Subgroups — C₁₉×#18252 #18024211

Order 4864.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3006	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3002	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2430	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1606	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1604	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1603	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1601	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1600	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1598	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1597	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1595	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1504	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1468	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
18	C₂×C₁₉×#135	—	2	1	no	—
19	C₁₉×#562	—	2	1	no	—
20	C₁₉×#560	—	2	1	no	—
21	C₁₉×#553	—	2	1	no	—
22	C₁₉×#551	—	2	1	no	—
23	C₁₉×#546	—	2	1	no	—
24	C₁₉×#546	—	2	1	no	—
25	C₁₉×#546	—	2	1	no	—
26	D₄²×C₁₉	—	2	1	no	—
27	C₁₉×#540	—	2	1	no	—
28	C₁₉×#539	—	2	1	no	—
29	C₁₉×#539	C₂²	1	1	yes	characteristic
30	C₁₉×#538	—	2	1	no	—
31	C₁₉×#538	C₂²	1	1	yes	characteristic
32	C₁₉×#537	C₂²	1	1	yes	characteristic
33	C₁₉×#534	—	2	1	no	—
34	C₁₉×#534	C₂²	1	1	yes	characteristic
35	C₁₉×#525	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#121	—	2	1	no	—
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₁₉×#452	—	2	1	no	—
40	C₁₉×#451	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#450	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#449	—	2	1	no	—
43	C₁₉×#449	—	2	1	no	—
44	C₁₉×#449	—	2	1	no	—
45	C₁₉×#448	C₂²	1	1	yes	characteristic
46	C₁₉×#448	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#448	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#447	C₂²	1	1	yes	characteristic
49	C₁₉×#447	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#447	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#417	—	2	1	no	—
52	C₁₉×#416	—	2	1	no	—
53	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#395	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#394	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#393	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#392	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#386	—	2	1	no	—
60	C₁₉×#386	—	2	1	no	—
61	C₁₉×#385	—	2	1	no	—
62	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#328	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#328	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#327	C₂²	1	1	yes	characteristic
66	C₁₉×#327	C₂²	1	1	yes	characteristic
67	C₁₉×#327	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#327	C₂²	1	1	yes	characteristic, complemented
69	C₁₉×#327	C₂²	1	1	yes	characteristic, complemented
70	C₁₉×#327	C₂²	1	1	yes	characteristic, complemented
71	C₁₉×#324	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#324	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#323	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#323	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₁₉	—	2	1	no	—
76	C₂×#41×C₁₉	—	2	1	no	—
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	—	4	4	no	—
81	C₂×#41×C₁₉	D₄	1	1	yes	characteristic, complemented
82	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₉	—	2	1	no	—
84	C₂²×D₄×C₁₉	—	2	1	no	—
85	C₂²×D₄×C₁₉	—	2	1	no	—
86	C₂²×D₄×C₁₉	—	2	1	no	—
87	C₂²×D₄×C₁₉	—	2	1	no	—
88	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic, complemented
90	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₉	—	2	1	no	—
92	C₂³×C₄×C₁₉	—	2	1	no	—
93	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
95	C₁₉×#135	—	4	4	no	—
