Subgroups — C₁₉×#25575 #18031534

Order 4864.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2540	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#553	—	2	4	no	—
19	C₁₉×#553	—	2	4	no	—
20	C₂×C₁₉×#126	—	2	1	no	—
21	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#123	—	2	1	no	—
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#121	—	2	1	no	—
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
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
31	C₂×C₄×D₄×C₁₉	—	2	1	no	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#488	—	2	4	no	—
37	C₁₉×#463	—	2	4	no	—
38	C₂×C₁₉×C₄⋊C₈	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×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
52	C₁₉×#399	—	2	1	no	—
53	C₁₉×#392	—	2	1	no	—
54	C₁₉×#390	—	2	1	no	—
55	C₁₉×#390	—	2	1	no	—
56	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
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×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	—	2	1	no	—
68	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	—	2	1	no	—
72	C₂³×C₄×C₁₉	—	2	1	no	—
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×SD₁₆×C₁₉	—	2	2	no	—
76	C₂×SD₁₆×C₁₉	—	4	1	no	—
77	C₂×SD₁₆×C₁₉	—	4	1	no	—
78	C₂×D₈×C₁₉	—	2	2	no	—
79	C₂×D₈×C₁₉	—	4	1	no	—
80	C₂×D₈×C₁₉	—	4	1	no	—
81	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#126	—	2	8	no	—
86	C₁₉×#125	—	2	2	no	—
87	C₁₉×#125	D₄	1	4	yes	complemented
88	C₁₉×#124	—	2	2	no	—
89	C₁₉×#124	—	2	2	no	—
90	C₁₉×#123	—	2	8	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	4	1	no	—
94	C₁₉×C₂²⋊Q₈	—	4	1	no	—
95	C₁₉×#121	—	2	8	no	—
96	C₁₉×#121	—	2	2	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₁₉×#121	—	4	1	no	—
103	C₁₉×#121	—	4	1	no	—
104	C₄×D₄×C₁₉	—	2	8	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₄×D₄×C₁₉	—	2	2	no	—
108	C₄×D₄×C₁₉	D₄	1	4	yes	complemented
109	C₁₉×#117	—	2	2	no	—
110	C₁₉×#117	—	2	2	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
136	C₂×C₄²×C₁₉	—	2	1	no	—
137	C₂×C₄²×C₁₉	—	2	1	no	—
138	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
139	C₁₉×C₄⋊C₈	—	2	2	no	—
140	C₁₉×#103	—	2	2	no	—
141	C₁₉×#103	—	2	2	no	—
142	C₁₉×#103	—	2	2	no	—
143	C₁₉×#102	—	2	2	no	—
144	C₁₉×#102	—	2	2	no	—
145	C₁₉×#102	—	2	2	no	—
146	C₁₉×#102	—	2	2	no	—
147	C₁₉×#102	—	2	2	no	—
148	C₁₉×C₂²⋊C₈	—	4	1	no	—
149	C₁₉×C₂²⋊C₈	—	4	1	no	—
150	C₁₉×C₂²⋊C₈	—	4	1	no	—
151	C₁₉×C₂²⋊C₈	—	4	1	no	—
152	C₄×C₈×C₁₉	—	2	2	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	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₉	—	2	1	no	—
159	C₂×Q₈×C₁₉	—	2	1	no	—
160	C₂×Q₈×C₁₉	—	2	1	no	—
161	C₂×Q₈×C₁₉	—	2	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	4	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	4	no	—
167	C₂×D₄×C₁₉	—	2	2	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	2	1	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	1	no	—
180	C₂×D₄×C₁₉	—	4	2	no	—
181	C₂×D₄×C₁₉	—	4	2	no	—
182	C₂×D₄×C₁₉	—	4	2	no	—
183	C₂×D₄×C₁₉	—	4	2	no	—
184	C₂×D₄×C₁₉	—	4	2	no	—
185	C₂×D₄×C₁₉	—	4	2	no	—
186	C₂×D₄×C₁₉	—	8	1	no	—
187	C₂×D₄×C₁₉	—	8	1	no	—
188	C₂×D₄×C₁₉	—	8	1	no	—
189	C₂×D₄×C₁₉	—	8	1	no	—
