Subgroups — C₁₉×#22434 #18028393

Order 4864.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1759	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	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×#550	C₄	1	1	yes	characteristic, complemented
21	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#548	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#548	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#547	—	2	1	no	—
25	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#546	—	2	1	no	—
27	C₁₉×#546	—	2	1	no	—
28	C₁₉×#546	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#546	C₄	1	1	yes	characteristic, complemented
30	D₄²×C₁₉	—	2	1	no	—
31	D₄²×C₁₉	C₄	1	1	yes	characteristic, complemented
32	C₁₉×#532	—	2	1	no	—
33	C₁₉×#532	C₂²	1	1	yes	characteristic
34	C₁₉×#525	—	2	1	no	—
35	C₁₉×#525	—	2	1	no	—
36	C₁₉×#525	C₂²	1	1	yes	characteristic
37	C₁₉×#525	C₂²	1	1	yes	characteristic
38	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₉	—	2	1	no	—
40	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#436	—	2	1	no	—
44	C₁₉×#435	—	2	1	no	—
45	C₁₉×#435	—	2	1	no	—
46	C₈×D₄×C₁₉	—	2	1	no	—
47	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#421	—	2	4	no	—
49	C₂×C₁₉×#104	—	2	4	no	—
50	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
54	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
64	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#388	—	2	1	no	—
66	C₁₉×#387	—	2	1	no	—
67	C₁₉×#386	—	2	1	no	—
68	C₁₉×#385	—	2	1	no	—
69	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#376	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
76	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
77	C₂×#41×C₁₉	—	2	1	no	—
78	C₂×#41×C₁₉	—	2	1	no	—
79	C₂×#41×C₁₉	—	2	1	no	—
80	C₂×#41×C₁₉	—	2	1	no	—
81	C₂×#41×C₁₉	—	2	2	no	—
82	C₂×#41×C₁₉	—	2	2	no	—
83	C₂×#41×C₁₉	—	2	2	no	—
84	C₂×#41×C₁₉	—	2	2	no	—
85	C₂×#41×C₁₉	—	4	1	no	—
86	C₂×#41×C₁₉	—	4	1	no	—
87	C₂×#41×C₁₉	—	4	1	no	—
88	C₂×#41×C₁₉	—	4	1	no	—
89	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
97	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂²×D₄×C₁₉	—	2	1	no	—
99	C₂²×D₄×C₁₉	—	2	1	no	—
100	C₂²×D₄×C₁₉	—	2	1	no	—
101	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
102	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
103	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
104	C₂³×C₄×C₁₉	—	2	1	no	—
105	C₂³×C₄×C₁₉	—	2	1	no	—
106	C₂³×C₄×C₁₉	—	2	1	no	—
107	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₁₉	—	2	1	no	—
110	C₂×M₁₆×C₁₉	—	2	1	no	—
111	C₂×M₁₆×C₁₉	—	2	2	no	—
112	C₂×M₁₆×C₁₉	—	2	2	no	—
113	C₂×M₁₆×C₁₉	—	4	1	no	—
114	C₂×M₁₆×C₁₉	—	4	1	no	—
115	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₉	—	2	1	no	—
120	C₂²×C₈×C₁₉	—	2	1	no	—
121	C₁₉×C₄⋊Q₈	—	2	1	no	—
122	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
123	C₁₉×#127	—	2	1	no	—
124	C₁₉×#127	C₂×C₄	1	1	yes	characteristic, complemented
125	C₁₉×#124	—	2	1	no	—
126	C₁₉×#124	—	2	1	no	—
127	C₁₉×#124	C₂×C₄	1	1	yes	characteristic, complemented
128	C₁₉×#124	C₂×C₄	1	1	yes	characteristic, complemented
129	C₁₉×#123	—	2	1	no	—
130	C₁₉×#123	—	2	1	no	—
131	C₁₉×#123	—	2	1	no	—
132	C₁₉×#123	—	2	1	no	—
133	C₁₉×#123	—	2	1	no	—
134	C₁₉×#123	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	—	2	1	no	—
136	C₁₉×C₂²⋊Q₈	—	2	1	no	—
137	C₁₉×C₂²⋊Q₈	—	2	1	no	—
138	C₁₉×C₂²⋊Q₈	—	2	1	no	—
139	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
140	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
141	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
142	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
143	C₁₉×#121	—	2	1	no	—
144	C₁₉×#121	—	2	1	no	—
145	C₁₉×#121	—	2	1	no	—
146	C₁₉×#121	—	2	1	no	—
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	—	2	1	no	—
149	C₁₉×#121	—	2	1	no	—
150	C₁₉×#121	—	2	1	no	—
151	C₁₉×#121	—	2	1	no	—
152	C₁₉×#121	—	2	1	no	—
153	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
154	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
155	C₁₉×#121	C₂×C₄	1	1	yes	characteristic, complemented
156	C₁₉×#121	C₂×C₄	1	1	yes	characteristic, complemented
157	C₁₉×#120	—	2	1	no	—
158	C₁₉×#120	—	2	1	no	—
159	C₁₉×#120	—	2	1	no	—
160	C₁₉×#120	—	2	1	no	—
161	C₁₉×#120	—	2	1	no	—
162	C₁₉×#120	—	2	1	no	—
163	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
164	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
165	C₄×D₄×C₁₉	—	2	1	no	—
166	C₄×D₄×C₁₉	—	2	1	no	—
