Subgroups — C₁₉×#17513 #18023472

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3475	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#556	C₄	1	1	yes	characteristic
17	C₁₉×#555	C₄	1	1	yes	characteristic
18	C₁₉×#554	C₄	1	1	yes	characteristic
19	C₁₉×#553	—	2	1	no	—
20	C₁₉×#552	—	2	1	no	—
21	C₁₉×#552	C₄	1	1	yes	characteristic
22	C₁₉×#552	C₄	1	1	yes	characteristic
23	C₁₉×#551	—	2	1	no	—
24	C₁₉×#551	—	2	1	no	—
25	C₁₉×#547	C₄	1	1	yes	characteristic
26	C₁₉×#546	C₄	1	1	yes	characteristic
27	C₁₉×#546	C₄	1	1	yes	characteristic
28	C₁₉×#533	C₂²	1	1	yes	characteristic
29	C₁₉×#529	—	2	1	no	—
30	C₁₉×#529	—	2	1	no	—
31	C₁₉×#529	C₂²	1	1	yes	characteristic
32	C₁₉×#529	C₂²	1	1	yes	characteristic
33	C₁₉×#525	—	2	1	no	—
34	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#117	—	2	1	no	—
39	C₁₉×#446	—	2	1	no	—
40	C₁₉×#436	—	2	1	no	—
41	C₁₉×#435	—	2	1	no	—
42	C₁₉×#435	—	2	1	no	—
43	C₁₉×#433	—	2	1	no	—
44	C₁₉×#433	—	2	1	no	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#431	C₂²	1	1	yes	characteristic
48	C₁₉×#431	C₂²	1	1	yes	characteristic
49	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#431	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#408	—	2	1	no	—
55	C₁₉×#405	—	2	1	no	—
56	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
72	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
73	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
74	C₁₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂²×C₈×C₁₉	—	2	1	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₁₉×#126	—	2	1	no	—
88	C₁₉×#126	—	2	1	no	—
89	C₁₉×#126	—	2	1	no	—
90	C₁₉×#126	—	2	1	no	—
91	C₁₉×#126	—	2	1	no	—
92	C₁₉×#126	—	2	1	no	—
93	C₁₉×#125	—	2	1	no	—
94	C₁₉×#125	—	2	1	no	—
95	C₁₉×#125	—	2	1	no	—
96	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
97	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
98	C₁₉×#124	—	2	1	no	—
99	C₁₉×#124	—	2	1	no	—
100	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
101	C₁₉×#124	C₂×C₄	1	1	yes	characteristic
102	C₁₉×#123	—	2	1	no	—
103	C₁₉×#123	—	2	1	no	—
104	C₁₉×#123	—	2	1	no	—
105	C₁₉×#123	—	2	1	no	—
106	C₁₉×#123	—	2	1	no	—
107	C₁₉×#123	—	2	1	no	—
108	C₁₉×#123	—	2	1	no	—
109	C₁₉×#123	—	2	1	no	—
110	C₁₉×C₂²⋊Q₈	—	2	1	no	—
111	C₁₉×C₂²⋊Q₈	—	2	1	no	—
112	C₁₉×C₂²⋊Q₈	—	2	1	no	—
113	C₁₉×C₂²⋊Q₈	—	2	1	no	—
114	C₁₉×C₂²⋊Q₈	—	2	1	no	—
115	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
116	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
118	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#121	—	2	1	no	—
120	C₁₉×#121	—	2	1	no	—
121	C₁₉×#121	—	2	1	no	—
122	C₁₉×#121	—	2	1	no	—
123	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
124	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
125	C₁₉×#120	—	2	1	no	—
126	C₁₉×#120	—	2	1	no	—
127	C₄×Q₈×C₁₉	—	2	1	no	—
128	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
129	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
132	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
133	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₁₉	—	2	1	no	—
135	C₄×D₄×C₁₉	—	2	1	no	—
136	C₄×D₄×C₁₉	—	2	1	no	—
137	C₄×D₄×C₁₉	—	2	1	no	—
138	C₄×D₄×C₁₉	—	2	1	no	—
139	C₄×D₄×C₁₉	—	2	1	no	—
140	C₄×D₄×C₁₉	—	2	1	no	—
141	C₄×D₄×C₁₉	—	2	1	no	—
142	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
143	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
145	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
146	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