190	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	2	1	no	—
193	C₂²×C₄×C₁₉	—	2	1	no	—
194	C₂²×C₄×C₁₉	—	2	1	no	—
195	C₂²×C₄×C₁₉	—	2	1	no	—
196	C₂²×C₄×C₁₉	—	2	4	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	4	no	—
210	C₂²×C₄×C₁₉	—	2	1	no	—
211	C₂²×C₄×C₁₉	—	8	1	no	—
212	C₂²×C₄×C₁₉	—	8	1	no	—
213	C₂²×C₄×C₁₉	—	8	1	no	—
214	C₂²×C₄×C₁₉	—	8	1	no	—
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	C₂⁴	1	1	yes	characteristic
220	SD₁₆×C₁₉	—	4	4	no	—
221	D₈×C₁₉	—	4	4	no	—
222	C₂×C₈×C₁₉	—	2	1	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	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	4	no	—
235	C₄⋊C₄×C₁₉	—	2	4	no	—
236	C₄⋊C₄×C₁₉	—	2	4	no	—
237	C₄⋊C₄×C₁₉	—	2	2	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	—	4	2	no	—
244	C₄⋊C₄×C₁₉	—	4	2	no	—
245	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
247	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₁₉	#41	1	2	yes	—
249	C₄⋊C₄×C₁₉	#41	1	2	yes	—
250	C₂²⋊C₄×C₁₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₉	—	2	2	no	—
255	C₂²⋊C₄×C₁₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₉	—	4	2	no	—
257	C₂²⋊C₄×C₁₉	—	4	2	no	—
258	C₂²⋊C₄×C₁₉	—	4	2	no	—
259	C₂²⋊C₄×C₁₉	—	4	2	no	—
260	C₂²⋊C₄×C₁₉	—	4	2	no	—
261	C₂²⋊C₄×C₁₉	—	4	2	no	—
262	C₄²×C₁₉	—	2	4	no	—
263	C₄²×C₁₉	—	8	1	no	—
264	C₄²×C₁₉	C₂×D₄	1	2	yes	—
265	C₄²×C₁₉	C₂×D₄	1	2	yes	—
266	#25575	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₁₉	—	2	1	no	—
268	C₂³×C₁₉	—	2	1	no	—
269	C₂³×C₁₉	—	2	1	no	—
270	C₂³×C₁₉	—	2	1	no	—
271	C₂³×C₁₉	—	2	1	no	—
272	C₂³×C₁₉	—	2	1	no	—
273	C₂³×C₁₉	—	2	1	no	—
274	C₂³×C₁₉	—	2	2	no	—
275	C₂³×C₁₉	—	2	1	no	—
276	C₂³×C₁₉	—	2	1	no	—
277	C₂³×C₁₉	—	2	1	no	—
278	C₂³×C₁₉	—	2	1	no	—
279	C₂³×C₁₉	—	2	1	no	—
280	C₂³×C₁₉	—	2	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	—	4	1	no	—
288	C₂³×C₁₉	—	4	1	no	—
289	C₂³×C₁₉	—	4	1	no	—
290	C₂³×C₁₉	—	4	1	no	—
291	C₂³×C₁₉	—	4	1	no	—
292	C₂³×C₁₉	—	4	1	no	—
293	C₂³×C₁₉	—	4	1	no	—
294	C₂³×C₁₉	#135	1	2	yes	—
295	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₁₉	—	4	1	no	—
297	Q₈×C₁₉	—	4	1	no	—
298	Q₈×C₁₉	—	4	1	no	—
299	Q₈×C₁₉	—	4	1	no	—
300	D₄×C₁₉	—	2	2	no	—
301	D₄×C₁₉	—	2	2	no	—
302	D₄×C₁₉	—	4	4	no	—
303	D₄×C₁₉	—	4	8	no	—
304	D₄×C₁₉	—	4	1	no	—
305	D₄×C₁₉	—	4	1	no	—
306	D₄×C₁₉	—	4	1	no	—
307	D₄×C₁₉	—	4	1	no	—
308	D₄×C₁₉	—	4	1	no	—
309	D₄×C₁₉	—	4	1	no	—
310	D₄×C₁₉	—	8	4	no	—
311	D₄×C₁₉	—	8	4	no	—
312	D₄×C₁₉	—	8	4	no	—
313	C₂×C₄×C₁₉	—	2	1	no	—
314	C₂×C₄×C₁₉	—	2	1	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	1	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	2	2	no	—
320	C₂×C₄×C₁₉	—	2	1	no	—
321	C₂×C₄×C₁₉	—	2	2	no	—
322	C₂×C₄×C₁₉	—	2	2	no	—
323	C₂×C₄×C₁₉	—	2	2	no	—
324	C₂×C₄×C₁₉	—	2	1	no	—
325	C₂×C₄×C₁₉	—	2	1	no	—
326	C₂×C₄×C₁₉	—	2	1	no	—
327	C₂×C₄×C₁₉	—	2	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	1	no	—
332	C₂×C₄×C₁₉	—	4	1	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	—	4	1	no	—
340	C₂×C₄×C₁₉	—	4	1	no	—
341	C₂×C₄×C₁₉	—	4	1	no	—
342	C₂×C₄×C₁₉	—	4	1	no	—
343	C₂×C₄×C₁₉	—	4	1	no	—
344	C₂×C₄×C₁₉	—	4	1	no	—
345	C₂×C₄×C₁₉	—	4	1	no	—
346	C₂×C₄×C₁₉	—	4	1	no	—
347	C₂×C₄×C₁₉	—	4	1	no	—
348	C₂×C₄×C₁₉	—	4	1	no	—
349	C₂×C₄×C₁₉	—	8	4	no	—