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₄×D₄×C₁₉	—	2	1	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	—	2	1	no	—
171	C₄×D₄×C₁₉	—	2	1	no	—
172	C₄×D₄×C₁₉	—	2	1	no	—
173	C₄×D₄×C₁₉	—	2	1	no	—
174	C₄×D₄×C₁₉	—	2	1	no	—
175	C₄×D₄×C₁₉	—	2	1	no	—
176	C₄×D₄×C₁₉	—	2	1	no	—
177	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
178	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
179	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
180	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
181	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
182	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
183	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
184	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
187	C₁₉×#117	—	2	1	no	—
188	C₁₉×#117	—	2	2	no	—
189	C₁₉×#117	—	4	1	no	—
190	C₁₉×#117	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
202	C₂×C₄²×C₁₉	—	2	1	no	—
203	C₂×C₄²×C₁₉	—	2	2	no	—
204	C₂×C₄²×C₁₉	—	2	1	no	—
205	C₂×C₄²×C₁₉	—	4	1	no	—
206	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
211	C₁₉×C₄⋊C₈	—	2	1	no	—
212	C₁₉×C₄⋊C₈	—	2	1	no	—
213	C₁₉×#104	—	2	2	no	—
214	C₁₉×#104	—	2	2	no	—
215	C₁₉×#104	—	2	2	no	—
216	C₁₉×#104	—	2	2	no	—
217	C₁₉×#104	—	2	2	no	—
218	C₁₉×#104	—	2	2	no	—
219	C₁₉×#104	—	2	2	no	—
220	C₁₉×#104	—	4	1	no	—
221	C₁₉×#104	—	4	1	no	—
222	C₁₉×#104	—	4	1	no	—
223	C₁₉×#104	—	4	1	no	—
224	C₁₉×#104	D₄	1	4	yes	complemented
225	C₁₉×C₂²⋊C₈	—	2	1	no	—
226	C₁₉×C₂²⋊C₈	—	2	1	no	—
227	C₁₉×C₂²⋊C₈	—	2	1	no	—
228	C₁₉×C₂²⋊C₈	—	2	1	no	—
229	C₁₉×#97	—	2	1	no	—
230	C₄×C₈×C₁₉	—	2	1	no	—
231	C₁₉×#95	—	2	1	no	—
232	C₁₉×#95	—	2	1	no	—
233	C₁₉×#95	—	2	1	no	—
234	C₁₉×#95	—	2	1	no	—
235	C₁₉×#95	—	2	1	no	—
236	C₂⁴×C₁₉	—	2	1	no	—
237	C₂⁴×C₁₉	—	2	1	no	—
238	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
240	#41×C₁₉	—	2	1	no	—
241	#41×C₁₉	—	2	1	no	—
242	#41×C₁₉	—	2	2	no	—
243	#41×C₁₉	—	2	2	no	—
244	#41×C₁₉	—	2	2	no	—
245	#41×C₁₉	—	2	2	no	—
246	#41×C₁₉	—	2	1	no	—
247	#41×C₁₉	—	2	1	no	—
248	#41×C₁₉	—	2	1	no	—
249	#41×C₁₉	—	2	1	no	—
250	#41×C₁₉	—	2	1	no	—
251	#41×C₁₉	—	2	1	no	—
252	#41×C₁₉	—	2	1	no	—
253	#41×C₁₉	—	2	1	no	—
254	#41×C₁₉	—	4	2	no	—
255	#41×C₁₉	—	4	2	no	—
256	#41×C₁₉	—	4	2	no	—
257	#41×C₁₉	—	4	2	no	—
258	#41×C₁₉	—	4	1	no	—
259	#41×C₁₉	—	4	1	no	—
260	#41×C₁₉	—	4	1	no	—
261	#41×C₁₉	—	4	1	no	—
262	#41×C₁₉	—	4	2	no	—
263	#41×C₁₉	—	4	2	no	—
264	#41×C₁₉	—	4	2	no	—
265	#41×C₁₉	—	4	2	no	—
266	#41×C₁₉	C₂×D₄	1	2	yes	—
267	#41×C₁₉	#41	1	2	yes	—
268	C₂×Q₈×C₁₉	—	2	1	no	—
269	C₂×Q₈×C₁₉	—	2	1	no	—
270	C₂×Q₈×C₁₉	—	2	2	no	—
271	C₂×Q₈×C₁₉	—	2	2	no	—
272	C₂×Q₈×C₁₉	—	4	1	no	—
273	C₂×Q₈×C₁₉	—	4	1	no	—
274	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
275	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
276	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
277	C₂×D₄×C₁₉	—	2	1	no	—
278	C₂×D₄×C₁₉	—	2	2	no	—
279	C₂×D₄×C₁₉	—	2	2	no	—
280	C₂×D₄×C₁₉	—	2	1	no	—
281	C₂×D₄×C₁₉	—	2	1	no	—
282	C₂×D₄×C₁₉	—	2	1	no	—
283	C₂×D₄×C₁₉	—	2	1	no	—
284	C₂×D₄×C₁₉	—	2	1	no	—
285	C₂×D₄×C₁₉	—	2	1	no	—
286	C₂×D₄×C₁₉	—	2	1	no	—
287	C₂×D₄×C₁₉	—	2	1	no	—
288	C₂×D₄×C₁₉	—	2	1	no	—
289	C₂×D₄×C₁₉	—	2	1	no	—
290	C₂×D₄×C₁₉	—	2	1	no	—
291	C₂×D₄×C₁₉	—	2	1	no	—
292	C₂×D₄×C₁₉	—	2	1	no	—
293	C₂×D₄×C₁₉	—	2	1	no	—
294	C₂×D₄×C₁₉	—	4	1	no	—
295	C₂×D₄×C₁₉	—	4	1	no	—
296	C₂×D₄×C₁₉	—	4	2	no	—
297	C₂×D₄×C₁₉	—	4	2	no	—
298	C₂×D₄×C₁₉	—	4	2	no	—
299	C₂×D₄×C₁₉	—	4	2	no	—
300	C₂×D₄×C₁₉	—	4	2	no	—
301	C₂×D₄×C₁₉	—	4	4	no	—
302	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
303	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
304	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
305	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
306	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
307	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
308	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₉	—	2	1	no	—
310	C₂²×C₄×C₁₉	—	2	1	no	—
311	C₂²×C₄×C₁₉	—	2	1	no	—
312	C₂²×C₄×C₁₉	—	2	1	no	—
313	C₂²×C₄×C₁₉	—	2	1	no	—
314	C₂²×C₄×C₁₉	—	2	1	no	—
315	C₂²×C₄×C₁₉	—	2	1	no	—
316	C₂²×C₄×C₁₉	—	2	1	no	—
317	C₂²×C₄×C₁₉	—	2	1	no	—
318	C₂²×C₄×C₁₉	—	2	1	no	—
319	C₂²×C₄×C₁₉	—	2	1	no	—
320	C₂²×C₄×C₁₉	—	2	1	no	—
321	C₂²×C₄×C₁₉	—	2	1	no	—
322	C₂²×C₄×C₁₉	—	2	1	no	—
323	C₂²×C₄×C₁₉	—	2	1	no	—
324	C₂²×C₄×C₁₉	—	2	1	no	—
325	C₂²×C₄×C₁₉	—	2	1	no	—
326	C₂²×C₄×C₁₉	—	2	1	no	—
327	C₂²×C₄×C₁₉	—	2	1	no	—
328	C₂²×C₄×C₁₉	—	2	1	no	—
329	C₂²×C₄×C₁₉	—	2	1	no	—
330	C₂²×C₄×C₁₉	—	2	1	no	—
331	C₂²×C₄×C₁₉	—	2	1	no	—
332	C₂²×C₄×C₁₉	—	4	2	no	—
