Subgroups — C₁₉×#62344 #18068303

Order 4864.

1812 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3551	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3352	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3351	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3301	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3300	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3297	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3296	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3277	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3275	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3273	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3256	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3201	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3198	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3063	C₂	1	2	yes	maximal, complemented
18	C₁₉×#3062	C₂	1	2	yes	maximal, complemented
19	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₉×#131	C₂²	1	2	yes	complemented
23	C₁₉×#563	—	2	2	no	—
24	C₁₉×#560	—	2	2	no	—
25	C₁₉×#555	—	2	2	no	—
26	C₁₉×#553	C₂²	1	2	yes	—
27	C₁₉×#553	C₂²	1	2	yes	complemented
28	C₁₉×#552	C₂²	1	2	yes	—
29	C₁₉×#552	C₂²	1	2	yes	complemented
30	C₁₉×#551	—	2	2	no	—
31	C₁₉×#548	C₂²	1	2	yes	—
32	C₁₉×#548	C₂²	1	2	yes	complemented
33	C₁₉×#546	C₂²	1	2	yes	—
34	C₁₉×#546	C₂²	1	2	yes	complemented
35	C₁₉×#540	—	2	2	no	—
36	C₁₉×#540	—	2	2	no	—
37	C₁₉×#538	—	2	2	no	—
38	C₁₉×#538	—	2	2	no	—
39	C₁₉×#537	C₂²	1	2	yes	—
40	C₁₉×#537	C₂²	1	2	yes	—
41	C₁₉×#536	C₂²	1	2	yes	complemented
42	C₁₉×#535	C₂²	1	2	yes	complemented
43	C₁₉×#532	C₂²	1	1	yes	characteristic
44	C₁₉×#529	C₂²	1	2	yes	complemented
45	C₁₉×#529	C₂²	1	2	yes	complemented
46	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#499	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#495	C₂²	1	1	yes	characteristic
49	C₁₉×#495	C₂²	1	1	yes	characteristic
50	C₁₉×#488	C₂²	1	2	yes	complemented
51	C₁₉×#488	C₂²	1	2	yes	complemented
52	C₁₉×#485	C₂²	1	2	yes	complemented
53	C₁₉×#485	C₂²	1	2	yes	complemented
54	C₁₉×#484	C₂²	1	2	yes	complemented
55	C₁₉×#483	C₂²	1	2	yes	complemented
56	C₁₉×#482	C₂²	1	2	yes	—
57	C₁₉×#482	C₂²	1	2	yes	complemented
58	C₁₉×#481	C₂²	1	2	yes	complemented
59	C₁₉×#480	C₂²	1	2	yes	complemented
60	C₁₉×#479	C₂²	1	2	yes	complemented
61	C₁₉×#479	C₂²	1	2	yes	complemented
62	C₁₉×#478	C₂²	1	2	yes	complemented
63	C₁₉×#478	C₂²	1	2	yes	complemented
64	C₁₉×#470	C₂²	1	2	yes	complemented
65	C₁₉×#470	C₂²	1	2	yes	complemented
66	C₁₉×#469	C₂²	1	2	yes	—
67	C₁₉×#469	C₂²	1	2	yes	—
68	C₁₉×#468	C₂²	1	2	yes	—
69	C₁₉×#468	C₂²	1	2	yes	complemented
70	C₁₉×#468	C₂²	1	2	yes	complemented
71	C₁₉×#468	C₂²	1	2	yes	complemented
72	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
73	C₁₉×#467	C₂²	1	1	yes	characteristic, complemented
74	C₁₉×#467	C₂²	1	2	yes	complemented
75	C₁₉×#466	C₂²	1	1	yes	characteristic
76	C₁₉×#466	C₂²	1	1	yes	characteristic
77	C₁₉×#466	C₂²	1	2	yes	—
78	C₁₉×#465	C₂²	1	2	yes	—
79	C₁₉×#465	C₂²	1	2	yes	complemented
80	C₁₉×#465	C₂²	1	2	yes	complemented
81	C₁₉×#465	C₂²	1	2	yes	complemented
82	C₁₉×#464	C₂²	1	2	yes	complemented
83	C₁₉×#464	C₂²	1	2	yes	complemented
84	C₁₉×#463	C₂²	1	2	yes	—
85	C₁₉×#463	C₂²	1	2	yes	—
86	C₁₉×#452	C₂²	1	2	yes	—
87	C₁₉×#452	C₂²	1	2	yes	—
88	C₁₉×#451	C₂²	1	2	yes	complemented
89	C₁₉×#450	C₂²	1	2	yes	complemented
90	C₁₉×#449	C₂²	1	2	yes	—
91	C₁₉×#449	C₂²	1	2	yes	—
92	C₁₉×#448	C₂²	1	2	yes	complemented
93	C₁₉×#447	C₂²	1	2	yes	—
94	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
95	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
96	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
98	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
99	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
100	C₁₉×#436	C₂²	1	1	yes	characteristic
101	C₁₉×#436	C₂²	1	2	yes	complemented
102	C₁₉×#436	C₂²	1	1	yes	characteristic, complemented
103	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