147	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
148	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
150	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
151	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
152	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₁₉×#117	—	2	1	no	—
155	C₁₉×#117	—	2	1	no	—
156	C₁₉×#117	—	2	1	no	—
157	C₁₉×#117	—	2	1	no	—
158	C₁₉×#117	—	2	1	no	—
159	C₁₉×#117	—	2	1	no	—
160	C₁₉×#117	—	2	1	no	—
161	C₁₉×#117	—	2	1	no	—
162	C₁₉×#117	—	2	1	no	—
163	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
164	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
165	C₁₉×#117	D₄	1	1	yes	characteristic
166	C₁₉×#117	D₄	1	1	yes	characteristic
167	C₁₉×#117	D₄	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
172	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂×C₄²×C₁₉	—	2	1	no	—
175	C₂×C₄²×C₁₉	—	2	1	no	—
176	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
179	C₁₉×C₄⋊C₈	—	2	1	no	—
180	C₁₉×C₄⋊C₈	—	2	1	no	—
181	C₁₉×C₄⋊C₈	—	2	1	no	—
182	C₁₉×C₄⋊C₈	—	2	1	no	—
183	C₁₉×C₄⋊C₈	—	2	1	no	—
184	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
185	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
186	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
187	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
188	C₁₉×C₂²⋊C₈	—	2	1	no	—
189	C₁₉×C₂²⋊C₈	—	2	1	no	—
190	C₁₉×C₂²⋊C₈	—	2	1	no	—
191	C₁₉×C₂²⋊C₈	—	2	1	no	—
192	C₁₉×C₂²⋊C₈	—	2	1	no	—
193	C₁₉×C₂²⋊C₈	—	2	1	no	—
194	C₁₉×C₂²⋊C₈	—	2	1	no	—
195	C₁₉×#97	—	2	1	no	—
196	C₁₉×#97	—	2	1	no	—
197	C₁₉×#97	—	2	1	no	—
198	C₁₉×#97	—	2	1	no	—
199	C₄×C₈×C₁₉	—	2	1	no	—
200	C₄×C₈×C₁₉	—	2	1	no	—
201	C₄×C₈×C₁₉	—	2	1	no	—
202	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
203	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
206	C₂⁴×C₁₉	—	2	1	no	—
207	#41×C₁₉	—	2	2	no	—
208	#41×C₁₉	—	2	2	no	—
209	#41×C₁₉	—	4	1	no	—
210	#41×C₁₉	—	4	1	no	—
211	#41×C₁₉	—	4	1	no	—
212	#41×C₁₉	—	4	1	no	—
213	C₂×Q₈×C₁₉	—	2	1	no	—
214	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
215	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₁₉	—	2	2	no	—
218	C₂×D₄×C₁₉	—	2	1	no	—
219	C₂×D₄×C₁₉	—	2	1	no	—
220	C₂×D₄×C₁₉	—	2	1	no	—
221	C₂×D₄×C₁₉	—	2	1	no	—
222	C₂×D₄×C₁₉	—	2	1	no	—
223	C₂×D₄×C₁₉	—	4	1	no	—
224	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
225	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
226	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
227	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
228	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	—	2	1	no	—
230	C₂²×C₄×C₁₉	—	2	1	no	—
231	C₂²×C₄×C₁₉	—	2	1	no	—
232	C₂²×C₄×C₁₉	—	2	1	no	—
233	C₂²×C₄×C₁₉	—	2	1	no	—
234	C₂²×C₄×C₁₉	—	2	1	no	—
235	C₂²×C₄×C₁₉	—	2	1	no	—
236	C₂²×C₄×C₁₉	—	2	1	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	4	2	no	—
239	C₂²×C₄×C₁₉	—	4	2	no	—
240	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
249	M₁₆×C₁₉	—	4	2	no	—
250	M₁₆×C₁₉	—	4	2	no	—
251	M₁₆×C₁₉	—	4	2	no	—
252	C₂×C₈×C₁₉	—	2	1	no	—
253	C₂×C₈×C₁₉	—	2	1	no	—
254	C₂×C₈×C₁₉	—	2	1	no	—
255	C₂×C₈×C₁₉	—	2	1	no	—
256	C₂×C₈×C₁₉	—	2	1	no	—
257	C₂×C₈×C₁₉	—	2	1	no	—
258	C₂×C₈×C₁₉	—	2	1	no	—
259	C₂×C₈×C₁₉	—	2	1	no	—
260	C₂×C₈×C₁₉	—	4	2	no	—
261	C₂×C₈×C₁₉	—	4	2	no	—
262	C₄⋊C₄×C₁₉	—	2	1	no	—
263	C₄⋊C₄×C₁₉	—	2	1	no	—
264	C₄⋊C₄×C₁₉	—	2	1	no	—
265	C₄⋊C₄×C₁₉	—	2	1	no	—
266	C₄⋊C₄×C₁₉	—	2	1	no	—
267	C₄⋊C₄×C₁₉	—	2	1	no	—
268	C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	no	—
273	C₄⋊C₄×C₁₉	—	2	1	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
