Subgroups — C₁₉×#34961 #18040920

Order 4864.

1954 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2585	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2573	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2556	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2553	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2523	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2517	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2466	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2463	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2460	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2455	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2395	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2392	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#125	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₉×#126	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₉×#123	C₂	1	2	yes	maximal, complemented
18	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₉	C₂	1	2	yes	maximal, complemented
20	C₂×C₁₉×#126	C₂²	1	2	yes	—
21	C₂×C₁₉×#125	C₂²	1	2	yes	—
22	C₂×C₁₉×#123	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#400	C₂²	1	1	yes	characteristic
34	C₁₉×#400	C₂²	1	2	yes	—
35	C₁₉×#399	C₂²	1	1	yes	characteristic
36	C₁₉×#399	C₂²	1	2	yes	—
37	C₁₉×#398	C₂²	1	2	yes	—
38	C₁₉×#398	C₂²	1	2	yes	—
39	C₁₉×#398	C₂²	1	1	yes	characteristic
40	C₁₉×#397	C₂²	1	2	yes	—
41	C₁₉×#397	C₂²	1	2	yes	—
42	C₁₉×#397	C₂²	1	1	yes	characteristic
43	C₁₉×#397	C₂²	1	2	yes	—
44	C₁₉×#396	C₂²	1	2	yes	—
45	C₁₉×#396	C₂²	1	2	yes	—
46	C₁₉×#395	C₂²	1	1	yes	characteristic
47	C₁₉×#394	C₂²	1	2	yes	—
48	C₁₉×#394	C₂²	1	2	yes	—
49	C₁₉×#394	C₂²	1	2	yes	—
50	C₁₉×#394	C₂²	1	1	yes	characteristic
51	C₁₉×#393	C₂²	1	1	yes	characteristic
52	C₁₉×#392	C₂²	1	1	yes	characteristic
53	C₁₉×#391	C₂²	1	2	yes	—
54	C₁₉×#389	C₂²	1	2	yes	—
55	C₁₉×#389	C₂²	1	2	yes	—
56	C₁₉×#389	C₂²	1	2	yes	—
57	C₁₉×#389	C₂²	1	2	yes	—
58	C₁₉×#389	C₂²	1	2	yes	—
59	C₁₉×#388	C₂²	1	2	yes	—
60	C₁₉×#388	C₂²	1	2	yes	—
61	C₁₉×#388	C₂²	1	2	yes	—
62	C₁₉×#388	C₂²	1	2	yes	—
63	C₁₉×#388	C₂²	1	2	yes	—
64	C₁₉×#387	C₂²	1	2	yes	—
65	C₁₉×#387	C₂²	1	2	yes	—
66	C₁₉×#387	C₂²	1	2	yes	—
67	C₁₉×#387	C₂²	1	2	yes	—
68	C₁₉×#387	C₂²	1	2	yes	—
69	C₁₉×#387	C₂²	1	2	yes	—
70	C₁₉×#387	C₂²	1	2	yes	—
71	C₁₉×#387	C₂²	1	2	yes	—
72	C₁₉×#387	C₂²	1	2	yes	—
73	C₁₉×#387	C₂²	1	2	yes	—
74	C₁₉×#387	C₂²	1	2	yes	—
75	C₁₉×#386	C₂²	1	2	yes	—
76	C₁₉×#385	C₂²	1	1	yes	characteristic
77	C₁₉×#385	C₂²	1	2	yes	—
78	C₁₉×#385	C₂²	1	1	yes	characteristic
79	C₁₉×#385	C₂²	1	2	yes	—
80	C₁₉×#385	C₂²	1	1	yes	characteristic
81	C₁₉×#385	C₂²	1	1	yes	characteristic
82	C₁₉×#385	C₂²	1	2	yes	—
83	C₁₉×#383	C₂²	1	2	yes	—
84	C₁₉×#382	C₂²	1	2	yes	—
85	C₁₉×#381	C₂²	1	2	yes	—
86	C₁₉×#380	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
106	C₄³×C₁₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
116	C₁₉×#126	—	2	8	no	—