104	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
105	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
106	C₁₉×#428	C₂²	1	2	yes	complemented
107	C₁₉×#428	C₂²	1	2	yes	complemented
108	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
109	C₁₉×#416	C₂²	1	2	yes	—
110	C₁₉×#416	C₂²	1	2	yes	complemented
111	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
112	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
113	C₁₉×#408	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₁₉	C₂³	1	2	yes	—
116	C₂×#41×C₁₉	C₂³	1	2	yes	—
117	C₂×#41×C₁₉	C₂³	1	2	yes	—
118	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
120	C₁₉×#137	—	4	4	no	—
121	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
122	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
129	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₁₉	C₂³	1	2	yes	—
132	C₁₉×#131	—	4	4	no	—
133	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
134	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
135	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
136	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
139	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
140	C₁₉×C₄⋊Q₈	—	2	2	no	—
141	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
142	C₁₉×#127	—	2	2	no	—
143	C₁₉×#127	D₄	1	1	yes	characteristic
144	C₁₉×#126	—	2	2	no	—
145	C₁₉×#126	—	2	2	no	—
146	C₁₉×#126	—	2	2	no	—
147	C₁₉×#126	—	2	2	no	—
148	C₁₉×#126	—	2	2	no	—
149	C₁₉×#126	—	2	2	no	—
150	C₁₉×#125	—	2	2	no	—
151	C₁₉×#125	—	2	2	no	—
152	C₁₉×#125	C₂³	1	2	yes	—
153	C₁₉×#125	C₂³	1	2	yes	—
154	C₁₉×#124	—	2	2	no	—
155	C₁₉×#124	—	2	2	no	—
156	C₁₉×#124	—	2	2	no	—
157	C₁₉×#124	—	2	2	no	—
158	C₁₉×#124	D₄	1	2	yes	—
159	C₁₉×#124	C₂³	1	2	yes	—
160	C₁₉×#124	C₂³	1	2	yes	—
161	C₁₉×#123	—	2	2	no	—
162	C₁₉×#123	—	2	2	no	—
163	C₁₉×#123	—	2	2	no	—
164	C₁₉×#123	—	2	2	no	—
165	C₁₉×#123	—	2	2	no	—
166	C₁₉×#123	—	2	2	no	—
167	C₁₉×#123	—	2	2	no	—
168	C₁₉×#123	—	2	2	no	—
169	C₁₉×#123	—	2	2	no	—
170	C₁₉×#123	—	2	2	no	—
171	C₁₉×C₂²⋊Q₈	—	2	2	no	—
172	C₁₉×C₂²⋊Q₈	—	2	2	no	—
173	C₁₉×C₂²⋊Q₈	—	2	2	no	—
174	C₁₉×C₂²⋊Q₈	—	2	2	no	—
175	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₁₉×#121	—	2	2	no	—
182	C₁₉×#121	—	2	2	no	—
183	C₁₉×#121	—	2	2	no	—
184	C₁₉×#121	—	2	2	no	—
185	C₁₉×#121	—	2	2	no	—
186	C₁₉×#121	—	2	2	no	—
187	C₁₉×#121	—	2	2	no	—
188	C₁₉×#121	—	2	2	no	—
189	C₁₉×#121	—	2	2	no	—
190	C₁₉×#121	—	2	2	no	—
191	C₁₉×#121	—	2	2	no	—
192	C₁₉×#121	—	2	2	no	—
193	C₁₉×#121	D₄	1	1	yes	characteristic
194	C₁₉×#121	D₄	1	2	yes	—
195	C₁₉×#121	D₄	1	1	yes	characteristic
196	C₁₉×#121	C₂³	1	2	yes	—
197	C₁₉×#121	C₂³	1	2	yes	—
198	C₁₉×#121	C₂³	1	2	yes	—
199	C₁₉×#121	C₂³	1	2	yes	—
200	C₁₉×#121	C₂³	1	2	yes	—
201	C₁₉×#121	C₂³	1	2	yes	—
202	C₁₉×#120	—	2	2	no	—
203	C₁₉×#120	—	2	2	no	—
204	C₁₉×#120	—	2	2	no	—
205	C₁₉×#120	—	2	2	no	—
206	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
208	C₄×D₄×C₁₉	—	2	2	no	—
209	C₄×D₄×C₁₉	—	2	2	no	—
210	C₄×D₄×C₁₉	—	2	2	no	—
211	C₄×D₄×C₁₉	—	2	2	no	—
212	C₄×D₄×C₁₉	—	2	2	no	—
213	C₄×D₄×C₁₉	—	2	2	no	—
214	C₄×D₄×C₁₉	C₂³	1	2	yes	—
215	C₄×D₄×C₁₉	C₂³	1	2	yes	—
216	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₁₉	C₂³	1	2	yes	—
218	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
219	C₁₉×#117	—	2	2	no	—
220	C₁₉×#117	—	2	2	no	—
221	C₁₉×#117	—	2	2	no	—
222	C₁₉×#117	—	2	2	no	—
223	C₁₉×#117	C₂³	1	2	yes	—
224	C₁₉×#117	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
226	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
230	C₁₉×#107	C₂³	1	1	yes	characteristic
231	C₁₉×#107	C₂³	1	1	yes	characteristic
232	C₁₉×#107	C₂³	1	2	yes	—
233	C₁₉×#107	C₂³	1	2	yes	—
234	C₁₉×#107	C₂³	1	1	yes	characteristic
235	C₁₉×#107	C₂³	1	1	yes	characteristic
236	C₁₉×#106	C₂³	1	2	yes	—
237	C₁₉×#106	C₂³	1	2	yes	—
238	C₁₉×#106	C₂³	1	2	yes	—
239	C₁₉×#106	C₂³	1	2	yes	—
240	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
241	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
242	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
243	C₁₉×#103	C₂³	1	2	yes	—