96	C₂×Q₁₆×C₁₉	—	2	1	no	—
97	C₂×SD₁₆×C₁₉	—	2	1	no	—
98	C₂×SD₁₆×C₁₉	—	2	1	no	—
99	C₂×SD₁₆×C₁₉	—	2	1	no	—
100	C₂×SD₁₆×C₁₉	—	2	1	no	—
101	C₂×D₈×C₁₉	—	2	1	no	—
102	C₂×D₈×C₁₉	—	2	1	no	—
103	C₂×D₈×C₁₉	—	2	1	no	—
104	C₂×M₁₆×C₁₉	—	2	1	no	—
105	C₂²×C₈×C₁₉	—	2	1	no	—
106	C₁₉×#127	—	2	1	no	—
107	C₁₉×#126	—	2	1	no	—
108	C₁₉×#126	—	2	1	no	—
109	C₁₉×#126	—	2	1	no	—
110	C₁₉×#126	—	2	1	no	—
111	C₁₉×#125	—	2	1	no	—
112	C₁₉×#125	—	2	1	no	—
113	C₁₉×#124	—	2	1	no	—
114	C₁₉×#124	—	2	1	no	—
115	C₁₉×#124	—	2	1	no	—
116	C₁₉×#123	—	2	1	no	—
117	C₁₉×#123	—	2	1	no	—
118	C₁₉×#123	—	2	1	no	—
119	C₁₉×#123	—	2	1	no	—
120	C₁₉×#123	—	2	1	no	—
121	C₁₉×#123	—	2	1	no	—
122	C₁₉×#123	—	2	1	no	—
123	C₁₉×#123	—	2	1	no	—
124	C₁₉×#123	—	2	1	no	—
125	C₁₉×#123	—	2	1	no	—
126	C₁₉×#123	—	2	1	no	—
127	C₁₉×#123	—	2	1	no	—
128	C₁₉×#123	—	2	1	no	—
129	C₁₉×#123	—	2	1	no	—
130	C₁₉×C₂²⋊Q₈	—	2	1	no	—
131	C₁₉×C₂²⋊Q₈	—	2	1	no	—
132	C₁₉×C₂²⋊Q₈	—	2	1	no	—
133	C₁₉×C₂²⋊Q₈	—	2	1	no	—
134	C₁₉×C₂²⋊Q₈	—	2	1	no	—
135	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
136	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₉×#121	—	2	1	no	—
138	C₁₉×#121	—	2	1	no	—
139	C₁₉×#121	—	2	1	no	—
140	C₁₉×#121	—	2	1	no	—
141	C₁₉×#121	—	2	1	no	—
142	C₁₉×#121	—	2	1	no	—
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	—	4	4	no	—
153	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
154	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
155	C₁₉×#121	D₄	1	1	yes	characteristic, complemented
156	C₁₉×#121	C₂³	1	1	yes	characteristic
157	C₁₉×#121	C₂³	1	1	yes	characteristic
158	C₁₉×#121	C₂³	1	1	yes	characteristic
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	C₁₉×#120	—	2	1	no	—
164	C₁₉×#120	—	2	1	no	—
165	C₁₉×#120	—	2	1	no	—
166	C₁₉×#120	—	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	C₁₉×#117	—	2	1	no	—
176	C₁₉×#117	D₄	1	1	yes	characteristic, complemented
177	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic, complemented
180	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
191	C₁₉×#103	—	2	1	no	—
192	C₁₉×#103	—	2	1	no	—
193	C₁₉×#103	—	2	1	no	—
194	C₁₉×#103	—	2	1	no	—
195	C₁₉×#102	—	2	1	no	—
196	C₁₉×#102	—	2	1	no	—
197	C₁₉×#102	—	2	1	no	—
198	C₁₉×#102	—	2	1	no	—
199	C₁₉×C₂²⋊C₈	—	2	1	no	—
200	C₁₉×C₂²⋊C₈	—	2	1	no	—
201	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
202	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
203	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
204	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
205	C₁₉×#95	—	2	1	no	—
206	C₁₉×#95	—	2	1	no	—
207	C₁₉×#95	—	2	1	no	—
208	C₁₉×#95	C₂³	1	1	yes	characteristic
209	C₁₉×#95	C₂³	1	1	yes	characteristic
210	C₂⁴×C₁₉	—	2	1	no	—
211	C₂⁴×C₁₉	—	2	1	no	—
212	C₂⁴×C₁₉	—	2	1	no	—
213	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
215	#41×C₁₉	—	2	4	no	—
216	#41×C₁₉	—	2	4	no	—
217	#41×C₁₉	—	4	2	no	—
218	#41×C₁₉	—	4	2	no	—
219	#41×C₁₉	—	4	2	no	—
220	#41×C₁₉	—	4	2	no	—
221	#41×C₁₉	—	4	2	no	—
222	#41×C₁₉	—	4	2	no	—
223	#41×C₁₉	—	4	2	no	—
224	#41×C₁₉	—	8	1	no	—
225	#41×C₁₉	—	8	1	no	—
226	C₂×Q₈×C₁₉	—	2	1	no	—
227	C₂×Q₈×C₁₉	—	2	1	no	—
228	C₂×Q₈×C₁₉	—	2	1	no	—
229	C₂×Q₈×C₁₉	—	4	2	no	—
230	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
231	C₂×D₄×C₁₉	—	2	4	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	—	2	1	no	—
234	C₂×D₄×C₁₉	—	2	1	no	—
235	C₂×D₄×C₁₉	—	2	1	no	—
236	C₂×D₄×C₁₉	—	2	1	no	—
237	C₂×D₄×C₁₉	—	2	1	no	—
238	C₂×D₄×C₁₉	—	2	1	no	—
239	C₂×D₄×C₁₉	—	2	1	no	—
240	C₂×D₄×C₁₉	—	2	1	no	—
241	C₂×D₄×C₁₉	—	2	1	no	—
242	C₂×D₄×C₁₉	—	2	1	no	—
243	C₂×D₄×C₁₉	—	2	1	no	—
244	C₂×D₄×C₁₉	—	2	1	no	—
245	C₂×D₄×C₁₉	—	2	1	no	—
246	C₂×D₄×C₁₉	—	2	1	no	—
247	C₂×D₄×C₁₉	—	2	1	no	—
248	C₂×D₄×C₁₉	—	2	1	no	—
249	C₂×D₄×C₁₉	—	2	1	no	—
250	C₂×D₄×C₁₉	—	2	1	no	—