117	C₁₉×#125	—	2	8	no	—
118	C₁₉×#123	—	2	8	no	—
119	C₁₉×C₂²⋊Q₈	—	2	8	no	—
120	C₄×Q₈×C₁₉	—	4	2	no	—
121	C₄×D₄×C₁₉	—	2	8	no	—
122	C₄×D₄×C₁₉	—	2	8	no	—
123	C₄×D₄×C₁₉	—	2	8	no	—
124	C₄×D₄×C₁₉	—	4	2	no	—
125	C₁₉×#117	—	2	4	no	—
126	C₁₉×#117	—	4	2	no	—
127	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₉	—	4	2	no	—
166	C₂×C₄²×C₁₉	—	4	4	no	—
167	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
181	C₁₉×#95	C₂³	1	2	yes	—
182	C₁₉×#95	C₂³	1	2	yes	—
183	C₁₉×#95	C₂³	1	2	yes	—
184	C₁₉×#95	C₂³	1	2	yes	—
185	C₁₉×#95	C₂³	1	2	yes	—
186	C₁₉×#95	C₂³	1	2	yes	—
187	C₁₉×#95	C₂³	1	2	yes	—
188	C₁₉×#95	C₂³	1	2	yes	—
189	C₁₉×#95	C₂³	1	2	yes	—
190	C₁₉×#95	C₂³	1	2	yes	—
191	C₁₉×#95	C₂³	1	2	yes	—
192	C₁₉×#95	C₂³	1	2	yes	—
193	C₁₉×#95	C₂³	1	2	yes	—
194	C₁₉×#95	C₂³	1	2	yes	—
195	C₁₉×#95	C₂³	1	2	yes	—
196	C₁₉×#95	C₂³	1	1	yes	characteristic
197	C₁₉×#95	C₂³	1	2	yes	—
198	C₁₉×#95	C₂³	1	2	yes	—
199	C₁₉×#95	C₂³	1	1	yes	characteristic
200	C₁₉×#95	C₂³	1	2	yes	—
201	C₁₉×#95	C₂³	1	2	yes	—
202	C₁₉×#95	C₂³	1	2	yes	—
203	C₁₉×#95	C₂³	1	2	yes	—
204	C₁₉×#95	C₂³	1	2	yes	—
205	C₁₉×#95	C₂³	1	1	yes	characteristic
206	C₁₉×#95	C₂³	1	1	yes	characteristic
207	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂×Q₈×C₁₉	—	2	4	no	—
210	C₂×Q₈×C₁₉	—	4	1	no	—
211	C₂×D₄×C₁₉	—	2	4	no	—
212	C₂×D₄×C₁₉	—	2	4	no	—
213	C₂×D₄×C₁₉	—	2	4	no	—
214	C₂×D₄×C₁₉	—	2	4	no	—
215	C₂×D₄×C₁₉	—	4	1	no	—
216	C₂²×C₄×C₁₉	—	2	2	no	—
217	C₂²×C₄×C₁₉	—	2	2	no	—
218	C₂²×C₄×C₁₉	—	2	4	no	—
219	C₂²×C₄×C₁₉	—	2	4	no	—
220	C₂²×C₄×C₁₉	—	2	4	no	—
221	C₂²×C₄×C₁₉	—	2	4	no	—
222	C₂²×C₄×C₁₉	—	2	4	no	—
223	C₂²×C₄×C₁₉	—	2	4	no	—
224	C₂²×C₄×C₁₉	—	2	4	no	—
225	C₂²×C₄×C₁₉	—	2	4	no	—
226	C₂²×C₄×C₁₉	—	2	4	no	—
227	C₂²×C₄×C₁₉	—	4	1	no	—
228	C₂²×C₄×C₁₉	—	4	1	no	—
229	C₂²×C₄×C₁₉	—	4	2	no	—
230	C₂²×C₄×C₁₉	—	4	2	no	—
231	C₂²×C₄×C₁₉	#41	1	4	yes	—
232	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₁₉	—	2	4	no	—
250	C₄⋊C₄×C₁₉	—	2	4	no	—
251	C₄⋊C₄×C₁₉	—	2	4	no	—
252	C₄⋊C₄×C₁₉	—	2	4	no	—
253	C₄⋊C₄×C₁₉	—	2	4	no	—
254	C₄⋊C₄×C₁₉	—	2	4	no	—
255	C₄⋊C₄×C₁₉	—	2	4	no	—
256	C₄⋊C₄×C₁₉	—	2	4	no	—
257	C₄⋊C₄×C₁₉	—	2	4	no	—
258	C₄⋊C₄×C₁₉	—	2	4	no	—
259	C₄⋊C₄×C₁₉	—	2	4	no	—
260	C₄⋊C₄×C₁₉	—	2	4	no	—
261	C₄⋊C₄×C₁₉	—	2	4	no	—
262	C₄⋊C₄×C₁₉	—	2	4	no	—
263	C₄⋊C₄×C₁₉	—	2	4	no	—
264	C₄⋊C₄×C₁₉	—	4	1	no	—
265	C₄⋊C₄×C₁₉	—	4	1	no	—
266	C₄⋊C₄×C₁₉	—	4	1	no	—
267	C₄⋊C₄×C₁₉	—	4	2	no	—
268	C₄⋊C₄×C₁₉	—	4	1	no	—
269	C₄⋊C₄×C₁₉	#41	1	8	yes	—
270	C₂²⋊C₄×C₁₉	—	2	2	no	—
271	C₂²⋊C₄×C₁₉	—	2	2	no	—
272	C₂²⋊C₄×C₁₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₉	—	2	4	no	—
277	C₂²⋊C₄×C₁₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₉	—	4	1	no	—
284	C₂²⋊C₄×C₁₉	—	4	1	no	—
285	C₂²⋊C₄×C₁₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₉	#41	1	8	yes	—
287	C₄²×C₁₉	—	2	4	no	—
288	C₄²×C₁₉	—	2	4	no	—
289	C₄²×C₁₉	—	2	4	no	—
290	C₄²×C₁₉	—	2	4	no	—
291	C₄²×C₁₉	—	2	4	no	—
292	C₄²×C₁₉	—	2	4	no	—
293	C₄²×C₁₉	—	2	4	no	—
294	C₄²×C₁₉	—	2	4	no	—