244	C₁₉×#103	C₂³	1	2	yes	—
245	C₁₉×#103	C₂³	1	2	yes	—
246	C₁₉×#103	C₂³	1	2	yes	—
247	C₁₉×#103	C₂³	1	2	yes	—
248	C₁₉×#103	C₂³	1	2	yes	—
249	C₁₉×#103	C₂³	1	2	yes	—
250	C₁₉×#103	C₂³	1	2	yes	—
251	C₁₉×#102	C₂³	1	2	yes	—
252	C₁₉×#102	C₂³	1	2	yes	—
253	C₁₉×#102	C₂³	1	2	yes	—
254	C₁₉×#102	C₂³	1	2	yes	—
255	C₁₉×#102	C₂³	1	2	yes	—
256	C₁₉×#102	C₂³	1	2	yes	—
257	C₁₉×#102	C₂³	1	2	yes	—
258	C₁₉×#102	C₂³	1	2	yes	—
259	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
266	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
267	C₂⁴×C₁₉	—	2	2	no	—
268	#41×C₁₉	—	4	2	no	—
269	#41×C₁₉	—	4	2	no	—
270	#41×C₁₉	—	4	2	no	—
271	#41×C₁₉	—	4	2	no	—
272	#41×C₁₉	—	4	2	no	—
273	#41×C₁₉	—	4	2	no	—
274	C₂×Q₈×C₁₉	—	2	2	no	—
275	C₂×Q₈×C₁₉	—	4	2	no	—
276	C₂×Q₈×C₁₉	—	4	2	no	—
277	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
278	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
279	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
280	C₂×D₄×C₁₉	—	2	2	no	—
281	C₂×D₄×C₁₉	—	2	2	no	—
282	C₂×D₄×C₁₉	—	2	2	no	—
283	C₂×D₄×C₁₉	—	2	2	no	—
284	C₂×D₄×C₁₉	—	2	2	no	—
285	C₂×D₄×C₁₉	—	2	2	no	—
286	C₂×D₄×C₁₉	—	2	2	no	—
287	C₂×D₄×C₁₉	—	2	2	no	—
288	C₂×D₄×C₁₉	—	2	2	no	—
289	C₂×D₄×C₁₉	—	4	2	no	—
290	C₂×D₄×C₁₉	—	4	2	no	—
291	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
292	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
294	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
295	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
296	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
297	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
298	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₉	—	2	2	no	—
300	C₂²×C₄×C₁₉	—	2	2	no	—
301	C₂²×C₄×C₁₉	—	2	2	no	—
302	C₂²×C₄×C₁₉	—	2	2	no	—
303	C₂²×C₄×C₁₉	—	2	2	no	—
304	C₂²×C₄×C₁₉	—	2	2	no	—
305	C₂²×C₄×C₁₉	—	2	2	no	—
306	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
311	Q₁₆×C₁₉	—	2	2	no	—
312	Q₁₆×C₁₉	—	4	1	no	—
313	Q₁₆×C₁₉	—	4	2	no	—
314	SD₁₆×C₁₉	—	2	4	no	—
315	SD₁₆×C₁₉	—	4	2	no	—
316	SD₁₆×C₁₉	—	4	2	no	—
317	SD₁₆×C₁₉	—	4	2	no	—
318	D₈×C₁₉	—	2	2	no	—
319	D₈×C₁₉	—	4	1	no	—
320	D₈×C₁₉	—	4	2	no	—
321	M₁₆×C₁₉	—	2	4	no	—
322	M₁₆×C₁₉	—	2	4	no	—
323	M₁₆×C₁₉	—	4	2	no	—
324	C₂×C₈×C₁₉	—	2	2	no	—
325	C₂×C₈×C₁₉	—	4	1	no	—
326	C₂×C₈×C₁₉	—	4	2	no	—
327	C₂×C₈×C₁₉	—	4	2	no	—
328	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
329	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
330	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
331	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
332	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄×C₁₉	—	2	2	no	—
335	C₄⋊C₄×C₁₉	—	2	2	no	—
336	C₄⋊C₄×C₁₉	—	2	2	no	—
337	C₄⋊C₄×C₁₉	—	2	2	no	—
338	C₄⋊C₄×C₁₉	—	2	2	no	—
339	C₄⋊C₄×C₁₉	—	2	2	no	—
340	C₄⋊C₄×C₁₉	—	2	2	no	—
341	C₄⋊C₄×C₁₉	—	2	2	no	—
342	C₄⋊C₄×C₁₉	—	2	2	no	—
343	C₄⋊C₄×C₁₉	—	2	2	no	—
344	C₄⋊C₄×C₁₉	—	2	2	no	—
345	C₄⋊C₄×C₁₉	—	2	2	no	—
346	C₄⋊C₄×C₁₉	—	2	2	no	—
347	C₄⋊C₄×C₁₉	—	2	2	no	—
348	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
351	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
352	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
355	C₂²⋊C₄×C₁₉	—	2	2	no	—
356	C₂²⋊C₄×C₁₉	—	2	2	no	—
357	C₂²⋊C₄×C₁₉	—	2	2	no	—
358	C₂²⋊C₄×C₁₉	—	2	2	no	—
359	C₂²⋊C₄×C₁₉	—	2	2	no	—
360	C₂²⋊C₄×C₁₉	—	2	2	no	—
361	C₂²⋊C₄×C₁₉	—	2	2	no	—
362	C₂²⋊C₄×C₁₉	—	2	2	no	—
363	C₂²⋊C₄×C₁₉	—	2	2	no	—
364	C₂²⋊C₄×C₁₉	—	2	2	no	—
365	C₂²⋊C₄×C₁₉	—	2	2	no	—
366	C₂²⋊C₄×C₁₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₉	—	2	2	no	—
369	C₂²⋊C₄×C₁₉	—	2	2	no	—
370	C₂²⋊C₄×C₁₉	—	2	2	no	—
371	C₂²⋊C₄×C₁₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₉	—	2	2	no	—
373	C₂²⋊C₄×C₁₉	—	2	2	no	—
374	C₂²⋊C₄×C₁₉	—	2	2	no	—
375	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
379	C₄²×C₁₉	—	2	2	no	—
380	C₄²×C₁₉	—	2	2	no	—
381	C₄²×C₁₉	—	2	2	no	—
382	C₄²×C₁₉	—	2	2	no	—
383	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
386	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
387	#62344	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂³×C₁₉	—	2	2	no	—