251	C₂×D₄×C₁₉	—	4	2	no	—
252	C₂×D₄×C₁₉	—	4	2	no	—
253	C₂×D₄×C₁₉	—	4	2	no	—
254	C₂×D₄×C₁₉	—	4	2	no	—
255	C₂×D₄×C₁₉	—	4	1	no	—
256	C₂×D₄×C₁₉	—	4	1	no	—
257	C₂×D₄×C₁₉	—	4	2	no	—
258	C₂×D₄×C₁₉	—	4	2	no	—
259	C₂×D₄×C₁₉	—	8	1	no	—
260	C₂×D₄×C₁₉	—	8	1	no	—
261	C₂×D₄×C₁₉	—	8	1	no	—
262	C₂×D₄×C₁₉	—	8	1	no	—
263	C₂×D₄×C₁₉	—	8	1	no	—
264	C₂×D₄×C₁₉	—	8	2	no	—
265	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
267	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₉	—	2	1	no	—
269	C₂²×C₄×C₁₉	—	2	1	no	—
270	C₂²×C₄×C₁₉	—	2	1	no	—
271	C₂²×C₄×C₁₉	—	2	1	no	—
272	C₂²×C₄×C₁₉	—	2	1	no	—
273	C₂²×C₄×C₁₉	—	2	1	no	—
274	C₂²×C₄×C₁₉	—	2	1	no	—
275	C₂²×C₄×C₁₉	—	2	1	no	—
276	C₂²×C₄×C₁₉	—	2	1	no	—
277	C₂²×C₄×C₁₉	—	2	1	no	—
278	C₂²×C₄×C₁₉	—	4	2	no	—
279	C₂²×C₄×C₁₉	—	4	2	no	—
280	C₂²×C₄×C₁₉	—	4	2	no	—
281	C₂²×C₄×C₁₉	—	4	2	no	—
282	C₂²×C₄×C₁₉	—	4	1	no	—
283	C₂²×C₄×C₁₉	—	4	1	no	—
284	C₂²×C₄×C₁₉	—	4	2	no	—
285	C₂²×C₄×C₁₉	—	8	1	no	—
286	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₁₉	—	4	2	no	—
296	SD₁₆×C₁₉	—	4	2	no	—
297	SD₁₆×C₁₉	—	4	2	no	—
298	SD₁₆×C₁₉	—	4	2	no	—
299	SD₁₆×C₁₉	—	4	2	no	—
300	D₈×C₁₉	—	4	2	no	—
301	D₈×C₁₉	—	4	2	no	—
302	D₈×C₁₉	—	4	2	no	—
303	M₁₆×C₁₉	—	4	2	no	—
304	C₂×C₈×C₁₉	—	2	1	no	—
305	C₂×C₈×C₁₉	—	2	1	no	—
306	C₂×C₈×C₁₉	—	2	1	no	—
307	C₂×C₈×C₁₉	—	2	1	no	—
308	C₂×C₈×C₁₉	—	4	2	no	—
309	C₄⋊C₄×C₁₉	—	2	1	no	—
310	C₄⋊C₄×C₁₉	—	2	1	no	—
311	C₄⋊C₄×C₁₉	—	2	1	no	—
312	C₄⋊C₄×C₁₉	—	2	1	no	—
313	C₄⋊C₄×C₁₉	—	2	1	no	—
314	C₄⋊C₄×C₁₉	—	2	1	no	—
315	C₄⋊C₄×C₁₉	—	2	1	no	—
316	C₄⋊C₄×C₁₉	—	2	1	no	—
317	C₄⋊C₄×C₁₉	—	2	1	no	—
318	C₄⋊C₄×C₁₉	—	2	1	no	—
319	C₄⋊C₄×C₁₉	—	2	1	no	—
320	C₄⋊C₄×C₁₉	—	2	1	no	—
321	C₄⋊C₄×C₁₉	—	2	1	no	—
322	C₄⋊C₄×C₁₉	—	4	2	no	—
323	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
324	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
325	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
326	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
333	C₂²⋊C₄×C₁₉	—	2	1	no	—
334	C₂²⋊C₄×C₁₉	—	2	1	no	—
335	C₂²⋊C₄×C₁₉	—	2	1	no	—
336	C₂²⋊C₄×C₁₉	—	2	1	no	—
337	C₂²⋊C₄×C₁₉	—	2	1	no	—
338	C₂²⋊C₄×C₁₉	—	2	1	no	—
339	C₂²⋊C₄×C₁₉	—	2	1	no	—
340	C₂²⋊C₄×C₁₉	—	2	1	no	—
341	C₂²⋊C₄×C₁₉	—	2	1	no	—
342	C₂²⋊C₄×C₁₉	—	2	1	no	—
343	C₂²⋊C₄×C₁₉	—	2	1	no	—
344	C₂²⋊C₄×C₁₉	—	2	1	no	—
345	C₂²⋊C₄×C₁₉	—	2	1	no	—
346	C₂²⋊C₄×C₁₉	—	2	1	no	—
347	C₂²⋊C₄×C₁₉	—	2	1	no	—
348	C₂²⋊C₄×C₁₉	—	2	1	no	—
349	C₂²⋊C₄×C₁₉	—	2	1	no	—
350	C₂²⋊C₄×C₁₉	—	2	1	no	—
351	C₂²⋊C₄×C₁₉	—	2	1	no	—
352	C₂²⋊C₄×C₁₉	—	4	2	no	—
353	C₂²⋊C₄×C₁₉	—	4	2	no	—
354	C₂²⋊C₄×C₁₉	—	4	2	no	—
355	C₂²⋊C₄×C₁₉	—	8	1	no	—
356	C₄²×C₁₉	—	2	1	no	—
357	C₄²×C₁₉	—	2	1	no	—
358	C₄²×C₁₉	—	2	1	no	—
359	#18252	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂³×C₁₉	—	2	1	no	—
361	C₂³×C₁₉	—	2	1	no	—
362	C₂³×C₁₉	—	2	2	no	—
363	C₂³×C₁₉	—	2	2	no	—
364	C₂³×C₁₉	—	2	1	no	—
365	C₂³×C₁₉	—	2	1	no	—
366	C₂³×C₁₉	—	2	1	no	—
367	C₂³×C₁₉	—	2	1	no	—
368	C₂³×C₁₉	—	2	1	no	—
369	C₂³×C₁₉	—	2	1	no	—
370	C₂³×C₁₉	—	4	1	no	—
371	C₂³×C₁₉	—	4	1	no	—
372	C₂³×C₁₉	—	4	1	no	—
373	C₂³×C₁₉	—	4	1	no	—
374	C₂³×C₁₉	—	4	1	no	—
375	C₂³×C₁₉	—	4	1	no	—
376	C₂³×C₁₉	—	4	1	no	—
377	C₂³×C₁₉	—	4	1	no	—
378	C₂³×C₁₉	—	4	1	no	—
379	C₂³×C₁₉	—	4	2	no	—
380	C₂³×C₁₉	—	8	1	no	—
381	C₂³×C₁₉	—	8	1	no	—
382	C₂³×C₁₉	—	8	1	no	—
383	C₂³×C₁₉	—	8	1	no	—
384	C₂³×C₁₉	—	8	1	no	—
385	C₂³×C₁₉	#120	1	1	yes	characteristic
386	C₂³×C₁₉	#120	1	1	yes	characteristic
387	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₁₉	—	2	2	no	—
389	Q₈×C₁₉	—	2	2	no	—
390	Q₈×C₁₉	—	4	1	no	—
391	Q₈×C₁₉	—	4	1	no	—
392	Q₈×C₁₉	—	4	1	no	—
393	Q₈×C₁₉	—	8	1	no	—
394	D₄×C₁₉	—	2	2	no	—
395	D₄×C₁₉	—	2	2	no	—
396	D₄×C₁₉	—	4	1	no	—
397	D₄×C₁₉	—	4	1	no	—
398	D₄×C₁₉	—	4	1	no	—
399	D₄×C₁₉	—	4	1	no	—
400	D₄×C₁₉	—	4	1	no	—
401	D₄×C₁₉	—	4	4	no	—