350	C₂×C₄×C₁₉	—	8	4	no	—
351	C₂×C₄×C₁₉	#120	1	2	yes	—
352	C₂×C₄×C₁₉	#120	1	2	yes	—
353	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
359	C₈×C₁₉	—	4	1	no	—
360	C₈×C₁₉	—	4	1	no	—
361	C₈×C₁₉	—	4	1	no	—
362	C₈×C₁₉	—	4	1	no	—
363	C₂×#553	C₂×C₁₉	1	1	yes	characteristic, complemented
364	C₂×#488	C₂×C₁₉	1	1	yes	characteristic, complemented
365	C₂×#463	C₂×C₁₉	1	1	yes	characteristic, complemented
366	#2540	C₂×C₁₉	1	1	yes	characteristic, complemented
367	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
368	#2000	C₂×C₁₉	1	1	yes	characteristic, complemented
369	#1999	C₂×C₁₉	1	1	yes	characteristic, complemented
370	#1999	C₂×C₁₉	1	1	yes	characteristic, complemented
371	#1989	C₂×C₁₉	1	1	yes	characteristic, complemented
372	#1954	C₂×C₁₉	1	1	yes	characteristic, complemented
373	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
374	#1874	C₂×C₁₉	1	1	yes	characteristic, complemented
375	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#1872	C₂×C₁₉	1	1	yes	characteristic, complemented
377	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
378	C₂²×C₁₉	—	2	2	no	—
379	C₂²×C₁₉	—	2	2	no	—
380	C₂²×C₁₉	—	2	2	no	—
381	C₂²×C₁₉	—	4	1	no	—
382	C₂²×C₁₉	—	4	1	no	—
383	C₂²×C₁₉	—	4	1	no	—
384	C₂²×C₁₉	—	4	1	no	—
385	C₂²×C₁₉	—	4	1	no	—
386	C₂²×C₁₉	—	4	2	no	—
387	C₂²×C₁₉	—	4	1	no	—
388	C₂²×C₁₉	—	4	2	no	—
389	C₂²×C₁₉	—	4	2	no	—
390	C₂²×C₁₉	—	4	1	no	—
391	C₂²×C₁₉	—	4	1	no	—
392	C₂²×C₁₉	—	4	1	no	—
393	C₂²×C₁₉	—	4	1	no	—
394	C₂²×C₁₉	—	4	1	no	—
395	C₂²×C₁₉	—	8	1	no	—
396	C₂²×C₁₉	—	8	1	no	—
397	C₂²×C₁₉	—	8	1	no	—
398	C₂²×C₁₉	—	8	1	no	—
399	C₂²×C₁₉	—	8	1	no	—
400	C₂²×C₁₉	—	8	1	no	—
401	C₂²×C₁₉	—	8	1	no	—
402	C₂²×C₁₉	—	8	1	no	—
403	C₂²×C₁₉	—	8	1	no	—
404	C₂²×C₁₉	—	8	1	no	—
405	C₂²×C₁₉	—	8	1	no	—
406	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
407	C₂²×C₁₉	#546	1	1	yes	characteristic
408	C₂²×C₁₉	#546	1	1	yes	characteristic
409	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
410	C₂²×C₁₉	#575	1	1	yes	characteristic
411	C₂²×C₁₉	#576	1	1	yes	characteristic
412	C₂²×C₁₉	#577	1	1	yes	characteristic
413	C₄×C₁₉	—	2	2	no	—
414	C₄×C₁₉	—	2	2	no	—
415	C₄×C₁₉	—	4	1	no	—
416	C₄×C₁₉	—	4	1	no	—
417	C₄×C₁₉	—	4	2	no	—
418	C₄×C₁₉	—	4	2	no	—
419	C₄×C₁₉	—	4	2	no	—
420	C₄×C₁₉	—	4	2	no	—
421	C₄×C₁₉	—	4	2	no	—
422	C₄×C₁₉	—	8	1	no	—
423	C₄×C₁₉	#532	1	1	yes	characteristic
424	C₄×C₁₉	#535	1	1	yes	characteristic
425	C₄×C₁₉	#550	1	1	yes	characteristic
426	C₄×C₁₉	#550	1	1	yes	characteristic
427	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
428	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
429	#553	—	2	4	no	—
430	#553	—	2	4	no	—
431	C₂×#126	—	2	1	no	—
432	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×#123	—	2	1	no	—
435	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
436	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×#121	—	2	1	no	—
438	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
439	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
441	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
442	C₂×C₄×D₄	—	2	1	no	—
443	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
446	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