333	C₂²×C₄×C₁₉	—	4	2	no	—
334	C₂²×C₄×C₁₉	—	4	2	no	—
335	C₂²×C₄×C₁₉	—	4	2	no	—
336	C₂²×C₄×C₁₉	—	4	2	no	—
337	C₂²×C₄×C₁₉	—	4	2	no	—
338	C₂²×C₄×C₁₉	—	4	2	no	—
339	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
340	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
352	M₁₆×C₁₉	—	2	1	no	—
353	M₁₆×C₁₉	—	2	1	no	—
354	M₁₆×C₁₉	—	2	1	no	—
355	M₁₆×C₁₉	—	2	1	no	—
356	M₁₆×C₁₉	—	2	1	no	—
357	M₁₆×C₁₉	—	2	1	no	—
358	M₁₆×C₁₉	—	2	1	no	—
359	M₁₆×C₁₉	—	4	2	no	—
360	M₁₆×C₁₉	—	4	2	no	—
361	M₁₆×C₁₉	C₂×D₄	1	2	yes	complemented
362	C₂×C₈×C₁₉	—	2	1	no	—
363	C₂×C₈×C₁₉	—	2	1	no	—
364	C₂×C₈×C₁₉	—	2	1	no	—
365	C₂×C₈×C₁₉	—	2	1	no	—
366	C₂×C₈×C₁₉	—	4	2	no	—
367	C₂×C₈×C₁₉	—	4	2	no	—
368	C₄⋊C₄×C₁₉	—	2	1	no	—
369	C₄⋊C₄×C₁₉	—	2	1	no	—
370	C₄⋊C₄×C₁₉	—	2	1	no	—
371	C₄⋊C₄×C₁₉	—	2	1	no	—
372	C₄⋊C₄×C₁₉	—	2	1	no	—
373	C₄⋊C₄×C₁₉	—	2	1	no	—
374	C₄⋊C₄×C₁₉	—	2	1	no	—
375	C₄⋊C₄×C₁₉	—	2	1	no	—
376	C₄⋊C₄×C₁₉	—	4	2	no	—
377	C₄⋊C₄×C₁₉	—	4	2	no	—
378	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
379	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
380	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
381	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
382	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
384	C₂²⋊C₄×C₁₉	—	2	1	no	—
385	C₂²⋊C₄×C₁₉	—	2	1	no	—
386	C₂²⋊C₄×C₁₉	—	2	1	no	—
387	C₂²⋊C₄×C₁₉	—	2	1	no	—
388	C₂²⋊C₄×C₁₉	—	2	1	no	—
389	C₂²⋊C₄×C₁₉	—	2	1	no	—
390	C₂²⋊C₄×C₁₉	—	2	1	no	—
391	C₂²⋊C₄×C₁₉	—	2	1	no	—
392	C₂²⋊C₄×C₁₉	—	2	1	no	—
393	C₂²⋊C₄×C₁₉	—	2	1	no	—
394	C₂²⋊C₄×C₁₉	—	2	1	no	—
395	C₂²⋊C₄×C₁₉	—	2	1	no	—
396	C₂²⋊C₄×C₁₉	—	2	1	no	—
397	C₂²⋊C₄×C₁₉	—	2	1	no	—
398	C₂²⋊C₄×C₁₉	—	2	1	no	—
399	C₂²⋊C₄×C₁₉	—	4	2	no	—
400	C₂²⋊C₄×C₁₉	—	4	2	no	—
401	C₂²⋊C₄×C₁₉	—	4	2	no	—
402	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
408	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
410	C₄²×C₁₉	—	2	1	no	—
411	C₄²×C₁₉	—	2	1	no	—
412	C₄²×C₁₉	—	2	1	no	—
413	C₄²×C₁₉	—	2	1	no	—
414	C₄²×C₁₉	—	2	1	no	—
415	C₄²×C₁₉	—	2	1	no	—
416	C₄²×C₁₉	—	2	1	no	—
417	C₄²×C₁₉	—	2	1	no	—
418	C₄²×C₁₉	—	2	1	no	—
419	C₄²×C₁₉	—	2	1	no	—
420	C₄²×C₁₉	—	4	2	no	—
421	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
422	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
423	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
425	C₄²×C₁₉	C₂×D₄	1	2	yes	complemented
426	#22434	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂³×C₁₉	—	2	1	no	—
428	C₂³×C₁₉	—	2	1	no	—
429	C₂³×C₁₉	—	2	1	no	—
430	C₂³×C₁₉	—	2	2	no	—
431	C₂³×C₁₉	—	2	1	no	—
432	C₂³×C₁₉	—	2	1	no	—
433	C₂³×C₁₉	—	2	1	no	—
434	C₂³×C₁₉	—	2	1	no	—
435	C₂³×C₁₉	—	4	1	no	—
436	C₂³×C₁₉	—	4	1	no	—
437	C₂³×C₁₉	—	4	1	no	—
438	C₂³×C₁₉	—	4	2	no	—
439	C₂³×C₁₉	—	4	2	no	—
440	C₂³×C₁₉	—	4	2	no	—
441	C₂³×C₁₉	—	4	2	no	—
442	C₂³×C₁₉	—	8	1	no	—
443	C₂³×C₁₉	—	8	1	no	—
444	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
445	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
446	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₁₉	—	2	1	no	—
450	Q₈×C₁₉	—	2	1	no	—
451	Q₈×C₁₉	—	2	1	no	—
452	Q₈×C₁₉	—	2	1	no	—
453	Q₈×C₁₉	—	2	1	no	—
454	Q₈×C₁₉	—	4	2	no	—
455	Q₈×C₁₉	—	4	2	no	—
456	Q₈×C₁₉	C₄×D₄	1	2	yes	—
457	D₄×C₁₉	—	2	2	no	—
458	D₄×C₁₉	—	2	2	no	—
459	D₄×C₁₉	—	2	2	no	—
460	D₄×C₁₉	—	2	2	no	—
461	D₄×C₁₉	—	2	1	no	—
462	D₄×C₁₉	—	2	1	no	—
463	D₄×C₁₉	—	2	1	no	—
464	D₄×C₁₉	—	2	1	no	—
465	D₄×C₁₉	—	2	1	no	—
466	D₄×C₁₉	—	4	1	no	—
467	D₄×C₁₉	—	4	1	no	—
468	D₄×C₁₉	—	4	2	no	—
469	D₄×C₁₉	—	4	2	no	—
470	D₄×C₁₉	—	4	2	no	—
471	D₄×C₁₉	—	4	2	no	—
472	D₄×C₁₉	—	4	2	no	—
473	D₄×C₁₉	—	4	2	no	—
474	D₄×C₁₉	—	4	2	no	—
475	D₄×C₁₉	—	4	2	no	—
476	D₄×C₁₉	—	4	1	no	—
477	D₄×C₁₉	—	4	1	no	—
478	D₄×C₁₉	—	4	1	no	—
479	D₄×C₁₉	—	4	1	no	—
480	D₄×C₁₉	—	4	2	no	—
481	D₄×C₁₉	—	8	1	no	—
482	D₄×C₁₉	—	8	1	no	—
483	D₄×C₁₉	—	8	1	no	—
484	D₄×C₁₉	C₄×D₄	1	2	yes	—
485	C₂×C₄×C₁₉	—	2	1	no	—
486	C₂×C₄×C₁₉	—	2	1	no	—
487	C₂×C₄×C₁₉	—	2	1	no	—
488	C₂×C₄×C₁₉	—	2	1	no	—
489	C₂×C₄×C₁₉	—	2	1	no	—
490	C₂×C₄×C₁₉	—	2	1	no	—
491	C₂×C₄×C₁₉	—	2	1	no	—
492	C₂×C₄×C₁₉	—	2	1	no	—
493	C₂×C₄×C₁₉	—	2	1	no	—
494	C₂×C₄×C₁₉	—	2	1	no	—
495	C₂×C₄×C₁₉	—	2	1	no	—
496	C₂×C₄×C₁₉	—	2	1	no	—
497	C₂×C₄×C₁₉	—	2	1	no	—
498	C₂×C₄×C₁₉	—	2	1	no	—
499	C₂×C₄×C₁₉	—	2	1	no	—
500	C₂×C₄×C₁₉	—	2	1	no	—
501	C₂×C₄×C₁₉	—	2	1	no	—
502	C₂×C₄×C₁₉	—	2	2	no	—
503	C₂×C₄×C₁₉	—	2	1	no	—
504	C₂×C₄×C₁₉	—	2	1	no	—
505	C₂×C₄×C₁₉	—	2	1	no	—
506	C₂×C₄×C₁₉	—	2	1	no	—
507	C₂×C₄×C₁₉	—	2	2	no	—
508	C₂×C₄×C₁₉	—	2	2	no	—
509	C₂×C₄×C₁₉	—	2	1	no	—
510	C₂×C₄×C₁₉	—	2	1	no	—
