Subgroups — C₁₉×#34743 #18040702

Order 4864.

3390 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2429	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2428	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2427	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2426	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2425	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2424	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2392	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₉×#121	C₂	1	4	yes	maximal, complemented
13	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#532	—	2	8	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#525	—	2	8	no	—
25	C₁₉×#525	—	2	8	no	—
26	C₂×C₁₉×#123	C₂²	1	2	yes	—
27	C₂×C₁₉×#123	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₉×#121	C₂²	1	2	yes	—
31	C₂×C₁₉×#121	C₂²	1	2	yes	—
32	C₂×C₁₉×#121	C₂²	1	4	yes	—
33	C₂×C₁₉×#121	C₂²	1	4	yes	—
34	C₂×C₁₉×#120	C₂²	1	2	yes	—
35	C₂×C₁₉×#120	C₂²	1	2	yes	—
36	C₄×#41×C₁₉	—	2	8	no	—
37	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
40	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
41	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	complemented
43	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
46	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₁₉	C₂²	1	2	yes	complemented
50	C₁₉×#398	C₂²	1	4	yes	complemented
51	C₁₉×#397	C₂²	1	4	yes	complemented
52	C₁₉×#396	C₂²	1	4	yes	—
53	C₁₉×#396	C₂²	1	4	yes	complemented
54	C₁₉×#394	C₂²	1	4	yes	—
55	C₁₉×#394	C₂²	1	4	yes	—
56	C₁₉×#394	C₂²	1	4	yes	complemented
57	C₁₉×#392	C₂²	1	4	yes	—
58	C₁₉×#391	C₂²	1	2	yes	complemented
59	C₁₉×#390	C₂²	1	4	yes	—
60	C₁₉×#390	C₂²	1	2	yes	complemented
61	C₁₉×#389	C₂²	1	4	yes	complemented
62	C₁₉×#389	C₂²	1	2	yes	complemented
63	C₁₉×#389	C₂²	1	2	yes	complemented
64	C₁₉×#388	C₂²	1	4	yes	—
65	C₁₉×#388	C₂²	1	4	yes	complemented
66	C₁₉×#386	C₂²	1	4	yes	—
67	C₁₉×#386	C₂²	1	4	yes	—
68	C₁₉×#386	C₂²	1	4	yes	complemented
69	C₁₉×#385	C₂²	1	4	yes	—
70	C₁₉×#380	C₂²	1	4	yes	complemented
71	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
72	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
78	C₂×C₁₉×#95	C₂²	1	2	yes	—
79	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×#41×C₁₉	—	2	4	no	—
81	C₂×#41×C₁₉	—	2	4	no	—
82	C₂×#41×C₁₉	—	2	4	no	—
83	C₂×#41×C₁₉	—	2	4	no	—
84	C₂×#41×C₁₉	—	2	4	no	—
85	C₂×#41×C₁₉	D₄	1	8	yes	complemented
86	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₉	—	2	4	no	—
96	C₂³×C₄×C₁₉	—	2	4	no	—
97	C₂³×C₄×C₁₉	—	2	4	no	—
98	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₁₉×C₄⋊Q₈	—	2	4	no	—
108	C₁₉×#127	—	2	4	no	—
109	C₁₉×#124	—	2	4	no	—
110	C₁₉×#124	—	2	4	no	—
111	C₁₉×#123	—	2	8	no	—
112	C₁₉×#123	—	2	8	no	—
113	C₁₉×C₂²⋊Q₈	—	2	8	no	—
114	C₁₉×C₂²⋊Q₈	—	2	8	no	—
115	C₁₉×#121	—	2	8	no	—
116	C₁₉×#121	—	2	16	no	—
117	C₁₉×#121	—	2	8	no	—
118	C₁₉×#121	—	2	16	no	—
119	C₁₉×#120	—	2	8	no	—
120	C₁₉×#120	—	2	8	no	—
121	C₄×Q₈×C₁₉	—	2	8	no	—
122	C₄×D₄×C₁₉	—	2	16	no	—
123	C₄×D₄×C₁₉	—	2	16	no	—
124	C₄×D₄×C₁₉	—	2	8	no	—
125	C₄×D₄×C₁₉	—	2	16	no	—