402	D₄×C₁₉	—	4	1	no	—
403	D₄×C₁₉	—	4	1	no	—
404	D₄×C₁₉	—	4	1	no	—
405	D₄×C₁₉	—	4	1	no	—
406	D₄×C₁₉	—	4	1	no	—
407	D₄×C₁₉	—	4	1	no	—
408	D₄×C₁₉	—	4	4	no	—
409	D₄×C₁₉	—	4	2	no	—
410	D₄×C₁₉	—	4	2	no	—
411	D₄×C₁₉	—	8	1	no	—
412	D₄×C₁₉	—	8	1	no	—
413	D₄×C₁₉	—	8	1	no	—
414	D₄×C₁₉	—	8	1	no	—
415	D₄×C₁₉	—	8	1	no	—
416	D₄×C₁₉	—	8	1	no	—
417	D₄×C₁₉	—	8	1	no	—
418	D₄×C₁₉	—	8	1	no	—
419	D₄×C₁₉	—	8	1	no	—
420	D₄×C₁₉	—	8	1	no	—
421	D₄×C₁₉	—	8	1	no	—
422	D₄×C₁₉	—	8	1	no	—
423	D₄×C₁₉	—	8	4	no	—
424	C₂×C₄×C₁₉	—	2	2	no	—
425	C₂×C₄×C₁₉	—	2	2	no	—
426	C₂×C₄×C₁₉	—	2	2	no	—
427	C₂×C₄×C₁₉	—	2	2	no	—
428	C₂×C₄×C₁₉	—	2	1	no	—
429	C₂×C₄×C₁₉	—	2	1	no	—
430	C₂×C₄×C₁₉	—	2	1	no	—
431	C₂×C₄×C₁₉	—	2	1	no	—
432	C₂×C₄×C₁₉	—	2	1	no	—
433	C₂×C₄×C₁₉	—	2	1	no	—
434	C₂×C₄×C₁₉	—	2	1	no	—
435	C₂×C₄×C₁₉	—	2	1	no	—
436	C₂×C₄×C₁₉	—	2	1	no	—
437	C₂×C₄×C₁₉	—	2	1	no	—
438	C₂×C₄×C₁₉	—	4	1	no	—
439	C₂×C₄×C₁₉	—	4	1	no	—
440	C₂×C₄×C₁₉	—	4	1	no	—
441	C₂×C₄×C₁₉	—	4	1	no	—
442	C₂×C₄×C₁₉	—	4	4	no	—
443	C₂×C₄×C₁₉	—	4	4	no	—
444	C₂×C₄×C₁₉	—	4	1	no	—
445	C₂×C₄×C₁₉	—	4	1	no	—
446	C₂×C₄×C₁₉	—	4	1	no	—
447	C₂×C₄×C₁₉	—	4	1	no	—
448	C₂×C₄×C₁₉	—	4	1	no	—
449	C₂×C₄×C₁₉	—	4	1	no	—
450	C₂×C₄×C₁₉	—	4	1	no	—
451	C₂×C₄×C₁₉	—	4	1	no	—
452	C₂×C₄×C₁₉	—	4	1	no	—
453	C₂×C₄×C₁₉	—	8	1	no	—
454	C₂×C₄×C₁₉	—	8	1	no	—
455	C₂×C₄×C₁₉	—	8	1	no	—
456	C₂×C₄×C₁₉	—	8	1	no	—
457	C₂×C₄×C₁₉	—	8	1	no	—
458	C₂×C₄×C₁₉	—	8	1	no	—
459	C₂×C₄×C₁₉	—	8	1	no	—
460	C₂×C₄×C₁₉	—	8	4	no	—
461	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
462	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
463	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
465	C₈×C₁₉	—	4	1	no	—
466	C₈×C₁₉	—	4	1	no	—
467	C₈×C₁₉	—	4	1	no	—
468	C₈×C₁₉	—	4	1	no	—
469	#3534	C₂×C₁₉	1	1	yes	characteristic, complemented
470	#3006	C₂×C₁₉	1	1	yes	characteristic, complemented
471	#3002	C₂×C₁₉	1	1	yes	characteristic, complemented
472	#2430	C₂×C₁₉	1	1	yes	characteristic, complemented
473	#1606	C₂×C₁₉	1	1	yes	characteristic, complemented
474	#1604	C₂×C₁₉	1	1	yes	characteristic, complemented
475	#1603	C₂×C₁₉	1	1	yes	characteristic, complemented
476	#1601	C₂×C₁₉	1	1	yes	characteristic, complemented
477	#1600	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#1598	C₂×C₁₉	1	1	yes	characteristic, complemented
479	#1597	C₂×C₁₉	1	1	yes	characteristic, complemented
480	#1595	C₂×C₁₉	1	1	yes	characteristic, complemented
481	#1504	C₂×C₁₉	1	1	yes	characteristic, complemented
482	C₂×#327	C₂×C₁₉	1	1	yes	characteristic, complemented
483	#1468	C₂×C₁₉	1	1	yes	characteristic, complemented
484	C₂²×C₁₉	—	2	1	no	—
485	C₂²×C₁₉	—	2	1	no	—
486	C₂²×C₁₉	—	2	1	no	—
487	C₂²×C₁₉	—	2	1	no	—
488	C₂²×C₁₉	—	2	1	no	—
489	C₂²×C₁₉	—	2	1	no	—
490	C₂²×C₁₉	—	2	1	no	—
491	C₂²×C₁₉	—	4	2	no	—
492	C₂²×C₁₉	—	4	2	no	—
493	C₂²×C₁₉	—	4	2	no	—
494	C₂²×C₁₉	—	4	2	no	—
495	C₂²×C₁₉	—	4	1	no	—
496	C₂²×C₁₉	—	4	1	no	—
497	C₂²×C₁₉	—	4	1	no	—
498	C₂²×C₁₉	—	4	1	no	—
499	C₂²×C₁₉	—	4	1	no	—
500	C₂²×C₁₉	—	4	1	no	—
501	C₂²×C₁₉	—	4	1	no	—
502	C₂²×C₁₉	—	4	1	no	—
503	C₂²×C₁₉	—	4	2	no	—
504	C₂²×C₁₉	—	4	1	no	—
505	C₂²×C₁₉	—	4	1	no	—
506	C₂²×C₁₉	—	4	1	no	—
507	C₂²×C₁₉	—	4	1	no	—
508	C₂²×C₁₉	—	8	1	no	—
509	C₂²×C₁₉	—	8	1	no	—
510	C₂²×C₁₉	—	8	1	no	—
511	C₂²×C₁₉	—	8	1	no	—
512	C₂²×C₁₉	—	8	1	no	—
513	C₂²×C₁₉	—	8	1	no	—
514	C₂²×C₁₉	—	16	2	no	—
515	C₂²×C₁₉	—	16	2	no	—
516	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
517	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
518	C₂²×C₁₉	#576	1	1	yes	characteristic
519	C₂²×C₁₉	#577	1	1	yes	characteristic
520	C₄×C₁₉	—	2	1	no	—
521	C₄×C₁₉	—	2	1	no	—
522	C₄×C₁₉	—	2	1	no	—
523	C₄×C₁₉	—	2	1	no	—
524	C₄×C₁₉	—	4	2	no	—
525	C₄×C₁₉	—	4	1	no	—
526	C₄×C₁₉	—	4	1	no	—
527	C₄×C₁₉	—	4	1	no	—
528	C₄×C₁₉	—	4	1	no	—