389	C₂³×C₁₉	—	2	2	no	—
390	C₂³×C₁₉	—	8	2	no	—
391	C₂³×C₁₉	—	8	2	no	—
392	C₂³×C₁₉	—	8	2	no	—
393	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
394	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
395	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
396	Q₈×C₁₉	—	2	2	no	—
397	Q₈×C₁₉	—	2	2	no	—
398	Q₈×C₁₉	—	2	2	no	—
399	Q₈×C₁₉	—	2	2	no	—
400	Q₈×C₁₉	—	4	2	no	—
401	Q₈×C₁₉	—	8	2	no	—
402	D₄×C₁₉	—	2	2	no	—
403	D₄×C₁₉	—	2	2	no	—
404	D₄×C₁₉	—	2	2	no	—
405	D₄×C₁₉	—	2	2	no	—
406	D₄×C₁₉	—	4	2	no	—
407	D₄×C₁₉	—	4	1	no	—
408	D₄×C₁₉	—	4	1	no	—
409	D₄×C₁₉	—	4	2	no	—
410	D₄×C₁₉	—	4	2	no	—
411	D₄×C₁₉	—	4	2	no	—
412	D₄×C₁₉	—	8	2	no	—
413	D₄×C₁₉	—	8	2	no	—
414	D₄×C₁₉	—	8	2	no	—
415	D₄×C₁₉	—	8	2	no	—
416	D₄×C₁₉	—	8	2	no	—
417	D₄×C₁₉	—	8	2	no	—
418	D₄×C₁₉	—	8	2	no	—
419	D₄×C₁₉	—	8	2	no	—
420	D₄×C₁₉	—	8	2	no	—
421	C₂×C₄×C₁₉	—	2	1	no	—
422	C₂×C₄×C₁₉	—	2	2	no	—
423	C₂×C₄×C₁₉	—	2	2	no	—
424	C₂×C₄×C₁₉	—	2	1	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	2	no	—
429	C₂×C₄×C₁₉	—	2	2	no	—
430	C₂×C₄×C₁₉	—	2	2	no	—
431	C₂×C₄×C₁₉	—	2	2	no	—
432	C₂×C₄×C₁₉	—	2	2	no	—
433	C₂×C₄×C₁₉	—	4	1	no	—
434	C₂×C₄×C₁₉	—	4	1	no	—
435	C₂×C₄×C₁₉	—	8	2	no	—
436	C₂×C₄×C₁₉	—	8	2	no	—
437	C₂×C₄×C₁₉	—	8	2	no	—
438	C₂×C₄×C₁₉	—	8	2	no	—
439	C₂×C₄×C₁₉	—	8	2	no	—
440	C₂×C₄×C₁₉	—	8	2	no	—
441	C₂×C₄×C₁₉	—	8	2	no	—
442	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
450	C₈×C₁₉	—	2	1	no	—
451	C₈×C₁₉	—	2	2	no	—
452	C₈×C₁₉	—	2	2	no	—
453	C₈×C₁₉	—	2	1	no	—
454	C₈×C₁₉	—	2	1	no	—
455	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
456	#3551	C₂×C₁₉	1	2	yes	complemented
457	#3355	C₂×C₁₉	1	1	yes	characteristic, complemented
458	#3352	C₂×C₁₉	1	1	yes	characteristic, complemented
459	#3351	C₂×C₁₉	1	2	yes	complemented
460	#3301	C₂×C₁₉	1	2	yes	complemented
461	#3300	C₂×C₁₉	1	2	yes	complemented
462	#3297	C₂×C₁₉	1	2	yes	complemented
463	#3296	C₂×C₁₉	1	2	yes	complemented
464	#3277	C₂×C₁₉	1	1	yes	characteristic, complemented
465	#3275	C₂×C₁₉	1	2	yes	complemented
466	#3273	C₂×C₁₉	1	1	yes	characteristic, complemented
467	#3256	C₂×C₁₉	1	2	yes	complemented
468	#3201	C₂×C₁₉	1	2	yes	complemented
469	#3198	C₂×C₁₉	1	2	yes	complemented
470	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
471	#3168	C₂×C₁₉	1	1	yes	characteristic, complemented
472	#3063	C₂×C₁₉	1	2	yes	complemented
473	#3062	C₂×C₁₉	1	2	yes	complemented
474	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
475	C₂²×C₁₉	—	2	1	no	—
476	C₂²×C₁₉	—	2	1	no	—
477	C₂²×C₁₉	—	2	2	no	—
478	C₂²×C₁₉	—	2	2	no	—
479	C₂²×C₁₉	—	2	2	no	—
480	C₂²×C₁₉	—	2	2	no	—
481	C₂²×C₁₉	—	2	2	no	—
482	C₂²×C₁₉	—	2	1	no	—
483	C₂²×C₁₉	—	2	2	no	—
484	C₂²×C₁₉	—	4	2	no	—
485	C₂²×C₁₉	—	4	2	no	—
486	C₂²×C₁₉	—	4	2	no	—
487	C₂²×C₁₉	—	4	2	no	—
488	C₂²×C₁₉	—	4	2	no	—
489	C₂²×C₁₉	—	4	2	no	—
490	C₂²×C₁₉	—	16	4	no	—
491	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
492	C₄×C₁₉	—	2	1	no	—
493	C₄×C₁₉	—	2	1	no	—
494	C₄×C₁₉	—	2	1	no	—
495	C₄×C₁₉	—	2	1	no	—
496	C₄×C₁₉	—	2	2	no	—
497	C₄×C₁₉	—	2	2	no	—
498	C₄×C₁₉	—	2	1	no	—
499	C₄×C₁₉	—	4	2	no	—
500	C₄×C₁₉	—	4	2	no	—
501	C₄×C₁₉	—	4	2	no	—
502	C₄×C₁₉	—	4	2	no	—
503	C₄×C₁₉	—	4	2	no	—
504	C₄×C₁₉	—	4	2	no	—
505	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	C₄×C₁₉	#585	1	1	yes	characteristic
507	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
508	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	2	yes	—
509	C₂×#131	C₂²×C₁₉	1	2	yes	complemented
510	#563	—	2	2	no	—
511	#560	—	2	2	no	—
512	#555	—	2	2	no	—
513	#553	C₂²×C₁₉	1	2	yes	—
514	#553	C₂²×C₁₉	1	2	yes	complemented
515	#552	C₂²×C₁₉	1	2	yes	—
516	#552	C₂²×C₁₉	1	2	yes	complemented
517	#551	—	2	2	no	—
518	#548	C₂²×C₁₉	1	2	yes	—
519	#548	C₂²×C₁₉	1	2	yes	complemented
520	#546	C₂²×C₁₉	1	2	yes	—
521	#546	C₂²×C₁₉	1	2	yes	complemented
522	#540	—	2	2	no	—
523	#540	—	2	2	no	—
524	#538	—	2	2	no	—
525	#538	—	2	2	no	—
526	#537	C₂²×C₁₉	1	2	yes	—
527	#537	C₂²×C₁₉	1	2	yes	—
528	#536	C₂²×C₁₉	1	2	yes	complemented
529	#535	C₂²×C₁₉	1	2	yes	complemented