126	C₄×D₄×C₁₉	—	2	16	no	—
127	C₁₉×#117	—	2	4	no	—
128	C₁₉×#117	—	2	8	no	—
129	C₁₉×#117	D₄	1	8	yes	complemented
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
139	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₉	—	2	4	no	—
155	C₂×C₄²×C₁₉	—	2	4	no	—
156	C₂×C₄²×C₁₉	—	2	8	no	—
157	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
166	C₁₉×#95	C₂³	1	2	yes	—
167	C₁₉×#95	C₂³	1	2	yes	—
168	C₁₉×#95	C₂³	1	2	yes	—
169	C₁₉×#95	C₂³	1	2	yes	—
170	C₁₉×#95	C₂³	1	4	yes	—
171	C₁₉×#95	C₂³	1	4	yes	—
172	C₁₉×#95	C₂³	1	4	yes	—
173	C₁₉×#95	C₂³	1	4	yes	—
174	C₂⁴×C₁₉	—	2	4	no	—
175	C₂⁴×C₁₉	—	2	2	no	—
176	C₂⁴×C₁₉	—	2	2	no	—
177	C₂⁴×C₁₉	—	2	2	no	—
178	C₂⁴×C₁₉	—	4	2	no	—
179	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
183	#41×C₁₉	—	2	32	no	—
184	#41×C₁₉	—	4	16	no	—
185	C₂×Q₈×C₁₉	—	2	2	no	—
186	C₂×Q₈×C₁₉	—	2	2	no	—
187	C₂×Q₈×C₁₉	—	2	2	no	—
188	C₂×Q₈×C₁₉	—	2	2	no	—
189	C₂×Q₈×C₁₉	—	2	2	no	—
190	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
191	C₂×D₄×C₁₉	—	2	4	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	2	8	no	—
194	C₂×D₄×C₁₉	—	2	8	no	—
195	C₂×D₄×C₁₉	—	2	4	no	—
196	C₂×D₄×C₁₉	—	2	4	no	—
197	C₂×D₄×C₁₉	—	2	8	no	—
198	C₂×D₄×C₁₉	—	2	8	no	—
199	C₂×D₄×C₁₉	—	2	4	no	—
200	C₂×D₄×C₁₉	—	2	2	no	—
201	C₂×D₄×C₁₉	—	2	8	no	—
202	C₂×D₄×C₁₉	—	2	2	no	—
203	C₂×D₄×C₁₉	—	2	2	no	—
204	C₂×D₄×C₁₉	—	2	2	no	—
205	C₂×D₄×C₁₉	—	2	8	no	—
206	C₂×D₄×C₁₉	—	2	2	no	—
207	C₂×D₄×C₁₉	—	4	4	no	—
208	C₂×D₄×C₁₉	—	4	4	no	—
209	C₂×D₄×C₁₉	—	4	4	no	—
210	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
211	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₉	—	2	4	no	—
213	C₂²×C₄×C₁₉	—	2	4	no	—
214	C₂²×C₄×C₁₉	—	2	4	no	—
215	C₂²×C₄×C₁₉	—	2	4	no	—
216	C₂²×C₄×C₁₉	—	2	2	no	—
217	C₂²×C₄×C₁₉	—	2	2	no	—
218	C₂²×C₄×C₁₉	—	2	2	no	—
219	C₂²×C₄×C₁₉	—	2	8	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	—	2	4	no	—
228	C₂²×C₄×C₁₉	—	2	8	no	—
229	C₂²×C₄×C₁₉	—	2	4	no	—
230	C₂²×C₄×C₁₉	—	2	4	no	—
231	C₂²×C₄×C₁₉	—	2	4	no	—
232	C₂²×C₄×C₁₉	—	4	4	no	—
233	C₂²×C₄×C₁₉	—	4	2	no	—
234	C₂²×C₄×C₁₉	—	4	2	no	—
235	C₂²×C₄×C₁₉	—	4	16	no	—
236	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
237	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₁₉	#41	1	4	yes	—
240	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₉	C₂⁴	1	4	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	4	yes	—
247	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₄⋊C₄×C₁₉	—	2	8	no	—
252	C₄⋊C₄×C₁₉	—	2	4	no	—
253	C₄⋊C₄×C₁₉	—	2	8	no	—
254	C₄⋊C₄×C₁₉	—	2	8	no	—
255	C₄⋊C₄×C₁₉	—	2	8	no	—
256	C₄⋊C₄×C₁₉	—	2	8	no	—
257	C₄⋊C₄×C₁₉	—	4	4	no	—
258	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
259	C₂²⋊C₄×C₁₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₉	—	2	8	no	—
264	C₂²⋊C₄×C₁₉	—	2	8	no	—
265	C₂²⋊C₄×C₁₉	—	2	8	no	—
266	C₂²⋊C₄×C₁₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
273	C₂²⋊C₄×C₁₉	#41	1	8	yes	complemented
274	C₄²×C₁₉	—	2	2	no	—
275	C₄²×C₁₉	—	2	2	no	—
276	C₄²×C₁₉	—	2	4	no	—
277	C₄²×C₁₉	—	2	8	no	—
278	C₄²×C₁₉	—	2	4	no	—
279	C₄²×C₁₉	—	2	2	no	—
280	C₄²×C₁₉	—	2	2	no	—
281	C₄²×C₁₉	—	2	4	no	—