529	C₄×C₁₉	—	4	1	no	—
530	C₄×C₁₉	—	4	1	no	—
531	C₄×C₁₉	—	4	2	no	—
532	C₄×C₁₉	—	4	1	no	—
533	C₄×C₁₉	—	4	1	no	—
534	C₄×C₁₉	—	8	1	no	—
535	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic, complemented
536	C₂×AGL(1,ℤ/8)	—	2	1	no	—
537	C₂×#135	—	2	1	no	—
538	#562	—	2	1	no	—
539	#560	—	2	1	no	—
540	#553	—	2	1	no	—
541	#551	—	2	1	no	—
542	#546	—	2	1	no	—
543	#546	—	2	1	no	—
544	#546	—	2	1	no	—
545	D₄²	—	2	1	no	—
546	#540	—	2	1	no	—
547	#539	—	2	1	no	—
548	#539	C₂²×C₁₉	1	1	yes	characteristic
549	#538	—	2	1	no	—
550	#538	C₂²×C₁₉	1	1	yes	characteristic
551	#537	C₂²×C₁₉	1	1	yes	characteristic
552	#534	—	2	1	no	—
553	#534	C₂²×C₁₉	1	1	yes	characteristic
554	#525	C₂²×C₁₉	1	1	yes	characteristic
555	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
556	C₂×#121	—	2	1	no	—
557	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
558	#452	—	2	1	no	—
559	#451	C₂²×C₁₉	1	1	yes	characteristic, complemented
560	#450	C₂²×C₁₉	1	1	yes	characteristic, complemented
561	#449	—	2	1	no	—
562	#449	—	2	1	no	—
563	#449	—	2	1	no	—
564	#448	C₂²×C₁₉	1	1	yes	characteristic
565	#448	C₂²×C₁₉	1	1	yes	characteristic, complemented
566	#448	C₂²×C₁₉	1	1	yes	characteristic, complemented
567	#447	C₂²×C₁₉	1	1	yes	characteristic
568	#447	C₂²×C₁₉	1	1	yes	characteristic, complemented
569	#447	C₂²×C₁₉	1	1	yes	characteristic, complemented
570	#417	—	2	1	no	—
571	#416	—	2	1	no	—
572	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
573	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
574	#395	C₂²×C₁₉	1	1	yes	characteristic, complemented
575	#394	C₂²×C₁₉	1	1	yes	characteristic, complemented
576	#393	C₂²×C₁₉	1	1	yes	characteristic, complemented
577	#392	C₂²×C₁₉	1	1	yes	characteristic, complemented
578	#386	—	2	1	no	—
579	#386	—	2	1	no	—
580	#385	—	2	1	no	—
581	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic, complemented
582	#328	C₂²×C₁₉	1	1	yes	characteristic, complemented
583	#328	C₂²×C₁₉	1	1	yes	characteristic, complemented
584	#327	C₂²×C₁₉	1	1	yes	characteristic
585	#327	C₂²×C₁₉	1	1	yes	characteristic
586	#327	C₂²×C₁₉	1	1	yes	characteristic, complemented
587	#327	C₂²×C₁₉	1	1	yes	characteristic, complemented
588	#327	C₂²×C₁₉	1	1	yes	characteristic, complemented
589	#327	C₂²×C₁₉	1	1	yes	characteristic, complemented
590	#324	C₂²×C₁₉	1	1	yes	characteristic, complemented
591	#324	C₂²×C₁₉	1	1	yes	characteristic, complemented
592	#323	C₂²×C₁₉	1	1	yes	characteristic, complemented
593	#323	C₂²×C₁₉	1	1	yes	characteristic, complemented
594	C₂×C₁₉	—	2	1	no	—
595	C₂×C₁₉	—	2	1	no	—
596	C₂×C₁₉	—	2	2	no	—
597	C₂×C₁₉	—	4	1	no	—
598	C₂×C₁₉	—	8	2	no	—
599	C₂×C₁₉	—	8	1	no	—
600	C₂×C₁₉	—	8	1	no	—
601	C₂×C₁₉	—	8	1	no	—
602	C₂×C₁₉	—	8	1	no	—
603	C₂×C₁₉	#3012	1	1	yes	characteristic
604	C₂×C₁₉	#3018	1	1	yes	characteristic
605	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
606	C₂×#41	—	2	1	no	—
607	C₂×#41	—	2	1	no	—
608	C₂×#41	—	2	1	no	—
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	—	4	4	no	—
612	C₂×#41	D₄×C₁₉	1	1	yes	characteristic, complemented
613	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
614	C₂²×D₄	—	2	1	no	—
615	C₂²×D₄	—	2	1	no	—
616	C₂²×D₄	—	2	1	no	—
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	1	no	—
619	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
620	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic, complemented
621	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
622	C₂³×C₄	—	2	1	no	—
623	C₂³×C₄	—	2	1	no	—
624	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
625	AGL(1,ℤ/8)	—	4	4	no	—
626	#135	—	4	4	no	—
627	C₂×Q₁₆	—	2	1	no	—
628	C₂×SD₁₆	—	2	1	no	—
629	C₂×SD₁₆	—	2	1	no	—
630	C₂×SD₁₆	—	2	1	no	—
631	C₂×SD₁₆	—	2	1	no	—
632	C₂×D₈	—	2	1	no	—