295	C₄²×C₁₉	—	2	2	no	—
296	C₄²×C₁₉	—	2	2	no	—
297	C₄²×C₁₉	—	2	4	no	—
298	C₄²×C₁₉	—	4	2	no	—
299	C₄²×C₁₉	—	4	2	no	—
300	C₄²×C₁₉	—	4	2	no	—
301	#34961	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂³×C₁₉	—	2	2	no	—
303	C₂³×C₁₉	—	2	2	no	—
304	C₂³×C₁₉	—	2	2	no	—
305	C₂³×C₁₉	—	2	2	no	—
306	C₂³×C₁₉	—	2	2	no	—
307	C₂³×C₁₉	—	2	2	no	—
308	C₂³×C₁₉	—	2	1	no	—
309	C₂³×C₁₉	—	2	2	no	—
310	C₂³×C₁₉	—	2	1	no	—
311	C₂³×C₁₉	—	2	2	no	—
312	C₂³×C₁₉	C₂×#41	1	2	yes	—
313	C₂³×C₁₉	C₂×#41	1	4	yes	—
314	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
315	Q₈×C₁₉	—	4	4	no	—
316	D₄×C₁₉	—	2	16	no	—
317	D₄×C₁₉	—	4	4	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	2	2	no	—
320	C₂×C₄×C₁₉	—	2	2	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	2	no	—
325	C₂×C₄×C₁₉	—	2	2	no	—
326	C₂×C₄×C₁₉	—	2	2	no	—
327	C₂×C₄×C₁₉	—	2	1	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	1	no	—
330	C₂×C₄×C₁₉	—	2	8	no	—
331	C₂×C₄×C₁₉	—	2	2	no	—
332	C₂×C₄×C₁₉	—	2	2	no	—
333	C₂×C₄×C₁₉	—	2	2	no	—
334	C₂×C₄×C₁₉	—	2	2	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	2	2	no	—
337	C₂×C₄×C₁₉	—	2	2	no	—
338	C₂×C₄×C₁₉	—	2	2	no	—
339	C₂×C₄×C₁₉	—	2	2	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	2	2	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	2	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
347	C₂×C₄×C₁₉	—	2	2	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	2	2	no	—
350	C₂×C₄×C₁₉	—	2	1	no	—
351	C₂×C₄×C₁₉	—	2	1	no	—
352	C₂×C₄×C₁₉	—	2	1	no	—
353	C₂×C₄×C₁₉	—	2	1	no	—
354	C₂×C₄×C₁₉	—	2	2	no	—
355	C₂×C₄×C₁₉	—	2	2	no	—
356	C₂×C₄×C₁₉	—	2	2	no	—
357	C₂×C₄×C₁₉	—	4	4	no	—
358	C₂×C₄×C₁₉	—	4	4	no	—
359	C₂×C₄×C₁₉	—	4	8	no	—
360	C₂×C₄×C₁₉	—	4	8	no	—
361	C₂×C₄×C₁₉	—	4	8	no	—
362	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
363	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
364	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
365	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
366	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
368	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
369	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
370	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
371	#2585	C₂×C₁₉	1	2	yes	complemented
372	#2573	C₂×C₁₉	1	2	yes	complemented
373	#2556	C₂×C₁₉	1	2	yes	complemented
374	#2553	C₂×C₁₉	1	2	yes	complemented
375	#2523	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#2517	C₂×C₁₉	1	1	yes	characteristic, complemented
377	#2466	C₂×C₁₉	1	2	yes	complemented
378	#2463	C₂×C₁₉	1	1	yes	characteristic
379	#2460	C₂×C₁₉	1	2	yes	complemented
380	#2455	C₂×C₁₉	1	1	yes	characteristic
381	#2396	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#2395	C₂×C₁₉	1	2	yes	complemented
383	#2392	C₂×C₁₉	1	1	yes	characteristic
384	C₄×#125	C₂×C₁₉	1	2	yes	complemented
385	C₄×#126	C₂×C₁₉	1	2	yes	complemented
386	C₄×C₂²⋊Q₈	C₂×C₁₉	1	2	yes	complemented
387	C₄×#123	C₂×C₁₉	1	2	yes	complemented