282	C₄²×C₁₉	C₂×D₄	1	8	yes	—
283	#34743	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₁₉	—	2	2	no	—
285	C₂³×C₁₉	—	2	2	no	—
286	C₂³×C₁₉	—	2	8	no	—
287	C₂³×C₁₉	—	2	2	no	—
288	C₂³×C₁₉	—	2	2	no	—
289	C₂³×C₁₉	—	2	2	no	—
290	C₂³×C₁₉	—	2	2	no	—
291	C₂³×C₁₉	—	2	2	no	—
292	C₂³×C₁₉	—	2	2	no	—
293	C₂³×C₁₉	—	2	4	no	—
294	C₂³×C₁₉	—	2	4	no	—
295	C₂³×C₁₉	—	2	2	no	—
296	C₂³×C₁₉	—	2	2	no	—
297	C₂³×C₁₉	—	2	2	no	—
298	C₂³×C₁₉	—	2	2	no	—
299	C₂³×C₁₉	—	2	4	no	—
300	C₂³×C₁₉	—	2	2	no	—
301	C₂³×C₁₉	—	2	4	no	—
302	C₂³×C₁₉	—	4	8	no	—
303	C₂³×C₁₉	—	4	8	no	—
304	C₂³×C₁₉	—	4	4	no	—
305	C₂³×C₁₉	—	4	4	no	—
306	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
307	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
309	C₂³×C₁₉	C₂×#41	1	4	yes	—
310	C₂³×C₁₉	C₂×#41	1	2	yes	—
311	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
312	Q₈×C₁₉	—	2	8	no	—
313	Q₈×C₁₉	—	4	4	no	—
314	D₄×C₁₉	—	2	16	no	—
315	D₄×C₁₉	—	2	8	no	—
316	D₄×C₁₉	—	4	16	no	—
317	D₄×C₁₉	—	4	16	no	—
318	D₄×C₁₉	—	4	16	no	—
319	D₄×C₁₉	—	4	8	no	—
320	D₄×C₁₉	—	4	4	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	4	no	—
325	C₂×C₄×C₁₉	—	2	2	no	—
326	C₂×C₄×C₁₉	—	2	4	no	—
327	C₂×C₄×C₁₉	—	2	2	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	16	no	—
330	C₂×C₄×C₁₉	—	2	2	no	—
331	C₂×C₄×C₁₉	—	2	2	no	—
332	C₂×C₄×C₁₉	—	2	4	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	4	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	4	no	—
344	C₂×C₄×C₁₉	—	2	2	no	—
345	C₂×C₄×C₁₉	—	4	16	no	—
346	C₂×C₄×C₁₉	—	4	8	no	—
347	C₂×C₄×C₁₉	—	4	8	no	—
348	C₂×C₄×C₁₉	—	4	4	no	—
349	C₂×C₄×C₁₉	—	4	8	no	—
350	C₂×C₄×C₁₉	—	4	8	no	—
351	C₂×C₄×C₁₉	—	4	8	no	—
352	C₂×C₄×C₁₉	#121	1	16	yes	complemented
353	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
354	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
355	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
360	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
361	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
363	C₂×#532	C₂×C₁₉	1	1	yes	characteristic, complemented
364	C₂×#525	C₂×C₁₉	1	1	yes	characteristic, complemented
365	C₂×#525	C₂×C₁₉	1	1	yes	characteristic, complemented
366	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
367	#2429	C₂×C₁₉	1	2	yes	complemented
368	#2428	C₂×C₁₉	1	2	yes	complemented
369	#2427	C₂×C₁₉	1	2	yes	complemented
370	#2426	C₂×C₁₉	1	2	yes	complemented
371	#2425	C₂×C₁₉	1	4	yes	complemented
372	#2424	C₂×C₁₉	1	4	yes	complemented
373	#2392	C₂×C₁₉	1	4	yes	complemented
374	C₄×#121	C₂×C₁₉	1	4	yes	complemented
375	#2297	C₂×C₁₉	1	1	yes	characteristic, complemented
376	#2296	C₂×C₁₉	1	1	yes	characteristic, complemented
377	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
378	C₂²×C₁₉	—	2	2	no	—
379	C₂²×C₁₉	—	2	2	no	—
380	C₂²×C₁₉	—	2	4	no	—
381	C₂²×C₁₉	—	2	4	no	—
382	C₂²×C₁₉	—	2	4	no	—
383	C₂²×C₁₉	—	2	4	no	—
384	C₂²×C₁₉	—	2	4	no	—
385	C₂²×C₁₉	—	2	4	no	—
386	C₂²×C₁₉	—	2	8	no	—
387	C₂²×C₁₉	—	4	16	no	—
388	C₂²×C₁₉	—	4	2	no	—
389	C₂²×C₁₉	—	4	2	no	—
390	C₂²×C₁₉	—	4	2	no	—
391	C₂²×C₁₉	—	4	2	no	—
392	C₂²×C₁₉	—	4	4	no	—
393	C₂²×C₁₉	—	4	2	no	—
394	C₂²×C₁₉	—	4	2	no	—