511	C₂×C₄×C₁₉	—	2	1	no	—
512	C₂×C₄×C₁₉	—	2	1	no	—
513	C₂×C₄×C₁₉	—	2	2	no	—
514	C₂×C₄×C₁₉	—	4	1	no	—
515	C₂×C₄×C₁₉	—	4	1	no	—
516	C₂×C₄×C₁₉	—	4	2	no	—
517	C₂×C₄×C₁₉	—	4	2	no	—
518	C₂×C₄×C₁₉	—	4	2	no	—
519	C₂×C₄×C₁₉	—	4	2	no	—
520	C₂×C₄×C₁₉	—	4	2	no	—
521	C₂×C₄×C₁₉	—	4	2	no	—
522	C₂×C₄×C₁₉	—	4	2	no	—
523	C₂×C₄×C₁₉	—	4	1	no	—
524	C₂×C₄×C₁₉	—	4	1	no	—
525	C₂×C₄×C₁₉	—	4	1	no	—
526	C₂×C₄×C₁₉	—	4	8	no	—
527	C₂×C₄×C₁₉	—	4	1	no	—
528	C₂×C₄×C₁₉	—	4	1	no	—
529	C₂×C₄×C₁₉	—	4	1	no	—
530	C₂×C₄×C₁₉	—	4	1	no	—
531	C₂×C₄×C₁₉	—	4	1	no	—
532	C₂×C₄×C₁₉	—	4	1	no	—
533	C₂×C₄×C₁₉	—	4	1	no	—
534	C₂×C₄×C₁₉	—	4	1	no	—
535	C₂×C₄×C₁₉	—	4	1	no	—
536	C₂×C₄×C₁₉	—	4	1	no	—
537	C₂×C₄×C₁₉	—	4	1	no	—
538	C₂×C₄×C₁₉	—	8	1	no	—
539	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
540	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
541	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
542	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
543	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
544	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
545	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
546	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
547	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
548	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
551	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
552	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
553	C₈×C₁₉	—	2	2	no	—
554	C₈×C₁₉	—	4	1	no	—
555	C₈×C₁₉	—	4	1	no	—
556	C₈×C₁₉	—	4	1	no	—
557	D₄×#41	C₂×C₁₉	1	1	yes	characteristic
558	D₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
559	C₂×#421	C₂×C₁₉	1	1	yes	characteristic, complemented
560	C₂²×#104	C₂×C₁₉	1	1	yes	characteristic, complemented
561	#2290	C₂×C₁₉	1	1	yes	characteristic, complemented
562	#1980	C₂×C₁₉	1	1	yes	characteristic, complemented
563	#1963	C₂×C₁₉	1	1	yes	characteristic, complemented
564	#1897	C₂×C₁₉	1	1	yes	characteristic, complemented
565	#1896	C₂×C₁₉	1	1	yes	characteristic, complemented
566	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
567	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
568	#1806	C₂×C₁₉	1	1	yes	characteristic, complemented
569	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
570	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
571	#1759	C₂×C₁₉	1	1	yes	characteristic, complemented
572	C₂²×C₁₉	—	2	1	no	—
573	C₂²×C₁₉	—	2	1	no	—
574	C₂²×C₁₉	—	2	1	no	—
575	C₂²×C₁₉	—	2	1	no	—
576	C₂²×C₁₉	—	2	1	no	—
577	C₂²×C₁₉	—	2	1	no	—
578	C₂²×C₁₉	—	2	1	no	—
579	C₂²×C₁₉	—	2	2	no	—
580	C₂²×C₁₉	—	2	1	no	—
581	C₂²×C₁₉	—	2	1	no	—
582	C₂²×C₁₉	—	2	1	no	—
583	C₂²×C₁₉	—	2	1	no	—
584	C₂²×C₁₉	—	2	1	no	—
585	C₂²×C₁₉	—	2	1	no	—
586	C₂²×C₁₉	—	4	2	no	—
587	C₂²×C₁₉	—	4	2	no	—
588	C₂²×C₁₉	—	4	1	no	—
589	C₂²×C₁₉	—	4	1	no	—
590	C₂²×C₁₉	—	4	1	no	—
591	C₂²×C₁₉	—	4	1	no	—
592	C₂²×C₁₉	—	4	1	no	—
593	C₂²×C₁₉	—	4	1	no	—
594	C₂²×C₁₉	—	4	1	no	—
595	C₂²×C₁₉	—	4	1	no	—
596	C₂²×C₁₉	—	8	1	no	—
597	C₂²×C₁₉	—	8	1	no	—
598	C₂²×C₁₉	—	8	4	no	—
599	C₂²×C₁₉	—	8	4	no	—
600	C₂²×C₁₉	#421	1	2	yes	complemented
601	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
602	C₂²×C₁₉	D₄²	1	1	yes	characteristic
603	C₂²×C₁₉	#546	1	1	yes	characteristic
604	C₄×C₁₉	—	2	1	no	—
605	C₄×C₁₉	—	2	1	no	—
606	C₄×C₁₉	—	2	1	no	—
607	C₄×C₁₉	—	2	1	no	—
608	C₄×C₁₉	—	2	2	no	—
609	C₄×C₁₉	—	2	1	no	—
610	C₄×C₁₉	—	2	1	no	—
611	C₄×C₁₉	—	2	1	no	—
612	C₄×C₁₉	—	2	1	no	—
613	C₄×C₁₉	—	4	2	no	—
614	C₄×C₁₉	—	4	2	no	—
615	C₄×C₁₉	—	4	1	no	—
616	C₄×C₁₉	—	4	1	no	—
617	C₄×C₁₉	—	4	1	no	—
618	C₄×C₁₉	—	4	1	no	—
619	C₄×C₁₉	—	8	1	no	—
620	C₄×C₁₉	—	8	1	no	—
621	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
622	C₄×C₁₉	#518	1	1	yes	characteristic
623	C₄×C₁₉	D₄²	1	1	yes	characteristic
624	C₄×C₁₉	#546	1	1	yes	characteristic
625	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
626	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
627	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
628	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
629	#550	C₄×C₁₉	1	1	yes	characteristic, complemented
630	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
631	#548	C₄×C₁₉	1	1	yes	characteristic, complemented
632	#548	C₄×C₁₉	1	1	yes	characteristic, complemented
633	#547	—	2	1	no	—
634	#547	C₄×C₁₉	1	1	yes	characteristic, complemented
635	#546	—	2	1	no	—
636	#546	—	2	1	no	—
637	#546	C₄×C₁₉	1	1	yes	characteristic, complemented
638	#546	C₄×C₁₉	1	1	yes	characteristic, complemented