388	#2296	C₂×C₁₉	1	1	yes	characteristic, complemented
389	C₄²×D₄	C₂×C₁₉	1	2	yes	complemented
390	C₂²×C₁₉	—	2	4	no	—
391	C₂²×C₁₉	—	2	4	no	—
392	C₂²×C₁₉	—	2	2	no	—
393	C₂²×C₁₉	—	2	4	no	—
394	C₂²×C₁₉	—	2	4	no	—
395	C₂²×C₁₉	—	4	2	no	—
396	C₂²×C₁₉	—	4	2	no	—
397	C₂²×C₁₉	—	4	2	no	—
398	C₂²×C₁₉	—	4	1	no	—
399	C₂²×C₁₉	—	4	1	no	—
400	C₂²×C₁₉	—	4	2	no	—
401	C₂²×C₁₉	—	4	2	no	—
402	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
403	C₂²×C₁₉	C₂²×#41	1	2	yes	—
404	C₂²×C₁₉	C₂²×#41	1	2	yes	—
405	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
406	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
407	C₄×C₁₉	—	2	4	no	—
408	C₄×C₁₉	—	2	2	no	—
409	C₄×C₁₉	—	2	4	no	—
410	C₄×C₁₉	—	2	4	no	—
411	C₄×C₁₉	—	2	4	no	—
412	C₄×C₁₉	—	2	4	no	—
413	C₄×C₁₉	—	4	2	no	—
414	C₄×C₁₉	—	4	2	no	—
415	C₄×C₁₉	—	4	2	no	—
416	C₄×C₁₉	—	4	2	no	—
417	C₄×C₁₉	—	4	1	no	—
418	C₄×C₁₉	—	4	1	no	—
419	C₄×C₁₉	—	4	2	no	—
420	C₄×C₁₉	—	4	1	no	—
421	C₄×C₁₉	—	4	1	no	—
422	C₄×C₁₉	—	4	2	no	—
423	C₄×C₁₉	#539	1	4	yes	—
424	C₂×#126	C₂²×C₁₉	1	2	yes	—
425	C₂×#125	C₂²×C₁₉	1	2	yes	—
426	C₂×#123	C₂²×C₁₉	1	2	yes	—
427	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
432	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
435	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
436	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
437	#400	C₂²×C₁₉	1	1	yes	characteristic
438	#400	C₂²×C₁₉	1	2	yes	—
439	#399	C₂²×C₁₉	1	2	yes	—
440	#399	C₂²×C₁₉	1	1	yes	characteristic
441	#398	C₂²×C₁₉	1	1	yes	characteristic
442	#398	C₂²×C₁₉	1	2	yes	—
443	#398	C₂²×C₁₉	1	2	yes	—
444	#397	C₂²×C₁₉	1	2	yes	—
445	#397	C₂²×C₁₉	1	1	yes	characteristic
446	#397	C₂²×C₁₉	1	2	yes	—
447	#397	C₂²×C₁₉	1	2	yes	—
448	#396	C₂²×C₁₉	1	2	yes	—
449	#396	C₂²×C₁₉	1	2	yes	—
450	#395	C₂²×C₁₉	1	1	yes	characteristic
451	#394	C₂²×C₁₉	1	2	yes	—
452	#394	C₂²×C₁₉	1	1	yes	characteristic
453	#394	C₂²×C₁₉	1	2	yes	—
454	#394	C₂²×C₁₉	1	2	yes	—
455	#393	C₂²×C₁₉	1	1	yes	characteristic
456	#392	C₂²×C₁₉	1	1	yes	characteristic
457	#391	C₂²×C₁₉	1	2	yes	—
458	#389	C₂²×C₁₉	1	2	yes	—
459	#389	C₂²×C₁₉	1	2	yes	—
460	#389	C₂²×C₁₉	1	2	yes	—
461	#389	C₂²×C₁₉	1	2	yes	—
462	#389	C₂²×C₁₉	1	2	yes	—
463	#388	C₂²×C₁₉	1	2	yes	—
464	#388	C₂²×C₁₉	1	2	yes	—
465	#388	C₂²×C₁₉	1	2	yes	—
466	#388	C₂²×C₁₉	1	2	yes	—
467	#388	C₂²×C₁₉	1	2	yes	—
468	#387	C₂²×C₁₉	1	2	yes	—
469	#387	C₂²×C₁₉	1	2	yes	—
470	#387	C₂²×C₁₉	1	2	yes	—
471	#387	C₂²×C₁₉	1	2	yes	—
472	#387	C₂²×C₁₉	1	2	yes	—
473	#387	C₂²×C₁₉	1	2	yes	—
474	#387	C₂²×C₁₉	1	2	yes	—
475	#387	C₂²×C₁₉	1	2	yes	—
476	#387	C₂²×C₁₉	1	2	yes	—
477	#387	C₂²×C₁₉	1	2	yes	—
478	#387	C₂²×C₁₉	1	2	yes	—
479	#386	C₂²×C₁₉	1	2	yes	—
480	#385	C₂²×C₁₉	1	2	yes	—
481	#385	C₂²×C₁₉	1	1	yes	characteristic
482	#385	C₂²×C₁₉	1	1	yes	characteristic
483	#385	C₂²×C₁₉	1	2	yes	—
484	#385	C₂²×C₁₉	1	1	yes	characteristic
485	#385	C₂²×C₁₉	1	1	yes	characteristic
486	#385	C₂²×C₁₉	1	2	yes	—
487	#383	C₂²×C₁₉	1	2	yes	—
488	#382	C₂²×C₁₉	1	2	yes	—