633	C₂×D₈	—	2	1	no	—
634	C₂×D₈	—	2	1	no	—
635	C₂×M₁₆	—	2	1	no	—
636	C₂²×C₈	—	2	1	no	—
637	#127	—	2	1	no	—
638	#126	—	2	1	no	—
639	#126	—	2	1	no	—
640	#126	—	2	1	no	—
641	#126	—	2	1	no	—
642	#125	—	2	1	no	—
643	#125	—	2	1	no	—
644	#124	—	2	1	no	—
645	#124	—	2	1	no	—
646	#124	—	2	1	no	—
647	#123	—	2	1	no	—
648	#123	—	2	1	no	—
649	#123	—	2	1	no	—
650	#123	—	2	1	no	—
651	#123	—	2	1	no	—
652	#123	—	2	1	no	—
653	#123	—	2	1	no	—
654	#123	—	2	1	no	—
655	#123	—	2	1	no	—
656	#123	—	2	1	no	—
657	#123	—	2	1	no	—
658	#123	—	2	1	no	—
659	#123	—	2	1	no	—
660	#123	—	2	1	no	—
661	C₂²⋊Q₈	—	2	1	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic, complemented
667	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
668	#121	—	2	1	no	—
669	#121	—	2	1	no	—
670	#121	—	2	1	no	—
671	#121	—	2	1	no	—
672	#121	—	2	1	no	—
673	#121	—	2	1	no	—
674	#121	—	2	1	no	—
675	#121	—	2	1	no	—
676	#121	—	2	1	no	—
677	#121	—	2	1	no	—
678	#121	—	2	1	no	—
679	#121	—	2	1	no	—
680	#121	—	2	1	no	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	—	4	4	no	—
684	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
685	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
686	#121	D₄×C₁₉	1	1	yes	characteristic, complemented
687	#121	C₂³×C₁₉	1	1	yes	characteristic
688	#121	C₂³×C₁₉	1	1	yes	characteristic
689	#121	C₂³×C₁₉	1	1	yes	characteristic
690	#120	—	2	1	no	—
691	#120	—	2	1	no	—
692	#120	—	2	1	no	—
693	#120	—	2	1	no	—
694	#120	—	2	1	no	—
695	#120	—	2	1	no	—
696	#120	—	2	1	no	—
697	#120	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	2	1	no	—
700	C₄×D₄	—	2	1	no	—
701	C₄×D₄	—	2	1	no	—
702	C₄×D₄	—	2	1	no	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	1	no	—
706	#117	—	2	1	no	—
707	#117	D₄×C₁₉	1	1	yes	characteristic, complemented
708	C₂×C₄⋊C₄	—	2	1	no	—
709	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
710	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic, complemented
711	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	—	2	1	no	—
713	C₂×C₂²⋊C₄	—	2	1	no	—
714	C₂×C₂²⋊C₄	—	2	1	no	—
715	C₂×C₂²⋊C₄	—	2	1	no	—
716	C₂×C₂²⋊C₄	—	2	1	no	—
717	C₂×C₂²⋊C₄	—	2	1	no	—
718	C₂×C₂²⋊C₄	—	2	1	no	—
719	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
722	#103	—	2	1	no	—
723	#103	—	2	1	no	—
724	#103	—	2	1	no	—
725	#103	—	2	1	no	—
726	#102	—	2	1	no	—
727	#102	—	2	1	no	—
728	#102	—	2	1	no	—
729	#102	—	2	1	no	—
730	C₂²⋊C₈	—	2	1	no	—
731	C₂²⋊C₈	—	2	1	no	—
732	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
733	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
734	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
735	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	C₂³×C₁₉	1	1	yes	characteristic
740	#95	C₂³×C₁₉	1	1	yes	characteristic
741	C₁₉	#18252	1	1	yes	characteristic, direct product factor, Sylow
742	C₂⁴	—	2	1	no	—
743	C₂⁴	—	2	1	no	—
744	C₂⁴	—	2	1	no	—
745	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
746	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
747	#41	—	2	4	no	—
748	#41	—	2	4	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	#41	—	4	2	no	—
754	#41	—	4	2	no	—
755	#41	—	4	2	no	—
756	#41	—	8	1	no	—
757	#41	—	8	1	no	—
758	C₂×Q₈	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	1	no	—
761	C₂×Q₈	—	4	2	no	—
762	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	1	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	—	4	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	1	no	—
788	C₂×D₄	—	4	1	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	8	1	no	—
792	C₂×D₄	—	8	1	no	—
793	C₂×D₄	—	8	1	no	—
794	C₂×D₄	—	8	1	no	—
795	C₂×D₄	—	8	1	no	—
796	C₂×D₄	—	8	2	no	—
797	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
798	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