530	#532	C₂²×C₁₉	1	1	yes	characteristic
531	#529	C₂²×C₁₉	1	2	yes	complemented
532	#529	C₂²×C₁₉	1	2	yes	complemented
533	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
534	#499	C₂²×C₁₉	1	1	yes	characteristic, complemented
535	#495	C₂²×C₁₉	1	1	yes	characteristic
536	#495	C₂²×C₁₉	1	1	yes	characteristic
537	#488	C₂²×C₁₉	1	2	yes	complemented
538	#488	C₂²×C₁₉	1	2	yes	complemented
539	#485	C₂²×C₁₉	1	2	yes	complemented
540	#485	C₂²×C₁₉	1	2	yes	complemented
541	#484	C₂²×C₁₉	1	2	yes	complemented
542	#483	C₂²×C₁₉	1	2	yes	complemented
543	#482	C₂²×C₁₉	1	2	yes	—
544	#482	C₂²×C₁₉	1	2	yes	complemented
545	#481	C₂²×C₁₉	1	2	yes	complemented
546	#480	C₂²×C₁₉	1	2	yes	complemented
547	#479	C₂²×C₁₉	1	2	yes	complemented
548	#479	C₂²×C₁₉	1	2	yes	complemented
549	#478	C₂²×C₁₉	1	2	yes	complemented
550	#478	C₂²×C₁₉	1	2	yes	complemented
551	#470	C₂²×C₁₉	1	2	yes	complemented
552	#470	C₂²×C₁₉	1	2	yes	complemented
553	#469	C₂²×C₁₉	1	2	yes	—
554	#469	C₂²×C₁₉	1	2	yes	—
555	#468	C₂²×C₁₉	1	2	yes	—
556	#468	C₂²×C₁₉	1	2	yes	complemented
557	#468	C₂²×C₁₉	1	2	yes	complemented
558	#468	C₂²×C₁₉	1	2	yes	complemented
559	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
560	#467	C₂²×C₁₉	1	1	yes	characteristic, complemented
561	#467	C₂²×C₁₉	1	2	yes	complemented
562	#466	C₂²×C₁₉	1	1	yes	characteristic
563	#466	C₂²×C₁₉	1	1	yes	characteristic
564	#466	C₂²×C₁₉	1	2	yes	—
565	#465	C₂²×C₁₉	1	2	yes	—
566	#465	C₂²×C₁₉	1	2	yes	complemented
567	#465	C₂²×C₁₉	1	2	yes	complemented
568	#465	C₂²×C₁₉	1	2	yes	complemented
569	#464	C₂²×C₁₉	1	2	yes	complemented
570	#464	C₂²×C₁₉	1	2	yes	complemented
571	#463	C₂²×C₁₉	1	2	yes	—
572	#463	C₂²×C₁₉	1	2	yes	—
573	#452	C₂²×C₁₉	1	2	yes	—
574	#452	C₂²×C₁₉	1	2	yes	—
575	#451	C₂²×C₁₉	1	2	yes	complemented
576	#450	C₂²×C₁₉	1	2	yes	complemented
577	#449	C₂²×C₁₉	1	2	yes	—
578	#449	C₂²×C₁₉	1	2	yes	—
579	#448	C₂²×C₁₉	1	2	yes	complemented
580	#447	C₂²×C₁₉	1	2	yes	—
581	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
582	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
583	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
584	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
585	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
586	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
587	#436	C₂²×C₁₉	1	1	yes	characteristic
588	#436	C₂²×C₁₉	1	2	yes	complemented
589	#436	C₂²×C₁₉	1	1	yes	characteristic, complemented
590	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
591	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
592	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
593	#428	C₂²×C₁₉	1	2	yes	complemented
594	#428	C₂²×C₁₉	1	2	yes	complemented
595	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
596	#416	C₂²×C₁₉	1	2	yes	—
597	#416	C₂²×C₁₉	1	2	yes	complemented
598	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
599	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
600	#408	C₂²×C₁₉	1	2	yes	complemented
601	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
602	C₂×C₁₉	—	4	1	no	—
603	C₂×C₁₉	—	4	2	no	—
604	C₂×C₁₉	—	4	2	no	—
605	C₂×C₁₉	—	8	2	no	—
606	C₂×C₁₉	—	8	2	no	—
607	C₂×C₁₉	#3496	1	1	yes	characteristic
608	C₂×C₁₉	#3584	1	1	yes	characteristic
609	C₂×C₁₉	#3584	1	1	yes	characteristic
610	C₂×#41	C₂³×C₁₉	1	2	yes	—
611	C₂×#41	C₂³×C₁₉	1	2	yes	—
612	C₂×#41	C₂³×C₁₉	1	2	yes	—
613	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
614	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
615	#137	—	4	4	no	—
616	AGL(1,ℤ/8)	—	4	4	no	—
617	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
618	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
619	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
620	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
623	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
624	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
625	C₂×D₈	C₂³×C₁₉	1	2	yes	—
626	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
627	#131	—	4	4	no	—
628	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