639	D₄²	—	2	1	no	—
640	D₄²	C₄×C₁₉	1	1	yes	characteristic, complemented
641	#532	—	2	1	no	—
642	#532	C₂²×C₁₉	1	1	yes	characteristic
643	#525	—	2	1	no	—
644	#525	—	2	1	no	—
645	#525	C₂²×C₁₉	1	1	yes	characteristic
646	#525	C₂²×C₁₉	1	1	yes	characteristic
647	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
648	C₂×C₄×D₄	—	2	1	no	—
649	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
650	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
651	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
652	#436	—	2	1	no	—
653	#435	—	2	1	no	—
654	#435	—	2	1	no	—
655	C₈×D₄	—	2	1	no	—
656	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
657	#421	—	2	4	no	—
658	C₂×#104	—	2	4	no	—
659	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
660	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
661	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
662	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
663	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
664	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
665	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
666	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
667	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
668	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
669	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
670	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
671	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
672	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
673	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
674	#388	—	2	1	no	—
675	#387	—	2	1	no	—
676	#386	—	2	1	no	—
677	#385	—	2	1	no	—
678	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
679	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
680	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
681	#376	C₂²×C₁₉	1	1	yes	characteristic, complemented
682	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
683	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
684	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
685	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
686	C₂×C₁₉	—	2	1	no	—
687	C₂×C₁₉	—	2	1	no	—
688	C₂×C₁₉	—	2	2	no	—
689	C₂×C₁₉	—	4	1	no	—
690	C₂×C₁₉	—	4	1	no	—
691	C₂×C₁₉	—	4	1	no	—
692	C₂×C₁₉	—	4	2	no	—
693	C₂×C₁₉	—	8	1	no	—
694	C₂×C₁₉	—	8	1	no	—
695	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
696	C₂×C₁₉	C₂×#421	1	1	yes	characteristic
697	C₂×C₁₉	#2901	1	1	yes	characteristic
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	2	no	—
703	C₂×#41	—	2	2	no	—
704	C₂×#41	—	2	2	no	—
705	C₂×#41	—	2	2	no	—
706	C₂×#41	—	4	1	no	—
707	C₂×#41	—	4	1	no	—
708	C₂×#41	—	4	1	no	—
709	C₂×#41	—	4	1	no	—
710	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
711	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
712	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
713	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
714	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
715	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
716	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
717	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
718	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	—	2	1	no	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
723	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
724	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
725	C₂³×C₄	—	2	1	no	—
726	C₂³×C₄	—	2	1	no	—
727	C₂³×C₄	—	2	1	no	—
728	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
729	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
730	C₂×M₁₆	—	2	1	no	—
731	C₂×M₁₆	—	2	1	no	—
732	C₂×M₁₆	—	2	2	no	—
733	C₂×M₁₆	—	2	2	no	—
734	C₂×M₁₆	—	4	1	no	—
735	C₂×M₁₆	—	4	1	no	—
736	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
740	C₂²×C₈	—	2	1	no	—
741	C₂²×C₈	—	2	1	no	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
744	#127	—	2	1	no	—
745	#127	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
746	#124	—	2	1	no	—
747	#124	—	2	1	no	—
748	#124	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
749	#124	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
750	#123	—	2	1	no	—
751	#123	—	2	1	no	—
752	#123	—	2	1	no	—
753	#123	—	2	1	no	—
754	#123	—	2	1	no	—
755	#123	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
761	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
763	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	1	no	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