279	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
280	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
281	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
282	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
283	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
284	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
285	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
286	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
287	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
288	C₂²⋊C₄×C₁₉	—	2	1	no	—
289	C₂²⋊C₄×C₁₉	—	2	1	no	—
290	C₂²⋊C₄×C₁₉	—	2	1	no	—
291	C₂²⋊C₄×C₁₉	—	2	1	no	—
292	C₂²⋊C₄×C₁₉	—	2	1	no	—
293	C₂²⋊C₄×C₁₉	—	2	1	no	—
294	C₂²⋊C₄×C₁₉	—	2	1	no	—
295	C₂²⋊C₄×C₁₉	—	2	1	no	—
296	C₂²⋊C₄×C₁₉	—	2	1	no	—
297	C₂²⋊C₄×C₁₉	—	2	1	no	—
298	C₂²⋊C₄×C₁₉	—	2	1	no	—
299	C₂²⋊C₄×C₁₉	—	2	1	no	—
300	C₂²⋊C₄×C₁₉	—	2	1	no	—
301	C₂²⋊C₄×C₁₉	—	2	1	no	—
302	C₂²⋊C₄×C₁₉	—	2	1	no	—
303	C₂²⋊C₄×C₁₉	—	2	1	no	—
304	C₂²⋊C₄×C₁₉	—	2	1	no	—
305	C₂²⋊C₄×C₁₉	—	2	1	no	—
306	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
307	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
308	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
309	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
310	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
311	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
312	C₄²×C₁₉	—	2	1	no	—
313	C₄²×C₁₉	—	2	1	no	—
314	C₄²×C₁₉	—	2	1	no	—
315	C₄²×C₁₉	—	2	1	no	—
316	C₄²×C₁₉	—	2	1	no	—
317	C₄²×C₁₉	—	2	1	no	—
318	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
319	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
320	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
321	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
328	#17513	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₁₉	—	2	1	no	—
330	C₂³×C₁₉	—	2	1	no	—
331	C₂³×C₁₉	—	4	2	no	—
332	C₂³×C₁₉	—	4	2	no	—
333	C₂³×C₁₉	—	8	1	no	—
334	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	Q₈×C₁₉	—	2	1	no	—
338	Q₈×C₁₉	—	2	1	no	—
339	Q₈×C₁₉	—	2	1	no	—
340	Q₈×C₁₉	—	2	1	no	—
341	Q₈×C₁₉	—	4	1	no	—
342	Q₈×C₁₉	—	8	1	no	—
343	D₄×C₁₉	—	2	1	no	—
344	D₄×C₁₉	—	2	1	no	—
345	D₄×C₁₉	—	2	1	no	—
346	D₄×C₁₉	—	4	1	no	—
347	D₄×C₁₉	—	4	1	no	—
348	D₄×C₁₉	—	4	1	no	—
349	D₄×C₁₉	—	4	2	no	—
350	D₄×C₁₉	—	4	2	no	—
351	D₄×C₁₉	—	4	2	no	—
352	D₄×C₁₉	—	8	1	no	—
353	D₄×C₁₉	—	8	1	no	—
354	D₄×C₁₉	#131	1	2	yes	—
355	C₂×C₄×C₁₉	—	2	1	no	—
356	C₂×C₄×C₁₉	—	2	1	no	—
357	C₂×C₄×C₁₉	—	2	1	no	—
358	C₂×C₄×C₁₉	—	2	1	no	—
359	C₂×C₄×C₁₉	—	2	1	no	—
360	C₂×C₄×C₁₉	—	2	1	no	—
361	C₂×C₄×C₁₉	—	2	1	no	—
362	C₂×C₄×C₁₉	—	2	1	no	—
363	C₂×C₄×C₁₉	—	2	1	no	—
364	C₂×C₄×C₁₉	—	2	1	no	—
365	C₂×C₄×C₁₉	—	2	1	no	—
366	C₂×C₄×C₁₉	—	2	1	no	—
367	C₂×C₄×C₁₉	—	2	1	no	—
368	C₂×C₄×C₁₉	—	2	1	no	—
369	C₂×C₄×C₁₉	—	2	1	no	—
370	C₂×C₄×C₁₉	—	2	1	no	—
371	C₂×C₄×C₁₉	—	2	1	no	—
372	C₂×C₄×C₁₉	—	2	1	no	—
373	C₂×C₄×C₁₉	—	4	1	no	—
374	C₂×C₄×C₁₉	—	4	1	no	—
375	C₂×C₄×C₁₉	—	4	1	no	—
376	C₂×C₄×C₁₉	—	4	2	no	—
377	C₂×C₄×C₁₉	—	4	2	no	—
378	C₂×C₄×C₁₉	—	4	2	no	—
379	C₂×C₄×C₁₉	—	4	2	no	—
380	C₂×C₄×C₁₉	—	4	2	no	—
381	C₂×C₄×C₁₉	—	4	1	no	—
382	C₂×C₄×C₁₉	—	4	1	no	—
383	C₂×C₄×C₁₉	—	4	1	no	—
384	C₂×C₄×C₁₉	—	4	1	no	—
385	C₂×C₄×C₁₉	—	8	1	no	—
386	C₂×C₄×C₁₉	—	8	1	no	—
387	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
397	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
399	C₈×C₁₉	—	2	2	no	—
400	C₈×C₁₉	—	4	1	no	—
401	C₈×C₁₉	—	4	1	no	—
402	C₈×C₁₉	—	4	1	no	—
403	C₈×C₁₉	—	4	1	no	—
404	C₈×C₁₉	—	4	1	no	—
405	C₈×C₁₉	—	4	1	no	—