629	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
630	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
631	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
632	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
633	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
634	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
637	#127	—	2	2	no	—
638	#127	D₄×C₁₉	1	1	yes	characteristic
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	C₂³×C₁₉	1	2	yes	—
648	#125	C₂³×C₁₉	1	2	yes	—
649	#124	—	2	2	no	—
650	#124	—	2	2	no	—
651	#124	—	2	2	no	—
652	#124	—	2	2	no	—
653	#124	D₄×C₁₉	1	2	yes	—
654	#124	C₂³×C₁₉	1	2	yes	—
655	#124	C₂³×C₁₉	1	2	yes	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
671	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
672	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
673	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
674	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
675	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	2	no	—
681	#121	—	2	2	no	—
682	#121	—	2	2	no	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	—	2	2	no	—
686	#121	—	2	2	no	—
687	#121	—	2	2	no	—
688	#121	D₄×C₁₉	1	1	yes	characteristic
689	#121	D₄×C₁₉	1	2	yes	—
690	#121	D₄×C₁₉	1	1	yes	characteristic
691	#121	C₂³×C₁₉	1	2	yes	—
692	#121	C₂³×C₁₉	1	2	yes	—
693	#121	C₂³×C₁₉	1	2	yes	—
694	#121	C₂³×C₁₉	1	2	yes	—
695	#121	C₂³×C₁₉	1	2	yes	—
696	#121	C₂³×C₁₉	1	2	yes	—
697	#120	—	2	2	no	—
698	#120	—	2	2	no	—
699	#120	—	2	2	no	—
700	#120	—	2	2	no	—
701	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
702	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	2	no	—
708	C₄×D₄	—	2	2	no	—
709	C₄×D₄	C₂³×C₁₉	1	2	yes	—
710	C₄×D₄	C₂³×C₁₉	1	2	yes	—
711	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
712	C₄×D₄	C₂³×C₁₉	1	2	yes	—
713	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
714	#117	—	2	2	no	—
715	#117	—	2	2	no	—
716	#117	—	2	2	no	—
717	#117	—	2	2	no	—
718	#117	C₂³×C₁₉	1	2	yes	—
719	#117	C₂³×C₁₉	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
722	C₂×C₂²⋊C₄	—	2	2	no	—
723	C₂×C₂²⋊C₄	—	2	2	no	—
724	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
725	#107	C₂³×C₁₉	1	1	yes	characteristic
726	#107	C₂³×C₁₉	1	1	yes	characteristic
727	#107	C₂³×C₁₉	1	2	yes	—
728	#107	C₂³×C₁₉	1	2	yes	—
729	#107	C₂³×C₁₉	1	1	yes	characteristic
730	#107	C₂³×C₁₉	1	1	yes	characteristic
731	#106	C₂³×C₁₉	1	2	yes	—
732	#106	C₂³×C₁₉	1	2	yes	—
733	#106	C₂³×C₁₉	1	2	yes	—
734	#106	C₂³×C₁₉	1	2	yes	—
735	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
736	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
737	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
738	#103	C₂³×C₁₉	1	2	yes	—
739	#103	C₂³×C₁₉	1	2	yes	—
740	#103	C₂³×C₁₉	1	2	yes	—
741	#103	C₂³×C₁₉	1	2	yes	—
742	#103	C₂³×C₁₉	1	2	yes	—
743	#103	C₂³×C₁₉	1	2	yes	—
744	#103	C₂³×C₁₉	1	2	yes	—
745	#103	C₂³×C₁₉	1	2	yes	—
746	#102	C₂³×C₁₉	1	2	yes	—
747	#102	C₂³×C₁₉	1	2	yes	—
748	#102	C₂³×C₁₉	1	2	yes	—
749	#102	C₂³×C₁₉	1	2	yes	—
750	#102	C₂³×C₁₉	1	2	yes	—
751	#102	C₂³×C₁₉	1	2	yes	—
752	#102	C₂³×C₁₉	1	2	yes	—
753	#102	C₂³×C₁₉	1	2	yes	—
754	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
756	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
758	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
759	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
760	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
761	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
762	C₁₉	#62344	1	1	yes	characteristic, direct product factor, Sylow
763	C₂⁴	—	2	2	no	—
764	#41	—	4	2	no	—
765	#41	—	4	2	no	—
766	#41	—	4	2	no	—
767	#41	—	4	2	no	—
768	#41	—	4	2	no	—
769	#41	—	4	2	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	—	4	2	no	—
773	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
774	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
775	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	4	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