799	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	1	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	8	1	no	—
818	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
821	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
822	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
823	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
824	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
825	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
827	Q₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	SD₁₆	—	4	2	no	—
832	D₈	—	4	2	no	—
833	D₈	—	4	2	no	—
834	D₈	—	4	2	no	—
835	M₁₆	—	4	2	no	—
836	C₂×C₈	—	2	1	no	—
837	C₂×C₈	—	2	1	no	—
838	C₂×C₈	—	2	1	no	—
839	C₂×C₈	—	2	1	no	—
840	C₂×C₈	—	4	2	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
856	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
857	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
858	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
859	C₂²⋊C₄	—	2	1	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	—	2	1	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	1	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	1	no	—
867	C₂²⋊C₄	—	2	1	no	—
868	C₂²⋊C₄	—	2	1	no	—
869	C₂²⋊C₄	—	2	1	no	—
870	C₂²⋊C₄	—	2	1	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	1	no	—
876	C₂²⋊C₄	—	2	1	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	1	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	1	no	—
884	C₂²⋊C₄	—	4	2	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	8	1	no	—
888	C₄²	—	2	1	no	—
889	C₄²	—	2	1	no	—
890	C₄²	—	2	1	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	4	1	no	—
902	C₂³	—	4	1	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	1	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	4	1	no	—
907	C₂³	—	4	1	no	—
908	C₂³	—	4	1	no	—
909	C₂³	—	4	1	no	—
910	C₂³	—	4	2	no	—
911	C₂³	—	8	1	no	—
912	C₂³	—	8	1	no	—
913	C₂³	—	8	1	no	—
914	C₂³	—	8	1	no	—
915	C₂³	—	8	1	no	—
916	C₂³	C₁₉×#120	1	1	yes	characteristic
917	C₂³	C₁₉×#120	1	1	yes	characteristic
918	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
919	Q₈	—	2	2	no	—
920	Q₈	—	2	2	no	—
921	Q₈	—	4	1	no	—
922	Q₈	—	4	1	no	—
923	Q₈	—	4	1	no	—
924	Q₈	—	8	1	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	4	2	no	—
935	D₄	—	4	2	no	—
936	D₄	—	4	1	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	1	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	1	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	1	no	—
947	D₄	—	8	1	no	—
948	D₄	—	8	1	no	—
949	D₄	—	8	1	no	—
950	D₄	—	8	1	no	—
951	D₄	—	8	1	no	—
952	D₄	—	8	1	no	—
953	D₄	—	8	1	no	—
954	D₄	—	8	4	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	1	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	1	no	—
978	C₂×C₄	—	4	1	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	1	no	—
982	C₂×C₄	—	4	1	no	—
983	C₂×C₄	—	4	1	no	—
984	C₂×C₄	—	8	1	no	—
985	C₂×C₄	—	8	1	no	—
986	C₂×C₄	—	8	1	no	—
987	C₂×C₄	—	8	1	no	—
988	C₂×C₄	—	8	1	no	—
989	C₂×C₄	—	8	1	no	—
990	C₂×C₄	—	8	1	no	—
991	C₂×C₄	—	8	4	no	—
992	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
993	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
994	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
995	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
996	C₈	—	4	1	no	—
997	C₈	—	4	1	no	—
998	C₈	—	4	1	no	—
999	C₈	—	4	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	8	1	no	—
1025	C₂²	—	8	1	no	—
1026	C₂²	—	8	1	no	—
1027	C₂²	—	8	1	no	—
1028	C₂²	—	8	1	no	—
1029	C₂²	—	8	1	no	—
1030	C₂²	—	16	2	no	—
1031	C₂²	—	16	2	no	—
1032	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
1033	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