447	#488	—	2	4	no	—
448	#463	—	2	4	no	—
449	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
450	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
451	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
454	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
455	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
460	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
463	#399	—	2	1	no	—
464	#392	—	2	1	no	—
465	#390	—	2	1	no	—
466	#390	—	2	1	no	—
467	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
468	#340	C₂²×C₁₉	1	1	yes	characteristic
469	#340	C₂²×C₁₉	1	1	yes	characteristic
470	#340	C₂²×C₁₉	1	1	yes	characteristic
471	#340	C₂²×C₁₉	1	1	yes	characteristic
472	#340	C₂²×C₁₉	1	1	yes	characteristic
473	#340	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×C₁₉	—	4	2	no	—
475	C₂×C₁₉	—	8	1	no	—
476	C₂×C₁₉	—	8	2	no	—
477	C₂×C₁₉	—	16	1	no	—
478	C₂×C₁₉	#2431	1	1	yes	characteristic
479	C₂×C₁₉	#3002	1	1	yes	characteristic
480	C₂×C₁₉	#3012	1	1	yes	characteristic
481	C₂×C₁₉	#3297	1	1	yes	characteristic
482	C₂×C₁₉	#3301	1	1	yes	characteristic
483	C₂×C₁₉	#3322	1	1	yes	characteristic
484	C₂×C₁₉	#3326	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	4	1	no	—
499	C₂×SD₁₆	—	4	1	no	—
500	C₂×D₈	—	2	2	no	—
501	C₂×D₈	—	4	1	no	—
502	C₂×D₈	—	4	1	no	—
503	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
507	#126	—	2	8	no	—
508	#125	—	2	2	no	—
509	#125	D₄×C₁₉	1	4	yes	complemented
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#123	—	2	8	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	4	1	no	—
516	C₂²⋊Q₈	—	4	1	no	—
517	#121	—	2	8	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	4	1	no	—
525	#121	—	4	1	no	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	D₄×C₁₉	1	4	yes	complemented
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
561	C₄⋊C₈	—	2	2	no	—
562	#103	—	2	2	no	—
563	#103	—	2	2	no	—
564	#103	—	2	2	no	—
565	#102	—	2	2	no	—
566	#102	—	2	2	no	—
567	#102	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	C₂²⋊C₈	—	4	1	no	—
571	C₂²⋊C₈	—	4	1	no	—
572	C₂²⋊C₈	—	4	1	no	—
573	C₂²⋊C₈	—	4	1	no	—
574	C₄×C₈	—	2	2	no	—
575	#95	—	2	1	no	—
576	C₁₉	#25575	1	1	yes	characteristic, direct product factor, Sylow
577	C₂⁴	—	2	1	no	—
578	C₂⁴	—	2	1	no	—
579	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
580	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	4	1	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	8	1	no	—
610	C₂×D₄	—	8	1	no	—
611	C₂×D₄	—	8	1	no	—
612	C₂×D₄	—	8	1	no	—
613	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	8	1	no	—
635	C₂²×C₄	—	8	1	no	—
636	C₂²×C₄	—	8	1	no	—
637	C₂²×C₄	—	8	1	no	—
638	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
643	SD₁₆	—	4	4	no	—
644	D₈	—	4	4	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
670	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
671	C₄⋊C₄	#41×C₁₉	1	2	yes	—
672	C₄⋊C₄	#41×C₁₉	1	2	yes	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	8	1	no	—
687	C₄²	C₂×D₄×C₁₉	1	2	yes	—
688	C₄²	C₂×D₄×C₁₉	1	2	yes	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	C₁₉×#135	1	2	yes	—
717	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