489	#381	C₂²×C₁₉	1	2	yes	—
490	#380	C₂²×C₁₉	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
510	C₄³	C₂²×C₁₉	1	2	yes	—
511	C₂×C₁₉	—	4	2	no	—
512	C₂×C₁₉	—	4	4	no	—
513	C₂×C₁₉	#3444	1	2	yes	—
514	C₂×C₁₉	C₂×#539	1	1	yes	characteristic
515	C₂×C₁₉	#3481	1	1	yes	characteristic
516	C₂×C₁₉	#3481	1	1	yes	characteristic
517	C₂×C₁₉	#3482	1	2	yes	—
518	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
520	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
522	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
525	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
526	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
527	#126	—	2	8	no	—
528	#125	—	2	8	no	—
529	#123	—	2	8	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₄×Q₈	—	4	2	no	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	4	2	no	—
536	#117	—	2	4	no	—
537	#117	—	4	2	no	—
538	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
576	C₂×C₄²	—	4	2	no	—
577	C₂×C₄²	—	4	4	no	—
578	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
581	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
582	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
583	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
584	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
586	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
587	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
588	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
589	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
590	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
592	#95	C₂³×C₁₉	1	2	yes	—
593	#95	C₂³×C₁₉	1	2	yes	—
594	#95	C₂³×C₁₉	1	2	yes	—
595	#95	C₂³×C₁₉	1	2	yes	—
596	#95	C₂³×C₁₉	1	2	yes	—
597	#95	C₂³×C₁₉	1	2	yes	—
598	#95	C₂³×C₁₉	1	2	yes	—
599	#95	C₂³×C₁₉	1	2	yes	—
600	#95	C₂³×C₁₉	1	2	yes	—
601	#95	C₂³×C₁₉	1	2	yes	—
602	#95	C₂³×C₁₉	1	2	yes	—
603	#95	C₂³×C₁₉	1	2	yes	—
604	#95	C₂³×C₁₉	1	2	yes	—
605	#95	C₂³×C₁₉	1	2	yes	—
606	#95	C₂³×C₁₉	1	2	yes	—
607	#95	C₂³×C₁₉	1	1	yes	characteristic
608	#95	C₂³×C₁₉	1	2	yes	—
609	#95	C₂³×C₁₉	1	2	yes	—
610	#95	C₂³×C₁₉	1	1	yes	characteristic
611	#95	C₂³×C₁₉	1	2	yes	—
612	#95	C₂³×C₁₉	1	2	yes	—
613	#95	C₂³×C₁₉	1	2	yes	—
614	#95	C₂³×C₁₉	1	2	yes	—
615	#95	C₂³×C₁₉	1	2	yes	—
616	#95	C₂³×C₁₉	1	1	yes	characteristic
617	#95	C₂³×C₁₉	1	1	yes	characteristic
618	C₁₉	#34961	1	1	yes	characteristic, direct product factor, Sylow
619	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
620	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	4	1	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	4	1	no	—
640	C₂²×C₄	—	4	1	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	#41×C₁₉	1	4	yes	—
644	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	#41×C₁₉	1	8	yes	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₂²⋊C₄	—	4	1	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	#41×C₁₉	1	8	yes	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	4	2	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	C₂×#41×C₁₉	1	2	yes	—