775	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
776	#121	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
777	#121	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
778	#120	—	2	1	no	—
779	#120	—	2	1	no	—
780	#120	—	2	1	no	—
781	#120	—	2	1	no	—
782	#120	—	2	1	no	—
783	#120	—	2	1	no	—
784	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
785	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
799	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
800	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
801	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
802	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
803	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
804	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
805	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
806	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
807	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	4	1	no	—
811	#117	C₂³×C₁₉	1	1	yes	characteristic
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	1	no	—
818	C₂×C₂²⋊C₄	—	2	1	no	—
819	C₂×C₂²⋊C₄	—	2	1	no	—
820	C₂×C₂²⋊C₄	—	2	1	no	—
821	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
822	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	—	2	2	no	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	—	4	1	no	—
827	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
828	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
829	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
830	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
831	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
832	C₄⋊C₈	—	2	1	no	—
833	C₄⋊C₈	—	2	1	no	—
834	#104	—	2	2	no	—
835	#104	—	2	2	no	—
836	#104	—	2	2	no	—
837	#104	—	2	2	no	—
838	#104	—	2	2	no	—
839	#104	—	2	2	no	—
840	#104	—	2	2	no	—
841	#104	—	4	1	no	—
842	#104	—	4	1	no	—
843	#104	—	4	1	no	—
844	#104	—	4	1	no	—
845	#104	D₄×C₁₉	1	4	yes	complemented
846	C₂²⋊C₈	—	2	1	no	—
847	C₂²⋊C₈	—	2	1	no	—
848	C₂²⋊C₈	—	2	1	no	—
849	C₂²⋊C₈	—	2	1	no	—
850	#97	—	2	1	no	—
851	C₄×C₈	—	2	1	no	—
852	#95	—	2	1	no	—
853	#95	—	2	1	no	—
854	#95	—	2	1	no	—
855	#95	—	2	1	no	—
856	#95	—	2	1	no	—
857	C₁₉	#22434	1	1	yes	characteristic, direct product factor, Sylow
858	C₂⁴	—	2	1	no	—
859	C₂⁴	—	2	1	no	—
860	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
861	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
862	#41	—	2	1	no	—
863	#41	—	2	1	no	—
864	#41	—	2	2	no	—
865	#41	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	2	2	no	—
868	#41	—	2	1	no	—
869	#41	—	2	1	no	—
870	#41	—	2	1	no	—
871	#41	—	2	1	no	—
872	#41	—	2	1	no	—
873	#41	—	2	1	no	—
874	#41	—	2	1	no	—
875	#41	—	2	1	no	—
876	#41	—	4	2	no	—
877	#41	—	4	2	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	4	1	no	—
881	#41	—	4	1	no	—
882	#41	—	4	1	no	—
883	#41	—	4	1	no	—
884	#41	—	4	2	no	—
885	#41	—	4	2	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	C₂×D₄×C₁₉	1	2	yes	—
889	#41	#41×C₁₉	1	2	yes	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	4	1	no	—
895	C₂×Q₈	—	4	1	no	—
896	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
897	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
898	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	4	1	no	—
917	C₂×D₄	—	4	1	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	2	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	4	no	—
924	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
925	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
926	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
927	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
928	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
929	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
930	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	4	2	no	—
955	C₂²×C₄	—	4	2	no	—
956	C₂²×C₄	—	4	2	no	—
957	C₂²×C₄	—	4	2	no	—
958	C₂²×C₄	—	4	2	no	—
959	C₂²×C₄	—	4	2	no	—
960	C₂²×C₄	—	4	2	no	—
961	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
962	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
963	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
964	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
966	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
968	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
969	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