395	C₂²×C₁₉	—	4	2	no	—
396	C₂²×C₁₉	—	4	2	no	—
397	C₂²×C₁₉	—	4	2	no	—
398	C₂²×C₁₉	—	4	4	no	—
399	C₂²×C₁₉	—	4	4	no	—
400	C₂²×C₁₉	C₂×#121	1	4	yes	—
401	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
402	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
403	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
404	C₂²×C₁₉	C₂²×#41	1	2	yes	—
405	C₂²×C₁₉	#585	1	2	yes	—
406	C₄×C₁₉	—	2	4	no	—
407	C₄×C₁₉	—	2	4	no	—
408	C₄×C₁₉	—	2	8	no	—
409	C₄×C₁₉	—	2	4	no	—
410	C₄×C₁₉	—	4	2	no	—
411	C₄×C₁₉	—	4	2	no	—
412	C₄×C₁₉	—	4	2	no	—
413	C₄×C₁₉	—	4	2	no	—
414	C₄×C₁₉	—	4	4	no	—
415	C₄×C₁₉	C₂×#121	1	4	yes	—
416	C₄×C₁₉	C₂×#121	1	4	yes	—
417	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
418	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
419	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
420	#532	—	2	8	no	—
421	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
422	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
423	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
425	#525	—	2	8	no	—
426	#525	—	2	8	no	—
427	C₂×#123	C₂²×C₁₉	1	2	yes	—
428	C₂×#123	C₂²×C₁₉	1	2	yes	—
429	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
430	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
431	C₂×#121	C₂²×C₁₉	1	2	yes	—
432	C₂×#121	C₂²×C₁₉	1	2	yes	—
433	C₂×#121	C₂²×C₁₉	1	4	yes	—
434	C₂×#121	C₂²×C₁₉	1	4	yes	—
435	C₂×#120	C₂²×C₁₉	1	2	yes	—
436	C₂×#120	C₂²×C₁₉	1	2	yes	—
437	C₄×#41	—	2	8	no	—
438	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
439	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
440	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
441	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
442	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	complemented
443	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
444	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
447	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
448	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
449	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
450	C₂²×C₄²	C₂²×C₁₉	1	2	yes	complemented
451	#398	C₂²×C₁₉	1	4	yes	complemented
452	#397	C₂²×C₁₉	1	4	yes	complemented
453	#396	C₂²×C₁₉	1	4	yes	—
454	#396	C₂²×C₁₉	1	4	yes	complemented
455	#394	C₂²×C₁₉	1	4	yes	—
456	#394	C₂²×C₁₉	1	4	yes	—
457	#394	C₂²×C₁₉	1	4	yes	complemented
458	#392	C₂²×C₁₉	1	4	yes	—
459	#391	C₂²×C₁₉	1	2	yes	complemented
460	#390	C₂²×C₁₉	1	4	yes	—
461	#390	C₂²×C₁₉	1	2	yes	complemented
462	#389	C₂²×C₁₉	1	4	yes	complemented
463	#389	C₂²×C₁₉	1	2	yes	complemented
464	#389	C₂²×C₁₉	1	2	yes	complemented
465	#388	C₂²×C₁₉	1	4	yes	—
466	#388	C₂²×C₁₉	1	4	yes	complemented
467	#386	C₂²×C₁₉	1	4	yes	—
468	#386	C₂²×C₁₉	1	4	yes	—
469	#386	C₂²×C₁₉	1	4	yes	complemented
470	#385	C₂²×C₁₉	1	4	yes	—
471	#380	C₂²×C₁₉	1	4	yes	complemented
472	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
473	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	complemented
478	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	complemented
479	C₂×#95	C₂²×C₁₉	1	2	yes	—
480	C₂×C₁₉	—	2	4	no	—