724	C₂³	C₂×#41×C₁₉	1	4	yes	—
725	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
726	Q₈	—	4	4	no	—
727	D₄	—	2	16	no	—
728	D₄	—	4	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	8	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
774	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
775	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
776	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
777	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
778	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
779	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
780	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
781	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
795	C₂²	C₂²×#41×C₁₉	1	2	yes	—
796	C₂²	C₂²×#41×C₁₉	1	2	yes	—
797	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
799	C₄	—	2	4	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	4	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	4	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	2	no	—
815	C₄	C₁₉×#539	1	4	yes	—
816	C₂	—	4	2	no	—
817	C₂	—	4	4	no	—
818	C₂	C₁₉×#3444	1	2	yes	—
819	C₂	C₂×C₁₉×#539	1	1	yes	characteristic
820	C₂	C₁₉×#3481	1	1	yes	characteristic
821	C₂	C₁₉×#3481	1	1	yes	characteristic
822	C₂	C₁₉×#3482	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₁₉×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2585	C₂	semidirect
2. C₁₉×#2573	C₂	semidirect
3. C₁₉×#2556	C₂	semidirect
4. C₁₉×#2553	C₂	semidirect
5. C₁₉×#2523	C₂	semidirect
6. C₁₉×#2517	C₂	semidirect
7. C₁₉×#2466	C₂	semidirect
9. C₁₉×#2460	C₂	semidirect
11. C₁₉×#2396	C₂	semidirect
12. C₁₉×#2395	C₂	semidirect
14. C₄×C₁₉×#125	C₂	semidirect
15. C₄×C₁₉×#126	C₂	semidirect
16. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₁₉×#123	C₂	semidirect
18. C₁₉×#2296	C₂	semidirect
19. C₄²×D₄×C₁₉	C₂	semidirect
301. #34961	C₁₉	direct (N × H)
371. #2585	C₂×C₁₉	semidirect
372. #2573	C₂×C₁₉	semidirect
373. #2556	C₂×C₁₉	semidirect
374. #2553	C₂×C₁₉	semidirect
375. #2523	C₂×C₁₉	semidirect
376. #2517	C₂×C₁₉	semidirect
377. #2466	C₂×C₁₉	semidirect
379. #2460	C₂×C₁₉	semidirect
381. #2396	C₂×C₁₉	semidirect
382. #2395	C₂×C₁₉	semidirect
384. C₄×#125	C₂×C₁₉	semidirect
385. C₄×#126	C₂×C₁₉	semidirect
386. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
387. C₄×#123	C₂×C₁₉	semidirect
388. #2296	C₂×C₁₉	semidirect
389. C₄²×D₄	C₂×C₁₉	semidirect
618. C₁₉	#34961	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2585	2
C₁₉×#2573	2
C₁₉×#2556	2
C₁₉×#2553	2
C₁₉×#2523	2
C₁₉×#2517	2
C₁₉×#2466	2
C₁₉×#2463	2
C₁₉×#2460	2
C₁₉×#2455	2
C₁₉×#2396	2
C₁₉×#2395	2
C₁₉×#2392	2
C₄×C₁₉×#125	2
C₄×C₁₉×#126	2
C₄×C₁₉×C₂²⋊Q₈	2
C₄×C₁₉×#123	2
C₁₉×#2296	2
C₄²×D₄×C₁₉	2
#34961	19

Subgroups — C19×#34961 #18040920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34961 #18040920