406	C₈×C₁₉	—	4	1	no	—
407	#3475	C₂×C₁₉	1	1	yes	characteristic
408	#2965	C₂×C₁₉	1	1	yes	characteristic, complemented
409	#2925	C₂×C₁₉	1	1	yes	characteristic, complemented
410	#1497	C₂×C₁₉	1	1	yes	characteristic, complemented
411	#1495	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#1490	C₂×C₁₉	1	1	yes	characteristic, complemented
414	#1489	C₂×C₁₉	1	1	yes	characteristic, complemented
415	#1488	C₂×C₁₉	1	1	yes	characteristic, complemented
416	#1485	C₂×C₁₉	1	1	yes	characteristic, complemented
417	#1483	C₂×C₁₉	1	1	yes	characteristic, complemented
418	#1482	C₂×C₁₉	1	1	yes	characteristic, complemented
419	#1478	C₂×C₁₉	1	1	yes	characteristic, complemented
420	#1477	C₂×C₁₉	1	1	yes	characteristic, complemented
421	#1476	C₂×C₁₉	1	1	yes	characteristic, complemented
422	C₂²×C₁₉	—	2	1	no	—
423	C₂²×C₁₉	—	2	1	no	—
424	C₂²×C₁₉	—	2	1	no	—
425	C₂²×C₁₉	—	2	2	no	—
426	C₂²×C₁₉	—	2	1	no	—
427	C₂²×C₁₉	—	2	1	no	—
428	C₂²×C₁₉	—	2	1	no	—
429	C₂²×C₁₉	—	2	1	no	—
430	C₂²×C₁₉	—	2	1	no	—
431	C₂²×C₁₉	—	2	1	no	—
432	C₂²×C₁₉	—	4	1	no	—
433	C₂²×C₁₉	—	4	1	no	—
434	C₂²×C₁₉	—	4	1	no	—
435	C₂²×C₁₉	—	4	1	no	—
436	C₂²×C₁₉	—	4	1	no	—
437	C₂²×C₁₉	—	8	4	no	—
438	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
439	C₄×C₁₉	—	2	1	no	—
440	C₄×C₁₉	—	2	1	no	—
441	C₄×C₁₉	—	2	1	no	—
442	C₄×C₁₉	—	2	1	no	—
443	C₄×C₁₉	—	2	1	no	—
444	C₄×C₁₉	—	2	1	no	—
445	C₄×C₁₉	—	2	1	no	—
446	C₄×C₁₉	—	2	1	no	—
447	C₄×C₁₉	—	2	1	no	—
448	C₄×C₁₉	—	2	1	no	—
449	C₄×C₁₉	—	4	1	no	—
450	C₄×C₁₉	—	4	1	no	—
451	C₄×C₁₉	—	4	1	no	—
452	C₄×C₁₉	—	4	1	no	—
453	C₄×C₁₉	—	4	1	no	—
454	C₄×C₁₉	—	4	1	no	—
455	C₄×C₁₉	C₂×#131	1	1	yes	characteristic
456	C₄×C₁₉	#568	1	1	yes	characteristic
457	C₄×C₁₉	#575	1	1	yes	characteristic
458	C₄×C₁₉	#575	1	1	yes	characteristic
459	#556	C₄×C₁₉	1	1	yes	characteristic
460	#555	C₄×C₁₉	1	1	yes	characteristic
461	#554	C₄×C₁₉	1	1	yes	characteristic
462	#553	—	2	1	no	—
463	#552	—	2	1	no	—
464	#552	C₄×C₁₉	1	1	yes	characteristic
465	#552	C₄×C₁₉	1	1	yes	characteristic
466	#551	—	2	1	no	—
467	#551	—	2	1	no	—
468	#547	C₄×C₁₉	1	1	yes	characteristic
469	#546	C₄×C₁₉	1	1	yes	characteristic
470	#546	C₄×C₁₉	1	1	yes	characteristic
471	#533	C₂²×C₁₉	1	1	yes	characteristic
472	#529	—	2	1	no	—
473	#529	—	2	1	no	—
474	#529	C₂²×C₁₉	1	1	yes	characteristic
475	#529	C₂²×C₁₉	1	1	yes	characteristic
476	#525	—	2	1	no	—
477	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
478	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
479	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
481	C₂×#117	—	2	1	no	—
482	#446	—	2	1	no	—
483	#436	—	2	1	no	—
484	#435	—	2	1	no	—
485	#435	—	2	1	no	—
486	#433	—	2	1	no	—
487	#433	—	2	1	no	—
488	#432	C₂²×C₁₉	1	1	yes	characteristic
489	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
490	#431	C₂²×C₁₉	1	1	yes	characteristic
491	#431	C₂²×C₁₉	1	1	yes	characteristic
492	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
493	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
494	#431	C₂²×C₁₉	1	1	yes	characteristic, complemented
495	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
496	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
497	#408	—	2	1	no	—
498	#405	—	2	1	no	—
499	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
500	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
501	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
502	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
503	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
504	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