481	C₂×C₁₉	—	4	4	no	—
482	C₂×C₁₉	—	4	4	no	—
483	C₂×C₁₉	—	8	2	no	—
484	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
485	C₂×C₁₉	#3444	1	1	yes	characteristic
486	C₂×C₁₉	#3455	1	1	yes	characteristic
487	C₂×C₁₉	D₄×#41	1	2	yes	—
488	C₂×C₁₉	D₄×#41	1	2	yes	—
489	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
490	C₂×#41	—	2	4	no	—
491	C₂×#41	—	2	4	no	—
492	C₂×#41	—	2	4	no	—
493	C₂×#41	—	2	4	no	—
494	C₂×#41	—	2	4	no	—
495	C₂×#41	D₄×C₁₉	1	8	yes	complemented
496	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
499	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
501	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
502	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
503	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
504	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
505	C₂³×C₄	—	2	4	no	—
506	C₂³×C₄	—	2	4	no	—
507	C₂³×C₄	—	2	4	no	—
508	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
509	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
511	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
514	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
515	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
516	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
517	C₄⋊Q₈	—	2	4	no	—
518	#127	—	2	4	no	—
519	#124	—	2	4	no	—
520	#124	—	2	4	no	—
521	#123	—	2	8	no	—
522	#123	—	2	8	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	C₂²⋊Q₈	—	2	8	no	—
525	#121	—	2	8	no	—
526	#121	—	2	16	no	—
527	#121	—	2	8	no	—
528	#121	—	2	16	no	—
529	#120	—	2	8	no	—
530	#120	—	2	8	no	—
531	C₄×Q₈	—	2	8	no	—
532	C₄×D₄	—	2	16	no	—
533	C₄×D₄	—	2	16	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	16	no	—
536	C₄×D₄	—	2	16	no	—
537	#117	—	2	4	no	—
538	#117	—	2	8	no	—
539	#117	D₄×C₁₉	1	8	yes	complemented
540	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
548	C₂×C₂²⋊C₄	—	2	8	no	—
549	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
564	C₂×C₄²	—	2	4	no	—
565	C₂×C₄²	—	2	4	no	—
566	C₂×C₄²	—	2	8	no	—
567	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
570	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
576	#95	C₂³×C₁₉	1	2	yes	—
577	#95	C₂³×C₁₉	1	2	yes	—
578	#95	C₂³×C₁₉	1	2	yes	—
579	#95	C₂³×C₁₉	1	2	yes	—
580	#95	C₂³×C₁₉	1	4	yes	—
581	#95	C₂³×C₁₉	1	4	yes	—
582	#95	C₂³×C₁₉	1	4	yes	—
583	#95	C₂³×C₁₉	1	4	yes	—
584	C₁₉	#34743	1	1	yes	characteristic, direct product factor, Sylow
585	C₂⁴	—	2	4	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
591	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
592	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
593	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
594	#41	—	2	32	no	—
595	#41	—	4	16	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	2	8	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	8	no	—
609	C₂×D₄	—	2	8	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
622	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	8	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	—	2	8	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	16	no	—
