	no	—
409	C₄×C₁₉	#449	1	4	yes	direct product factor
410	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
411	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
412	C₄×C₁₉	#525	1	1	yes	characteristic
413	C₄×C₁₉	#525	1	1	yes	characteristic
414	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
418	C₄×#41	—	2	4	no	—
419	C₄×#41	—	2	4	no	—
420	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×C₄×D₄	—	2	1	no	—
423	C₂×C₄×D₄	—	2	1	no	—
424	C₂×C₄×D₄	—	2	1	no	—
425	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#117	—	2	1	no	—
429	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
430	C₂²×C₄²	—	2	1	no	—
431	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
432	#449	C₄×C₁₉	1	8	yes	direct product factor
433	C₄×SD₁₆	—	2	4	no	—
434	C₄×D₈	—	2	4	no	—
435	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
436	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
438	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
439	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
441	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
442	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
444	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
447	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
449	#390	C₂²×C₁₉	1	1	yes	characteristic
450	#389	C₂²×C₁₉	1	1	yes	characteristic
451	#388	—	2	1	no	—
452	#386	—	2	1	no	—
453	#380	C₂²×C₁₉	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	#340	C₂²×C₁₉	1	1	yes	characteristic
457	#340	C₂²×C₁₉	1	1	yes	characteristic
458	#340	C₂²×C₁₉	1	1	yes	characteristic
459	#340	C₂²×C₁₉	1	1	yes	characteristic
460	#336	C₂²×C₁₉	1	1	yes	characteristic
461	#336	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×C₁₉	—	4	2	no	—
463	C₂×C₁₉	—	4	4	no	—
464	C₂×C₁₉	—	8	2	no	—
465	C₂×C₁₉	C₄×#120	1	1	yes	characteristic
466	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
467	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
468	C₂×C₁₉	C₂×#449	1	1	yes	characteristic
469	C₂×C₁₉	#3002	1	1	yes	characteristic
470	C₂×C₁₉	#3102	1	1	yes	characteristic
471	C₂×C₁₉	#3106	1	1	yes	characteristic
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	2	no	—
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	C₂×C₄×C₁₉	1	4	yes	complemented
478	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
488	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
490	C₂×SD₁₆	—	2	2	no	—
491	C₂×SD₁₆	—	2	2	no	—
492	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
493	C₂×D₈	—	2	2	no	—
494	C₂×D₈	—	2	2	no	—
495	C₂×D₈	C₂×C₄×C₁₉	1	4	yes	complemented
496	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
500	#121	—	2	2	no	—
501	#121	C₂×C₄×C₁₉	1	4	yes	complemented
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	D₄×C₁₉	1	4	yes	complemented
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	4	4	no	—
514	C₄×D₄	D₄×C₁₉	1	4	yes	complemented
515	#117	—	2	8	no	—
516	#117	—	2	2	no	—
517	#117	—	2	2	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₄²	—	2	8	no	—
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	—	2	2	no	—
539	C₂×C₄²	—	2	2	no	—
540	C₂×C₄²	—	2	1	no	—
541	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
542	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
545	#107	—	2	2	no	—
546	#106	—	2	2	no	—
547	#103	—	2	2	no	—
548	#103	—	2	2	no	—
549	#103	C₂×C₄×C₁₉	1	4	yes	complemented
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	—	2	2	no	—
553	#102	—	2	2	no	—
554	#102	C₂×C₄×C₁₉	1	4	yes	complemented
555	C₂²⋊C₈	—	2	2	no	—
556	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
557	C₄×C₈	—	2	2	no	—
558	C₄×C₈	—	2	2	no	—
559	#95	—	2	1	no	—
560	#95	—	2	1	no	—
561	#95	—	2	1	no	—
562	C₁₉	C₄×#449	1	1	yes	characteristic, direct product factor, Sylow
563	C₂⁴	—	2	1	no	—
564	C₂⁴	—	2	1	no	—
565	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
566	#41	—	2	8	no	—
567	#41	—	2	8	no	—
568	#41	—	2	8	no	—
569	#41	—	2	8	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
574	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
575	C₂×Q₈	#41×C₁₉	1	2	yes	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
591	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
592	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
593	C₂×D₄	#41×C₁₉	1	2	yes	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
623	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₂²×C₄	#41×C₁₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
630	SD₁₆	—	2	8	no	—
631	D₈	—	2	8	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
643	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	4	2	no	—
673	C₄²	C₂×D₄×C₁₉	1	2	yes	—