718	Q₈	—	4	1	no	—
719	Q₈	—	4	1	no	—
720	Q₈	—	4	1	no	—
721	Q₈	—	4	1	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	4	4	no	—
725	D₄	—	4	8	no	—
726	D₄	—	4	1	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	1	no	—
732	D₄	—	8	4	no	—
733	D₄	—	8	4	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	8	4	no	—
772	C₂×C₄	—	8	4	no	—
773	C₂×C₄	C₁₉×#120	1	2	yes	—
774	C₂×C₄	C₁₉×#120	1	2	yes	—
775	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
777	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
778	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
779	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
780	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
781	C₈	—	4	1	no	—
782	C₈	—	4	1	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	1	no	—
812	C₂²	—	8	1	no	—
813	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
814	C₂²	C₁₉×#546	1	1	yes	characteristic
815	C₂²	C₁₉×#546	1	1	yes	characteristic
816	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
817	C₂²	C₁₉×#575	1	1	yes	characteristic
818	C₂²	C₁₉×#576	1	1	yes	characteristic
819	C₂²	C₁₉×#577	1	1	yes	characteristic
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	8	1	no	—
830	C₄	C₁₉×#532	1	1	yes	characteristic
831	C₄	C₁₉×#535	1	1	yes	characteristic
832	C₄	C₁₉×#550	1	1	yes	characteristic
833	C₄	C₁₉×#550	1	1	yes	characteristic
834	C₂	—	4	2	no	—
835	C₂	—	8	1	no	—
836	C₂	—	8	2	no	—
837	C₂	—	16	1	no	—
838	C₂	C₁₉×#2431	1	1	yes	characteristic
839	C₂	C₁₉×#3002	1	1	yes	characteristic
840	C₂	C₁₉×#3012	1	1	yes	characteristic
841	C₂	C₁₉×#3297	1	1	yes	characteristic
842	C₂	C₁₉×#3301	1	1	yes	characteristic
843	C₂	C₁₉×#3322	1	1	yes	characteristic
844	C₂	C₁₉×#3326	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×C₁₉×#553	C₂	semidirect
2. C₂×C₁₉×#488	C₂	semidirect
3. C₂×C₁₉×#463	C₂	semidirect
4. C₁₉×#2540	C₂	semidirect
5. C₁₉×#2000	C₂	semidirect
6. C₁₉×#2000	C₂	semidirect
7. C₁₉×#1999	C₂	semidirect
8. C₁₉×#1999	C₂	semidirect
9. C₁₉×#1989	C₂	semidirect
10. C₁₉×#1954	C₂	semidirect
11. C₁₉×#1875	C₂	semidirect
12. C₁₉×#1874	C₂	semidirect
13. C₁₉×#1873	C₂	semidirect
14. C₁₉×#1872	C₂	semidirect
15. C₄×C₁₉×#102	C₂	semidirect
87. C₁₉×#125	D₄	semidirect
108. C₄×D₄×C₁₉	D₄	semidirect
266. #25575	C₁₉	direct (N × H)
363. C₂×#553	C₂×C₁₉	semidirect
364. C₂×#488	C₂×C₁₉	semidirect
365. C₂×#463	C₂×C₁₉	semidirect
366. #2540	C₂×C₁₉	semidirect
367. #2000	C₂×C₁₉	semidirect
368. #2000	C₂×C₁₉	semidirect
369. #1999	C₂×C₁₉	semidirect
370. #1999	C₂×C₁₉	semidirect
371. #1989	C₂×C₁₉	semidirect
372. #1954	C₂×C₁₉	semidirect
373. #1875	C₂×C₁₉	semidirect
374. #1874	C₂×C₁₉	semidirect
375. #1873	C₂×C₁₉	semidirect
376. #1872	C₂×C₁₉	semidirect
377. C₄×#102	C₂×C₁₉	semidirect
509. #125	D₄×C₁₉	semidirect
530. C₄×D₄	D₄×C₁₉	semidirect
576. C₁₉	#25575	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×C₁₉×#553	2
C₂×C₁₉×#488	2
C₂×C₁₉×#463	2
C₁₉×#2540	2
C₁₉×#2000	2
C₁₉×#1999	2
C₁₉×#1989	2
C₁₉×#1954	2
C₁₉×#1875	2
C₁₉×#1874	2
C₁₉×#1873	2
C₁₉×#1872	2
C₄×C₁₉×#102	2
#25575	19

Subgroups — C19×#25575 #18031534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#25575 #18031534