647	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
648	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
649	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
650	C₂²×C₄	#41×C₁₉	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
657	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
662	C₄⋊C₄	—	2	8	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	2	8	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	8	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	2	8	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
684	C₂²⋊C₄	#41×C₁₉	1	8	yes	complemented
685	C₄²	—	2	2	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	8	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	C₂×D₄×C₁₉	1	8	yes	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	8	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	8	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
717	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
718	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
719	C₂³	C₂×#41×C₁₉	1	4	yes	—
720	C₂³	C₂×#41×C₁₉	1	2	yes	—
721	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
722	Q₈	—	2	8	no	—
723	Q₈	—	4	4	no	—
724	D₄	—	2	16	no	—
725	D₄	—	2	8	no	—
726	D₄	—	4	16	no	—
727	D₄	—	4	16	no	—
728	D₄	—	4	16	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	16	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	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	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	16	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	8	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	C₁₉×#121	1	16	yes	complemented
763	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
764	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
769	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
770	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
771	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
772	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	16	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	C₂×C₁₉×#121	1	4	yes	—
796	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
797	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
798	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
799	C₂²	C₂²×#41×C₁₉	1	2	yes	—
800	C₂²	C₁₉×#585	1	2	yes	—
801	C₄	—	2	4	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	8	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	4	no	—
810	C₄	C₂×C₁₉×#121	1	4	yes	—
811	C₄	C₂×C₁₉×#121	1	4	yes	—
812	C₂	—	2	4	no	—
813	C₂	—	4	4	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
817	C₂	C₁₉×#3444	1	1	yes	characteristic
818	C₂	C₁₉×#3455	1	1	yes	characteristic
819	C₂	D₄×#41×C₁₉	1	2	yes	—
820	C₂	D₄×#41×C₁₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
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. C₂×C₁₉×#532	C₂	semidirect
2. C₂×C₁₉×#525	C₂	semidirect
3. C₂×C₁₉×#525	C₂	semidirect
4. C₂×C₄×#41×C₁₉	C₂	semidirect
5. C₁₉×#2429	C₂	semidirect
6. C₁₉×#2428	C₂	semidirect
7. C₁₉×#2427	C₂	semidirect