674	C₄²	C₂×D₄×C₁₉	1	2	yes	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	C₄×D₄×C₁₉	1	2	yes	—
696	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	C₄×D₄×C₁₉	1	4	yes	complemented
701	D₄	—	2	16	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	2	no	—
706	D₄	—	2	2	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	1	no	—
709	D₄	—	4	1	no	—
710	D₄	C₄×D₄×C₁₉	1	4	yes	complemented
711	C₂×C₄	—	2	16	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	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	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	8	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
749	C₂×C₄	C₁₉×#120	1	2	yes	—
750	C₂×C₄	C₁₉×#120	1	2	yes	—
751	C₂×C₄	C₁₉×#135	1	2	yes	—
752	C₂×C₄	C₁₉×#135	1	2	yes	—
753	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
754	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
757	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
758	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
759	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₈	—	4	1	no	—
763	C₈	—	4	1	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	—	8	1	no	—
785	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
786	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
787	C₂²	C₁₉×#525	1	1	yes	characteristic
788	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
789	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
790	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
791	C₂²	C₁₉×#575	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	4	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	8	1	no	—
801	C₄	—	8	1	no	—
802	C₄	C₁₉×#449	1	4	yes	direct product factor
803	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
804	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
805	C₄	C₁₉×#525	1	1	yes	characteristic
806	C₄	C₁₉×#525	1	1	yes	characteristic
807	C₂	—	4	2	no	—
808	C₂	—	4	4	no	—
809	C₂	—	8	2	no	—
810	C₂	C₄×C₁₉×#120	1	1	yes	characteristic
811	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
812	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
813	C₂	C₂×C₁₉×#449	1	1	yes	characteristic
814	C₂	C₁₉×#3002	1	1	yes	characteristic
815	C₂	C₁₉×#3102	1	1	yes	characteristic
816	C₂	C₁₉×#3106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
prime radical	C₂×C₁₉×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₁₉	C₂	semidirect
3. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
4. C₂×C₄×D₈×C₁₉	C₂	semidirect
5. C₄×C₁₉×#121	C₂	semidirect
6. C₁₉×#1880	C₂	semidirect
7. C₁₉×#1879	C₂	semidirect
8. C₁₉×#1875	C₂	semidirect
9. C₁₉×#1864	C₂	semidirect
10. C₁₉×#1863	C₂	semidirect
11. C₁₉×#1854	C₂	semidirect
12. C₁₉×#1788	C₂	semidirect
13. C₄×C₁₉×#103	C₂	semidirect
14. C₄×C₁₉×#102	C₂	semidirect
15. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
34. C₁₉×#449	C₄	direct (N × H)
69. C₂×#41×C₁₉	C₂×C₄	semidirect
84. C₂×SD₁₆×C₁₉	C₂×C₄	semidirect
87. C₂×D₈×C₁₉	C₂×C₄	semidirect
93. C₁₉×#121	C₂×C₄	semidirect
97. C₄×Q₈×C₁₉	D₄	semidirect
106. C₄×D₄×C₁₉	D₄	semidirect
141. C₁₉×#103	C₂×C₄	semidirect
146. C₁₉×#102	C₂×C₄	semidirect
148. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
266. C₄×#449	C₁₉	direct (N × H)
292. Q₈×C₁₉	C₄×D₄	semidirect
302. D₄×C₁₉	C₄×D₄	semidirect
356. C₂×C₄×#41	C₂×C₁₉	semidirect
358. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
359. C₂×C₄×D₈	C₂×C₁₉	semidirect
360. C₄×#121	C₂×C₁₉	semidirect
361. #1880	C₂×C₁₉	semidirect
362. #1879	C₂×C₁₉	semidirect
363. #1875	C₂×C₁₉	semidirect
364. #1864	C₂×C₁₉	semidirect
365. #1863	C₂×C₁₉	semidirect
366. #1854	C₂×C₁₉	semidirect
367. #1788	C₂×C₁₉	semidirect
368. C₄×#103	C₂×C₁₉	semidirect
369. C₄×#102	C₂×C₁₉	semidirect
370. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
409. C₄×C₁₉	#449	direct (N × H)
432. #449	C₄×C₁₉	direct (N × H)
477. C₂×#41	C₂×C₄×C₁₉	semidirect
492. C₂×SD₁₆	C₂×C₄×C₁₉	semidirect
495. C₂×D₈	C₂×C₄×C₁₉	semidirect
501. #121	C₂×C₄×C₁₉	semidirect
505. C₄×Q₈	D₄×C₁₉	semidirect
514. C₄×D₄	D₄×C₁₉	semidirect
549. #103	C₂×C₄×C₁₉	semidirect
554. #102	C₂×C₄×C₁₉	semidirect
556. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
562. C₁₉	C₄×#449	direct (N × H)
700. Q₈	C₄×D₄×C₁₉	semidirect
710. D₄	C₄×D₄×C₁₉	semidirect
802. C₄	C₁₉×#449	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₂×C₁₉×#449	2
C₂×C₄×SD₁₆×C₁₉	2
C₂×C₄×D₈×C₁₉	2
C₄×C₁₉×#121	2
C₁₉×#1880	2
C₁₉×#1879	2
C₁₉×#1875	2
C₁₉×#1864	2
C₁₉×#1863	2
C₁₉×#1854	2
C₁₉×#1788	2
C₄×C₁₉×#103	2
C₄×C₁₉×#102	2
C₄×C₁₉×C₂²⋊C₈	2
C₄×#449	19

Subgroups — C4×C19×#449 #18027409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#449 #18027409