505	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
506	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
507	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
508	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
509	Q₈⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
510	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
511	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
512	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
513	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
514	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
515	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
516	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
517	D₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
518	C₂×C₁₉	—	4	1	no	—
519	C₂×C₁₉	—	4	1	no	—
520	C₂×C₁₉	—	4	1	no	—
521	C₂×C₁₉	—	4	2	no	—
522	C₂×C₁₉	—	8	1	no	—
523	C₂×C₁₉	#2880	1	1	yes	characteristic
524	C₂×C₁₉	#2896	1	1	yes	characteristic
525	C₂×C₁₉	#2901	1	1	yes	characteristic
526	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
527	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
528	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
529	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
530	C₂³×C₄	—	2	1	no	—
531	C₂×M₁₆	—	2	1	no	—
532	C₂×M₁₆	—	2	1	no	—
533	C₂×M₁₆	—	2	1	no	—
534	C₂²×C₈	—	2	1	no	—
535	C₂²×C₈	—	2	1	no	—
536	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
537	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
538	#126	—	2	1	no	—
539	#126	—	2	1	no	—
540	#126	—	2	1	no	—
541	#126	—	2	1	no	—
542	#126	—	2	1	no	—
543	#126	—	2	1	no	—
544	#125	—	2	1	no	—
545	#125	—	2	1	no	—
546	#125	—	2	1	no	—
547	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
548	#125	C₂×C₄×C₁₉	1	1	yes	characteristic
549	#124	—	2	1	no	—
550	#124	—	2	1	no	—
551	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
552	#124	C₂×C₄×C₁₉	1	1	yes	characteristic
553	#123	—	2	1	no	—
554	#123	—	2	1	no	—
555	#123	—	2	1	no	—
556	#123	—	2	1	no	—
557	#123	—	2	1	no	—
558	#123	—	2	1	no	—
559	#123	—	2	1	no	—
560	#123	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
567	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
568	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
569	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	1	no	—
574	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
575	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
576	#120	—	2	1	no	—
577	#120	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
580	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
581	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
582	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
594	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
595	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
596	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
597	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
598	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
599	C₄×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
600	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
601	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
602	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
605	#117	—	2	1	no	—
606	#117	—	2	1	no	—
607	#117	—	2	1	no	—
608	#117	—	2	1	no	—
609	#117	—	2	1	no	—
610	#117	—	2	1	no	—
611	#117	—	2	1	no	—
612	#117	—	2	1	no	—
613	#117	—	2	1	no	—
614	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