8. C₁₉×#2426	C₂	semidirect
9. C₁₉×#2425	C₂	semidirect
10. C₁₉×#2424	C₂	semidirect
11. C₁₉×#2392	C₂	semidirect
12. C₄×C₁₉×#121	C₂	semidirect
13. C₁₉×#2297	C₂	semidirect
14. C₁₉×#2296	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
20. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₉×#127	C₂²	semidirect
22. C₂×C₁₉×#124	C₂²	semidirect
23. C₂×C₁₉×#124	C₂²	semidirect
37. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
41. C₂×C₄×D₄×C₁₉	C₂²	semidirect
42. C₂×C₄×D₄×C₁₉	C₂²	semidirect
45. C₂×C₁₉×#117	C₂²	semidirect
49. C₂²×C₄²×C₁₉	C₂²	semidirect
50. C₁₉×#398	C₂²	semidirect
51. C₁₉×#397	C₂²	semidirect
53. C₁₉×#396	C₂²	semidirect
56. C₁₉×#394	C₂²	semidirect
58. C₁₉×#391	C₂²	semidirect
60. C₁₉×#390	C₂²	semidirect
61. C₁₉×#389	C₂²	semidirect
62. C₁₉×#389	C₂²	semidirect
63. C₁₉×#389	C₂²	semidirect
65. C₁₉×#388	C₂²	semidirect
68. C₁₉×#386	C₂²	semidirect
70. C₁₉×#380	C₂²	semidirect
71. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
77. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
85. C₂×#41×C₁₉	D₄	semidirect
129. C₁₉×#117	D₄	semidirect
273. C₂²⋊C₄×C₁₉	#41	semidirect
283. #34743	C₁₉	direct (N × H)
352. C₂×C₄×C₁₉	#121	semidirect
363. C₂×#532	C₂×C₁₉	semidirect
364. C₂×#525	C₂×C₁₉	semidirect
365. C₂×#525	C₂×C₁₉	semidirect
366. C₂×C₄×#41	C₂×C₁₉	semidirect
367. #2429	C₂×C₁₉	semidirect
368. #2428	C₂×C₁₉	semidirect
369. #2427	C₂×C₁₉	semidirect
370. #2426	C₂×C₁₉	semidirect
371. #2425	C₂×C₁₉	semidirect
372. #2424	C₂×C₁₉	semidirect
373. #2392	C₂×C₁₉	semidirect
374. C₄×#121	C₂×C₁₉	semidirect
375. #2297	C₂×C₁₉	semidirect
376. #2296	C₂×C₁₉	semidirect
377. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
421. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
422. C₂×#127	C₂²×C₁₉	semidirect
423. C₂×#124	C₂²×C₁₉	semidirect
424. C₂×#124	C₂²×C₁₉	semidirect
438. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
442. C₂×C₄×D₄	C₂²×C₁₉	semidirect
443. C₂×C₄×D₄	C₂²×C₁₉	semidirect
446. C₂×#117	C₂²×C₁₉	semidirect
450. C₂²×C₄²	C₂²×C₁₉	semidirect
451. #398	C₂²×C₁₉	semidirect
452. #397	C₂²×C₁₉	semidirect
454. #396	C₂²×C₁₉	semidirect
457. #394	C₂²×C₁₉	semidirect
459. #391	C₂²×C₁₉	semidirect
461. #390	C₂²×C₁₉	semidirect
462. #389	C₂²×C₁₉	semidirect
463. #389	C₂²×C₁₉	semidirect
464. #389	C₂²×C₁₉	semidirect
466. #388	C₂²×C₁₉	semidirect
469. #386	C₂²×C₁₉	semidirect
471. #380	C₂²×C₁₉	semidirect
472. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
477. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
478. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
495. C₂×#41	D₄×C₁₉	semidirect
539. #117	D₄×C₁₉	semidirect
584. C₁₉	#34743	direct (N × H)
684. C₂²⋊C₄	#41×C₁₉	semidirect
762. C₂×C₄	C₁₉×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#532	2
C₂×C₁₉×#525	2
C₂×C₄×#41×C₁₉	2
C₁₉×#2429	2
C₁₉×#2428	2
C₁₉×#2427	2
C₁₉×#2426	2
C₁₉×#2425	2
C₁₉×#2424	2
C₁₉×#2392	2
C₄×C₁₉×#121	2
C₁₉×#2297	2
C₁₉×#2296	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#34743	19

Subgroups — C19×#34743 #18040702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34743 #18040702