788	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
789	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
790	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
791	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
792	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
793	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
794	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
807	Q₁₆	—	2	2	no	—
808	Q₁₆	—	4	1	no	—
809	Q₁₆	—	4	2	no	—
810	SD₁₆	—	2	4	no	—
811	SD₁₆	—	4	2	no	—
812	SD₁₆	—	4	2	no	—
813	SD₁₆	—	4	2	no	—
814	D₈	—	2	2	no	—
815	D₈	—	4	1	no	—
816	D₈	—	4	2	no	—
817	M₁₆	—	2	4	no	—
818	M₁₆	—	2	4	no	—
819	M₁₆	—	4	2	no	—
820	C₂×C₈	—	2	2	no	—
821	C₂×C₈	—	4	1	no	—
822	C₂×C₈	—	4	2	no	—
823	C₂×C₈	—	4	2	no	—
824	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
825	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
826	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
827	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
828	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
829	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
845	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
846	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
872	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
873	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
874	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
880	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
881	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
882	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	8	2	no	—
886	C₂³	—	8	2	no	—
887	C₂³	—	8	2	no	—
888	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
889	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
890	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	2	no	—
896	Q₈	—	8	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	2	2	no	—
899	D₄	—	2	2	no	—
900	D₄	—	2	2	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	2	no	—
903	D₄	—	4	2	no	—
904	D₄	—	4	2	no	—
905	D₄	—	4	1	no	—
906	D₄	—	4	1	no	—
907	D₄	—	8	2	no	—
908	D₄	—	8	2	no	—
909	D₄	—	8	2	no	—
910	D₄	—	8	2	no	—
911	D₄	—	8	2	no	—
912	D₄	—	8	2	no	—
913	D₄	—	8	2	no	—
914	D₄	—	8	2	no	—
915	D₄	—	8	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	2	no	—
937	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
939	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
940	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
944	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
945	C₈	—	2	1	no	—
946	C₈	—	2	2	no	—
947	C₈	—	2	2	no	—
948	C₈	—	2	1	no	—
949	C₈	—	2	1	no	—
950	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	16	4	no	—
967	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	1	no	—
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
982	C₄	C₁₉×#585	1	1	yes	characteristic
983	C₂	—	4	2	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	1	no	—
986	C₂	—	8	2	no	—
987	C₂	—	8	2	no	—
988	C₂	C₁₉×#3496	1	1	yes	characteristic
989	C₂	C₁₉×#3584	1	1	yes	characteristic
990	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3551	C₂	semidirect
2. C₁₉×#3355	C₂	semidirect
3. C₁₉×#3352	C₂	semidirect
4. C₁₉×#3351	C₂	semidirect
5. C₁₉×#3301	C₂	semidirect
6. C₁₉×#3300	C₂	semidirect
7. C₁₉×#3297	C₂	semidirect
8. C₁₉×#3296	C₂	semidirect
9. C₁₉×#3277	C₂	semidirect
10. C₁₉×#3275	C₂	semidirect
11. C₁₉×#3273	C₂	semidirect
12. C₁₉×#3256	C₂	semidirect
13. C₁₉×#3201	C₂	semidirect
14. C₁₉×#3198	C₂	semidirect
15. C₁₉×#3168	C₂	semidirect
16. C₁₉×#3168	C₂	semidirect
17. C₁₉×#3063	C₂	semidirect
18. C₁₉×#3062	C₂	semidirect
19. C₁₉×#2931	C₂	semidirect
20. C₂×C₁₉×#137	C₂²	semidirect
22. C₂×C₁₉×#131	C₂²	semidirect
27. C₁₉×#553	C₂²	semidirect
29. C₁₉×#552	C₂²	semidirect
32. C₁₉×#548	C₂²	semidirect
34. C₁₉×#546	C₂²	semidirect
41. C₁₉×#536	C₂²	semidirect
42. C₁₉×#535	C₂²	semidirect
44. C₁₉×#529	C₂²	semidirect
45. C₁₉×#529	C₂²	semidirect
46. C₁₉×#499	C₂²	semidirect
47. C₁₉×#499	C₂²	semidirect
50. C₁₉×#488	C₂²	semidirect