1034	C₂²	C₁₉×#576	1	1	yes	characteristic
1035	C₂²	C₁₉×#577	1	1	yes	characteristic
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	8	1	no	—
1051	C₂	—	2	1	no	—
1052	C₂	—	2	1	no	—
1053	C₂	—	2	2	no	—
1054	C₂	—	4	1	no	—
1055	C₂	—	8	2	no	—
1056	C₂	—	8	1	no	—
1057	C₂	—	8	1	no	—
1058	C₂	—	8	1	no	—
1059	C₂	—	8	1	no	—
1060	C₂	C₁₉×#3012	1	1	yes	characteristic
1061	C₂	C₁₉×#3018	1	1	yes	characteristic
1062	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3534	C₂	semidirect
2. C₁₉×#3006	C₂	semidirect
3. C₁₉×#3002	C₂	semidirect
4. C₁₉×#2430	C₂	semidirect
5. C₁₉×#1606	C₂	semidirect
6. C₁₉×#1604	C₂	semidirect
7. C₁₉×#1603	C₂	semidirect
8. C₁₉×#1601	C₂	semidirect
9. C₁₉×#1600	C₂	semidirect
10. C₁₉×#1598	C₂	semidirect
11. C₁₉×#1597	C₂	semidirect
12. C₁₉×#1595	C₂	semidirect
13. C₁₉×#1504	C₂	semidirect
14. C₂×C₁₉×#327	C₂	semidirect
15. C₁₉×#1468	C₂	semidirect
16. C₂²×#41×C₁₉	C₂²	semidirect
40. C₁₉×#451	C₂²	semidirect
41. C₁₉×#450	C₂²	semidirect
46. C₁₉×#448	C₂²	semidirect
47. C₁₉×#448	C₂²	semidirect
49. C₁₉×#447	C₂²	semidirect
50. C₁₉×#447	C₂²	semidirect
53. C₁₉×#407	C₂²	semidirect
54. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
55. C₁₉×#395	C₂²	semidirect
56. C₁₉×#394	C₂²	semidirect
57. C₁₉×#393	C₂²	semidirect
58. C₁₉×#392	C₂²	semidirect
62. C₂×C₁₉×#95	C₂²	semidirect
63. C₁₉×#328	C₂²	semidirect
64. C₁₉×#328	C₂²	semidirect
67. C₁₉×#327	C₂²	semidirect
68. C₁₉×#327	C₂²	semidirect
69. C₁₉×#327	C₂²	semidirect
70. C₁₉×#327	C₂²	semidirect
71. C₁₉×#324	C₂²	semidirect
72. C₁₉×#324	C₂²	semidirect
73. C₁₉×#323	C₂²	semidirect
74. C₁₉×#323	C₂²	semidirect
81. C₂×#41×C₁₉	D₄	semidirect
89. C₂²×D₄×C₁₉	D₄	semidirect
135. C₁₉×C₂²⋊Q₈	D₄	semidirect
153. C₁₉×#121	D₄	semidirect
154. C₁₉×#121	D₄	semidirect
155. C₁₉×#121	D₄	semidirect
176. C₁₉×#117	D₄	semidirect
179. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
359. #18252	C₁₉	direct (N × H)
469. #3534	C₂×C₁₉	semidirect
470. #3006	C₂×C₁₉	semidirect
471. #3002	C₂×C₁₉	semidirect
472. #2430	C₂×C₁₉	semidirect
473. #1606	C₂×C₁₉	semidirect
474. #1604	C₂×C₁₉	semidirect
475. #1603	C₂×C₁₉	semidirect
476. #1601	C₂×C₁₉	semidirect
477. #1600	C₂×C₁₉	semidirect
478. #1598	C₂×C₁₉	semidirect
479. #1597	C₂×C₁₉	semidirect
480. #1595	C₂×C₁₉	semidirect
481. #1504	C₂×C₁₉	semidirect
482. C₂×#327	C₂×C₁₉	semidirect
483. #1468	C₂×C₁₉	semidirect
535. C₂²×#41	C₂²×C₁₉	semidirect
559. #451	C₂²×C₁₉	semidirect
560. #450	C₂²×C₁₉	semidirect
565. #448	C₂²×C₁₉	semidirect
566. #448	C₂²×C₁₉	semidirect
568. #447	C₂²×C₁₉	semidirect
569. #447	C₂²×C₁₉	semidirect
572. #407	C₂²×C₁₉	semidirect
573. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
574. #395	C₂²×C₁₉	semidirect
575. #394	C₂²×C₁₉	semidirect
576. #393	C₂²×C₁₉	semidirect
577. #392	C₂²×C₁₉	semidirect
581. C₂×#95	C₂²×C₁₉	semidirect
582. #328	C₂²×C₁₉	semidirect
583. #328	C₂²×C₁₉	semidirect
586. #327	C₂²×C₁₉	semidirect
587. #327	C₂²×C₁₉	semidirect
588. #327	C₂²×C₁₉	semidirect
589. #327	C₂²×C₁₉	semidirect
590. #324	C₂²×C₁₉	semidirect
591. #324	C₂²×C₁₉	semidirect
592. #323	C₂²×C₁₉	semidirect
593. #323	C₂²×C₁₉	semidirect
612. C₂×#41	D₄×C₁₉	semidirect
620. C₂²×D₄	D₄×C₁₉	semidirect
666. C₂²⋊Q₈	D₄×C₁₉	semidirect
684. #121	D₄×C₁₉	semidirect
685. #121	D₄×C₁₉	semidirect
686. #121	D₄×C₁₉	semidirect
707. #117	D₄×C₁₉	semidirect
710. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
741. C₁₉	#18252	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×#3534	2
C₁₉×#3006	2
C₁₉×#3002	2
C₁₉×#2430	2
C₁₉×#1606	2
C₁₉×#1604	2
C₁₉×#1603	2
C₁₉×#1601	2
C₁₉×#1600	2
C₁₉×#1598	2
C₁₉×#1597	2
C₁₉×#1595	2
C₁₉×#1504	2
C₂×C₁₉×#327	2
C₁₉×#1468	2
#18252	19

Subgroups — C19×#18252 #18024211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18252 #18024211