615	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
616	#117	D₄×C₁₉	1	1	yes	characteristic
617	#117	D₄×C₁₉	1	1	yes	characteristic
618	#117	D₄×C₁₉	1	1	yes	characteristic
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₄²	—	2	1	no	—
626	C₂×C₄²	—	2	1	no	—
627	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
630	C₄⋊C₈	—	2	1	no	—
631	C₄⋊C₈	—	2	1	no	—
632	C₄⋊C₈	—	2	1	no	—
633	C₄⋊C₈	—	2	1	no	—
634	C₄⋊C₈	—	2	1	no	—
635	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
636	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
637	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
639	C₂²⋊C₈	—	2	1	no	—
640	C₂²⋊C₈	—	2	1	no	—
641	C₂²⋊C₈	—	2	1	no	—
642	C₂²⋊C₈	—	2	1	no	—
643	C₂²⋊C₈	—	2	1	no	—
644	C₂²⋊C₈	—	2	1	no	—
645	C₂²⋊C₈	—	2	1	no	—
646	#97	—	2	1	no	—
647	#97	—	2	1	no	—
648	#97	—	2	1	no	—
649	#97	—	2	1	no	—
650	C₄×C₈	—	2	1	no	—
651	C₄×C₈	—	2	1	no	—
652	C₄×C₈	—	2	1	no	—
653	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
654	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
655	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
656	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
657	C₁₉	#17513	1	1	yes	characteristic, direct product factor, Sylow
658	C₂⁴	—	2	1	no	—
659	#41	—	2	2	no	—
660	#41	—	2	2	no	—
661	#41	—	4	1	no	—
662	#41	—	4	1	no	—
663	#41	—	4	1	no	—
664	#41	—	4	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
667	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
668	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	4	1	no	—
676	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
677	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
678	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
679	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
680	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
693	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
694	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
701	M₁₆	—	4	2	no	—
702	M₁₆	—	4	2	no	—
703	M₁₆	—	4	2	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	4	2	no	—
713	C₂×C₈	—	4	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
731	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
732	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
733	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
734	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
735	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
759	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
760	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
761	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
762	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
763	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	1	no	—
770	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
771	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
772	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
779	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	8	1	no	—
785	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
786	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
787	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
788	Q₈	—	2	1	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	4	1	no	—
793	Q₈	—	8	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	1	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	1	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	4	2	no	—
803	D₄	—	8	1	no	—
804	D₄	—	8	1	no	—