970	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
971	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
972	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
973	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
974	M₁₆	—	2	1	no	—
975	M₁₆	—	2	1	no	—
976	M₁₆	—	2	1	no	—
977	M₁₆	—	2	1	no	—
978	M₁₆	—	2	1	no	—
979	M₁₆	—	2	1	no	—
980	M₁₆	—	2	1	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	M₁₆	C₂×D₄×C₁₉	1	2	yes	complemented
984	C₂×C₈	—	2	1	no	—
985	C₂×C₈	—	2	1	no	—
986	C₂×C₈	—	2	1	no	—
987	C₂×C₈	—	2	1	no	—
988	C₂×C₈	—	4	2	no	—
989	C₂×C₈	—	4	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	4	2	no	—
999	C₄⋊C₄	—	4	2	no	—
1000	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1001	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1003	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1004	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
1005	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	4	2	no	—
1022	C₂²⋊C₄	—	4	2	no	—
1023	C₂²⋊C₄	—	4	2	no	—
1024	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1025	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1026	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1029	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1030	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1031	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
1044	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
1045	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1046	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
1047	C₄²	C₂×D₄×C₁₉	1	2	yes	complemented
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	4	2	no	—
1061	C₂³	—	4	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	1	no	—
1065	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1066	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1067	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1068	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1069	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	4	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	C₄×D₄×C₁₉	1	2	yes	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	4	1	no	—
1088	D₄	—	4	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	1	no	—
1099	D₄	—	4	1	no	—
1100	D₄	—	4	1	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	1	no	—
1104	D₄	—	8	1	no	—
1105	D₄	C₄×D₄×C₁₉	1	2	yes	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	8	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	8	1	no	—
1160	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1161	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1162	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1163	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1164	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1165	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1166	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1167	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1168	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1170	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1171	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
1172	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1174	C₈	—	2	2	no	—
1175	C₈	—	4	1	no	—
1176	C₈	—	4	1	no	—
1177	C₈	—	4	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	8	1	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	4	no	—
1205	C₂²	—	8	4	no	—
1206	C₂²	C₁₉×#421	1	2	yes	complemented
1207	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1208	C₂²	D₄²×C₁₉	1	1	yes	characteristic
1209	C₂²	C₁₉×#546	1	1	yes	characteristic
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
1228	C₄	C₁₉×#518	1	1	yes	characteristic
1229	C₄	D₄²×C₁₉	1	1	yes	characteristic
1230	C₄	C₁₉×#546	1	1	yes	characteristic
1231	C₂	—	2	1	no	—
1232	C₂	—	2	1	no	—
1233	C₂	—	2	2	no	—
1234	C₂	—	4	1	no	—
1235	C₂	—	4	1	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	2	no	—
1238	C₂	—	8	1	no	—
1239	C₂	—	8	1	no	—
1240	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
1241	C₂	C₂×C₁₉×#421	1	1	yes	characteristic
1242	C₂	C₁₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	D₄×#41×C₁₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₁₉	C₂	semidirect
3. C₂×C₁₉×#421	C₂	semidirect
4. C₂²×C₁₉×#104	C₂	semidirect
5. C₁₉×#2290	C₂	semidirect
6. C₁₉×#1980	C₂	semidirect
7. C₁₉×#1963	C₂	semidirect
8. C₁₉×#1897	C₂	semidirect
9. C₁₉×#1896	C₂	semidirect