51. C₁₉×#488	C₂²	semidirect
52. C₁₉×#485	C₂²	semidirect
53. C₁₉×#485	C₂²	semidirect
54. C₁₉×#484	C₂²	semidirect
55. C₁₉×#483	C₂²	semidirect
57. C₁₉×#482	C₂²	semidirect
58. C₁₉×#481	C₂²	semidirect
59. C₁₉×#480	C₂²	semidirect
60. C₁₉×#479	C₂²	semidirect
61. C₁₉×#479	C₂²	semidirect
62. C₁₉×#478	C₂²	semidirect
63. C₁₉×#478	C₂²	semidirect
64. C₁₉×#470	C₂²	semidirect
65. C₁₉×#470	C₂²	semidirect
69. C₁₉×#468	C₂²	semidirect
70. C₁₉×#468	C₂²	semidirect
71. C₁₉×#468	C₂²	semidirect
72. C₁₉×#467	C₂²	semidirect
73. C₁₉×#467	C₂²	semidirect
74. C₁₉×#467	C₂²	semidirect
79. C₁₉×#465	C₂²	semidirect
80. C₁₉×#465	C₂²	semidirect
81. C₁₉×#465	C₂²	semidirect
82. C₁₉×#464	C₂²	semidirect
83. C₁₉×#464	C₂²	semidirect
88. C₁₉×#451	C₂²	semidirect
89. C₁₉×#450	C₂²	semidirect
92. C₁₉×#448	C₂²	semidirect
94. C₄×Q₁₆×C₁₉	C₂²	semidirect
95. C₄×Q₁₆×C₁₉	C₂²	semidirect
96. C₄×SD₁₆×C₁₉	C₂²	semidirect
97. C₄×SD₁₆×C₁₉	C₂²	semidirect
101. C₁₉×#436	C₂²	semidirect
102. C₁₉×#436	C₂²	semidirect
104. C₈×D₄×C₁₉	C₂²	semidirect
105. C₈×D₄×C₁₉	C₂²	semidirect
106. C₁₉×#428	C₂²	semidirect
107. C₁₉×#428	C₂²	semidirect
108. C₁₉×#423	C₂²	semidirect
110. C₁₉×#416	C₂²	semidirect
111. C₂×C₁₉×#103	C₂²	semidirect
112. C₂×C₁₉×#102	C₂²	semidirect
113. C₁₉×#408	C₂²	semidirect
114. C₂×C₄×C₈×C₁₉	C₂²	semidirect
387. #62344	C₁₉	direct (N × H)
456. #3551	C₂×C₁₉	semidirect
457. #3355	C₂×C₁₉	semidirect
458. #3352	C₂×C₁₉	semidirect
459. #3351	C₂×C₁₉	semidirect
460. #3301	C₂×C₁₉	semidirect
461. #3300	C₂×C₁₉	semidirect
462. #3297	C₂×C₁₉	semidirect
463. #3296	C₂×C₁₉	semidirect
464. #3277	C₂×C₁₉	semidirect
465. #3275	C₂×C₁₉	semidirect
466. #3273	C₂×C₁₉	semidirect
467. #3256	C₂×C₁₉	semidirect
468. #3201	C₂×C₁₉	semidirect
469. #3198	C₂×C₁₉	semidirect
470. #3168	C₂×C₁₉	semidirect
471. #3168	C₂×C₁₉	semidirect
472. #3063	C₂×C₁₉	semidirect
473. #3062	C₂×C₁₉	semidirect
474. #2931	C₂×C₁₉	semidirect
507. C₂×#137	C₂²×C₁₉	semidirect
509. C₂×#131	C₂²×C₁₉	semidirect
514. #553	C₂²×C₁₉	semidirect
516. #552	C₂²×C₁₉	semidirect
519. #548	C₂²×C₁₉	semidirect
521. #546	C₂²×C₁₉	semidirect
528. #536	C₂²×C₁₉	semidirect
529. #535	C₂²×C₁₉	semidirect
531. #529	C₂²×C₁₉	semidirect
532. #529	C₂²×C₁₉	semidirect
533. #499	C₂²×C₁₉	semidirect
534. #499	C₂²×C₁₉	semidirect
537. #488	C₂²×C₁₉	semidirect
538. #488	C₂²×C₁₉	semidirect
539. #485	C₂²×C₁₉	semidirect
540. #485	C₂²×C₁₉	semidirect
541. #484	C₂²×C₁₉	semidirect
542. #483	C₂²×C₁₉	semidirect
544. #482	C₂²×C₁₉	semidirect
545. #481	C₂²×C₁₉	semidirect
546. #480	C₂²×C₁₉	semidirect
547. #479	C₂²×C₁₉	semidirect
548. #479	C₂²×C₁₉	semidirect
549. #478	C₂²×C₁₉	semidirect
550. #478	C₂²×C₁₉	semidirect
551. #470	C₂²×C₁₉	semidirect
552. #470	C₂²×C₁₉	semidirect
556. #468	C₂²×C₁₉	semidirect
557. #468	C₂²×C₁₉	semidirect
558. #468	C₂²×C₁₉	semidirect
559. #467	C₂²×C₁₉	semidirect
560. #467	C₂²×C₁₉	semidirect
561. #467	C₂²×C₁₉	semidirect
566. #465	C₂²×C₁₉	semidirect
567. #465	C₂²×C₁₉	semidirect
568. #465	C₂²×C₁₉	semidirect
569. #464	C₂²×C₁₉	semidirect
570. #464	C₂²×C₁₉	semidirect
575. #451	C₂²×C₁₉	semidirect
576. #450	C₂²×C₁₉	semidirect
579. #448	C₂²×C₁₉	semidirect
581. C₄×Q₁₆	C₂²×C₁₉	semidirect
582. C₄×Q₁₆	C₂²×C₁₉	semidirect
583. C₄×SD₁₆	C₂²×C₁₉	semidirect
584. C₄×SD₁₆	C₂²×C₁₉	semidirect
588. #436	C₂²×C₁₉	semidirect
589. #436	C₂²×C₁₉	semidirect
591. C₈×D₄	C₂²×C₁₉	semidirect
592. C₈×D₄	C₂²×C₁₉	semidirect
593. #428	C₂²×C₁₉	semidirect
594. #428	C₂²×C₁₉	semidirect
595. #423	C₂²×C₁₉	semidirect
597. #416	C₂²×C₁₉	semidirect
598. C₂×#103	C₂²×C₁₉	semidirect
599. C₂×#102	C₂²×C₁₉	semidirect
600. #408	C₂²×C₁₉	semidirect
601. C₂×C₄×C₈	C₂²×C₁₉	semidirect
762. C₁₉	#62344	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×#3551	2
C₁₉×#3355	2
C₁₉×#3352	2
C₁₉×#3351	2
C₁₉×#3301	2
C₁₉×#3300	2
C₁₉×#3297	2
C₁₉×#3296	2
C₁₉×#3277	2
C₁₉×#3275	2
C₁₉×#3273	2
C₁₉×#3256	2
C₁₉×#3201	2
C₁₉×#3198	2
C₁₉×#3168	2
C₁₉×#3063	2
C₁₉×#3062	2
C₁₉×#2931	2
#62344	19

Subgroups — C19×#62344 #18068303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62344 #18068303