805	D₄	C₁₉×#131	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
839	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
840	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
841	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
842	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
843	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
844	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
845	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
846	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
847	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	4	1	no	—
852	C₈	—	4	1	no	—
853	C₈	—	4	1	no	—
854	C₈	—	4	1	no	—
855	C₈	—	4	1	no	—
856	C₈	—	4	1	no	—
857	C₈	—	4	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	8	4	no	—
874	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	C₂×C₁₉×#131	1	1	yes	characteristic
892	C₄	C₁₉×#568	1	1	yes	characteristic
893	C₄	C₁₉×#575	1	1	yes	characteristic
894	C₄	C₁₉×#575	1	1	yes	characteristic
895	C₂	—	4	1	no	—
896	C₂	—	4	1	no	—
897	C₂	—	4	1	no	—
898	C₂	—	4	2	no	—
899	C₂	—	8	1	no	—
900	C₂	C₁₉×#2880	1	1	yes	characteristic
901	C₂	C₁₉×#2896	1	1	yes	characteristic
902	C₂	C₁₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₁₉×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2965	C₂	semidirect
3. C₁₉×#2925	C₂	semidirect
4. C₁₉×#1497	C₂	semidirect
5. C₁₉×#1495	C₂	semidirect
6. C₁₉×#1494	C₂	semidirect
7. C₁₉×#1490	C₂	semidirect
8. C₁₉×#1489	C₂	semidirect
9. C₁₉×#1488	C₂	semidirect
10. C₁₉×#1485	C₂	semidirect
11. C₁₉×#1483	C₂	semidirect
12. C₁₉×#1482	C₂	semidirect
13. C₁₉×#1478	C₂	semidirect
14. C₁₉×#1477	C₂	semidirect
15. C₁₉×#1476	C₂	semidirect
46. C₁₉×#432	C₂²	semidirect
49. C₁₉×#431	C₂²	semidirect
50. C₁₉×#431	C₂²	semidirect
51. C₁₉×#431	C₂²	semidirect
52. C₁₉×#423	C₂²	semidirect
53. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
57. C₄×M₁₆×C₁₉	C₂²	semidirect
58. C₂×C₄×C₈×C₁₉	C₂²	semidirect
59. C₁₉×Q₈⋊C₈	C₂²	semidirect
60. C₁₉×Q₈⋊C₈	C₂²	semidirect
61. C₁₉×Q₈⋊C₈	C₂²	semidirect
62. C₁₉×Q₈⋊C₈	C₂²	semidirect
63. C₁₉×Q₈⋊C₈	C₂²	semidirect
64. C₁₉×Q₈⋊C₈	C₂²	semidirect
65. C₁₉×Q₈⋊C₈	C₂²	semidirect
66. C₁₉×Q₈⋊C₈	C₂²	semidirect
328. #17513	C₁₉	direct (N × H)
408. #2965	C₂×C₁₉	semidirect
409. #2925	C₂×C₁₉	semidirect
410. #1497	C₂×C₁₉	semidirect
411. #1495	C₂×C₁₉	semidirect
412. #1494	C₂×C₁₉	semidirect
413. #1490	C₂×C₁₉	semidirect
414. #1489	C₂×C₁₉	semidirect
415. #1488	C₂×C₁₉	semidirect
416. #1485	C₂×C₁₉	semidirect
417. #1483	C₂×C₁₉	semidirect
418. #1482	C₂×C₁₉	semidirect
419. #1478	C₂×C₁₉	semidirect
420. #1477	C₂×C₁₉	semidirect
421. #1476	C₂×C₁₉	semidirect
489. #432	C₂²×C₁₉	semidirect
492. #431	C₂²×C₁₉	semidirect
493. #431	C₂²×C₁₉	semidirect
494. #431	C₂²×C₁₉	semidirect
495. #423	C₂²×C₁₉	semidirect
496. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
500. C₄×M₁₆	C₂²×C₁₉	semidirect
501. C₂×C₄×C₈	C₂²×C₁₉	semidirect
502. Q₈⋊C₈	C₂²×C₁₉	semidirect
503. Q₈⋊C₈	C₂²×C₁₉	semidirect
504. Q₈⋊C₈	C₂²×C₁₉	semidirect
505. Q₈⋊C₈	C₂²×C₁₉	semidirect
506. Q₈⋊C₈	C₂²×C₁₉	semidirect
507. Q₈⋊C₈	C₂²×C₁₉	semidirect
508. Q₈⋊C₈	C₂²×C₁₉	semidirect
509. Q₈⋊C₈	C₂²×C₁₉	semidirect
657. C₁₉	#17513	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×#3475	2
C₁₉×#2965	2
C₁₉×#2925	2
C₁₉×#1497	2
C₁₉×#1495	2
C₁₉×#1494	2
C₁₉×#1490	2
C₁₉×#1489	2
C₁₉×#1488	2
C₁₉×#1485	2
C₁₉×#1483	2
C₁₉×#1482	2
C₁₉×#1478	2
C₁₉×#1477	2
C₁₉×#1476	2
#17513	19

Subgroups — C19×#17513 #18023472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17513 #18023472