10. C₁₉×#1871	C₂	semidirect
11. C₁₉×#1871	C₂	semidirect
12. C₁₉×#1806	C₂	semidirect
13. C₁₉×#1789	C₂	semidirect
14. C₁₉×#1789	C₂	semidirect
15. C₁₉×#1759	C₂	semidirect
18. C₂²×M₁₆×C₁₉	C₂²	semidirect
19. C₂²×M₁₆×C₁₉	C₂²	semidirect
20. C₁₉×#550	C₄	semidirect
21. D₄×Q₈×C₁₉	C₄	semidirect
22. C₁₉×#548	C₄	semidirect
23. C₁₉×#548	C₄	semidirect
25. C₁₉×#547	C₄	semidirect
28. C₁₉×#546	C₄	semidirect
29. C₁₉×#546	C₄	semidirect
31. D₄²×C₁₉	C₄	semidirect
41. C₂×C₁₉×#117	C₂²	semidirect
42. C₂²×C₄²×C₁₉	C₂²	semidirect
47. C₁₉×#423	C₂²	semidirect
54. C₂×C₁₉×#104	C₂²	semidirect
55. C₂×C₁₉×#104	C₂²	semidirect
56. C₂×C₁₉×#104	C₂²	semidirect
57. C₂×C₁₉×#104	C₂²	semidirect
58. C₂×C₁₉×#104	C₂²	semidirect
59. C₂×C₁₉×#104	C₂²	semidirect
60. C₂×C₁₉×#104	C₂²	semidirect
61. C₂×C₁₉×#104	C₂²	semidirect
62. C₁₉×#407	C₂²	semidirect
63. C₁₉×#407	C₂²	semidirect
64. C₄×M₁₆×C₁₉	C₂²	semidirect
69. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
72. C₁₉×#376	C₂²	semidirect
73. C₁₉×#339	C₂²	semidirect
74. C₁₉×#339	C₂²	semidirect
75. C₁₉×#339	C₂²	semidirect
76. C₁₉×#339	C₂²	semidirect
91. C₂×#41×C₁₉	C₂×C₄	semidirect
92. C₂×#41×C₁₉	C₂×C₄	semidirect
97. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
102. C₂²×D₄×C₁₉	C₂×C₄	semidirect
122. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
124. C₁₉×#127	C₂×C₄	semidirect
127. C₁₉×#124	C₂×C₄	semidirect
128. C₁₉×#124	C₂×C₄	semidirect
141. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
142. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
155. C₁₉×#121	C₂×C₄	semidirect
156. C₁₉×#121	C₂×C₄	semidirect
163. C₄×Q₈×C₁₉	C₂×C₄	semidirect
164. C₄×Q₈×C₁₉	C₂×C₄	semidirect
181. C₄×D₄×C₁₉	C₂×C₄	semidirect
182. C₄×D₄×C₁₉	C₂×C₄	semidirect
224. C₁₉×#104	D₄	semidirect
361. M₁₆×C₁₉	C₂×D₄	semidirect
425. C₄²×C₁₉	C₂×D₄	semidirect
426. #22434	C₁₉	direct (N × H)
558. D₄×M₁₆	C₂×C₁₉	semidirect
559. C₂×#421	C₂×C₁₉	semidirect
560. C₂²×#104	C₂×C₁₉	semidirect
561. #2290	C₂×C₁₉	semidirect
562. #1980	C₂×C₁₉	semidirect
563. #1963	C₂×C₁₉	semidirect
564. #1897	C₂×C₁₉	semidirect
565. #1896	C₂×C₁₉	semidirect
566. #1871	C₂×C₁₉	semidirect
567. #1871	C₂×C₁₉	semidirect
568. #1806	C₂×C₁₉	semidirect
569. #1789	C₂×C₁₉	semidirect
570. #1789	C₂×C₁₉	semidirect
571. #1759	C₂×C₁₉	semidirect
600. C₂²×C₁₉	#421	semidirect
627. C₂²×M₁₆	C₂²×C₁₉	semidirect
628. C₂²×M₁₆	C₂²×C₁₉	semidirect
629. #550	C₄×C₁₉	semidirect
630. D₄×Q₈	C₄×C₁₉	semidirect
631. #548	C₄×C₁₉	semidirect
632. #548	C₄×C₁₉	semidirect
634. #547	C₄×C₁₉	semidirect
637. #546	C₄×C₁₉	semidirect
638. #546	C₄×C₁₉	semidirect
640. D₄²	C₄×C₁₉	semidirect
650. C₂×#117	C₂²×C₁₉	semidirect
651. C₂²×C₄²	C₂²×C₁₉	semidirect
656. #423	C₂²×C₁₉	semidirect
663. C₂×#104	C₂²×C₁₉	semidirect
664. C₂×#104	C₂²×C₁₉	semidirect
665. C₂×#104	C₂²×C₁₉	semidirect
666. C₂×#104	C₂²×C₁₉	semidirect
667. C₂×#104	C₂²×C₁₉	semidirect
668. C₂×#104	C₂²×C₁₉	semidirect
669. C₂×#104	C₂²×C₁₉	semidirect
670. C₂×#104	C₂²×C₁₉	semidirect
671. #407	C₂²×C₁₉	semidirect
672. #407	C₂²×C₁₉	semidirect
673. C₄×M₁₆	C₂²×C₁₉	semidirect
678. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
679. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
680. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
681. #376	C₂²×C₁₉	semidirect
682. #339	C₂²×C₁₉	semidirect
683. #339	C₂²×C₁₉	semidirect
684. #339	C₂²×C₁₉	semidirect
685. #339	C₂²×C₁₉	semidirect
712. C₂×#41	C₂×C₄×C₁₉	semidirect
713. C₂×#41	C₂×C₄×C₁₉	semidirect
718. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
723. C₂²×D₄	C₂×C₄×C₁₉	semidirect
743. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
745. #127	C₂×C₄×C₁₉	semidirect
748. #124	C₂×C₄×C₁₉	semidirect
749. #124	C₂×C₄×C₁₉	semidirect
762. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
763. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
776. #121	C₂×C₄×C₁₉	semidirect
777. #121	C₂×C₄×C₁₉	semidirect
784. C₄×Q₈	C₂×C₄×C₁₉	semidirect
785. C₄×Q₈	C₂×C₄×C₁₉	semidirect
802. C₄×D₄	C₂×C₄×C₁₉	semidirect
803. C₄×D₄	C₂×C₄×C₁₉	semidirect
845. #104	D₄×C₁₉	semidirect
857. C₁₉	#22434	direct (N × H)
983. M₁₆	C₂×D₄×C₁₉	semidirect
1047. C₄²	C₂×D₄×C₁₉	semidirect
1206. C₂²	C₁₉×#421	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₁₉	2
D₄×M₁₆×C₁₉	2
C₂×C₁₉×#421	2
C₂²×C₁₉×#104	2
C₁₉×#2290	2
C₁₉×#1980	2
C₁₉×#1963	2
C₁₉×#1897	2
C₁₉×#1896	2
C₁₉×#1871	2
C₁₉×#1806	2
C₁₉×#1789	2
C₁₉×#1759	2
#22434	19

Subgroups — C19×#22434 #18028393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22434 #18028393