Subgroups — C₁₉×#62402 #18068361

Order 4864.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3554	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3400	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3372	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3371	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3260	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3178	C₂	1	2	yes	maximal, complemented
21	C₁₉×#3174	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#564	—	2	2	no	—
25	C₁₉×#562	—	2	2	no	—
26	C₁₉×#559	C₂²	1	1	yes	characteristic
27	C₁₉×#559	C₂²	1	2	yes	—
28	C₁₉×#557	—	2	1	no	—
29	C₁₉×#557	—	2	1	no	—
30	C₁₉×#557	C₂²	1	1	yes	characteristic
31	C₁₉×#557	C₂²	1	2	yes	—
32	C₁₉×#557	C₂²	1	1	yes	characteristic
33	C₁₉×#557	C₂²	1	1	yes	characteristic
34	C₁₉×#557	C₂²	1	1	yes	characteristic
35	C₁₉×#557	C₂²	1	1	yes	characteristic
36	C₁₉×#557	C₂²	1	2	yes	—
37	C₁₉×#554	C₂²	1	2	yes	—
38	C₁₉×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#548	—	2	1	no	—
41	C₁₉×#547	—	2	1	no	—
42	C₁₉×#542	—	2	1	no	—
43	C₁₉×#542	C₂²	1	2	yes	—
44	C₁₉×#541	—	2	1	no	—
45	C₁₉×#541	—	2	1	no	—
46	C₁₉×#541	—	2	2	no	—
47	C₁₉×#541	C₂²	1	2	yes	—
48	C₁₉×#541	C₂²	1	2	yes	—
49	C₁₉×#540	C₂²	1	2	yes	—
50	C₁₉×#539	—	2	2	no	—
51	C₁₉×#536	—	2	1	no	—
52	C₁₉×#533	C₂²	1	1	yes	characteristic
53	C₁₉×#533	C₂²	1	1	yes	characteristic
54	C₁₉×#533	C₂²	1	1	yes	characteristic
55	C₁₉×#532	C₂²	1	1	yes	characteristic
56	C₁₉×#529	C₂²	1	1	yes	characteristic
57	C₁₉×#501	C₂²	1	1	yes	characteristic
58	C₁₉×#501	C₂²	1	2	yes	—
59	C₁₉×#500	C₂²	1	1	yes	characteristic
60	C₁₉×#499	C₂²	1	2	yes	—
61	C₁₉×#497	C₂²	1	1	yes	characteristic
62	C₁₉×#497	C₂²	1	2	yes	—
63	C₁₉×#492	C₂²	1	2	yes	—
64	C₁₉×#492	C₂²	1	1	yes	characteristic
65	C₁₉×#491	C₂²	1	1	yes	characteristic
66	C₁₉×#491	C₂²	1	2	yes	—
67	C₁₉×#490	C₂²	1	2	yes	—
68	C₁₉×#489	C₂²	1	1	yes	characteristic
69	C₁₉×#488	C₂²	1	2	yes	—
70	C₁₉×#487	C₂²	1	2	yes	—
71	C₁₉×#487	C₂²	1	1	yes	characteristic
72	C₁₉×#486	C₂²	1	1	yes	characteristic
73	C₁₉×#479	C₂²	1	2	yes	—
74	C₁₉×#479	C₂²	1	2	yes	—
75	C₁₉×#479	C₂²	1	2	yes	—
76	C₁₉×#479	C₂²	1	2	yes	—
77	C₁₉×#478	C₂²	1	2	yes	—
78	C₁₉×#478	C₂²	1	2	yes	—
79	C₁₉×#478	C₂²	1	2	yes	—
80	C₁₉×#477	C₂²	1	2	yes	—
81	C₁₉×#476	C₂²	1	2	yes	—
82	C₁₉×#475	C₂²	1	1	yes	characteristic
83	C₁₉×#475	C₂²	1	1	yes	characteristic
84	C₁₉×#475	C₂²	1	1	yes	characteristic
85	C₁₉×#475	C₂²	1	2	yes	—
86	C₁₉×#474	C₂²	1	1	yes	characteristic
87	C₁₉×#470	C₂²	1	1	yes	characteristic
88	C₁₉×#470	C₂²	1	1	yes	characteristic
89	C₁₉×#468	C₂²	1	1	yes	characteristic
90	C₁₉×#468	C₂²	1	1	yes	characteristic
91	C₁₉×#468	C₂²	1	2	yes	—
92	C₁₉×#468	C₂²	1	2	yes	—
93	C₁₉×#467	C₂²	1	2	yes	—
94	C₁₉×#465	C₂²	1	2	yes	—
95	C₁₉×#465	C₂²	1	2	yes	—
96	C₁₉×#465	C₂²	1	2	yes	—
97	C₁₉×#464	C₂²	1	2	yes	—
98	C₁₉×#464	C₂²	1	2	yes	—
99	C₁₉×#464	C₂²	1	2	yes	—
100	C₁₉×#462	C₂²	1	1	yes	characteristic
101	C₁₉×#462	C₂²	1	2	yes	—
102	C₁₉×#461	C₂²	1	2	yes	—
103	C₁₉×#461	C₂²	1	1	yes	characteristic
104	C₁₉×#461	C₂²	1	2	yes	—
105	C₁₉×#461	C₂²	1	2	yes	—
106	C₁₉×#461	C₂²	1	2	yes	—
107	C₁₉×#460	C₂²	1	1	yes	characteristic
108	C₁₉×#460	C₂²	1	1	yes	characteristic
109	C₁₉×#460	C₂²	1	2	yes	—
110	C₁₉×#460	C₂²	1	2	yes	—
111	C₁₉×#446	C₂²	1	1	yes	characteristic
112	C₁₉×#446	C₂²	1	2	yes	—
113	C₁₉×#446	C₂²	1	1	yes	characteristic
114	C₁₉×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
117	C₁₉×#441	C₂²	1	2	yes	—
118	C₁₉×#440	C₂²	1	2	yes	—
119	C₁₉×#440	C₂²	1	2	yes	—
120	C₁₉×#440	C₂²	1	2	yes	—
121	C₁₉×#440	C₂²	1	2	yes	—
122	C₁₉×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
125	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
129	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
130	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
131	C₁₉×#424	C₂²	1	2	yes	—
132	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
133	C₁₉×#405	C₂²	1	2	yes	—
134	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₁₉	—	2	1	no	—
136	C₂×#41×C₁₉	—	2	1	no	—
137	C₂²×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
148	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
151	C₁₉×C₄⋊Q₈	—	2	1	no	—
152	C₁₉×C₄⋊Q₈	—	2	1	no	—
153	C₁₉×C₄⋊Q₈	—	2	1	no	—
154	C₁₉×C₄⋊Q₈	—	2	2	no	—
155	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₉×#127	C₂³	1	1	yes	characteristic
166	C₁₉×#127	C₂³	1	2	yes	—
167	C₁₉×#126	—	2	2	no	—
168	C₁₉×#126	—	2	2	no	—
169	C₁₉×#126	—	2	2	no	—
170	C₁₉×#126	—	2	2	no	—
171	C₁₉×#126	—	2	2	no	—
172	C₁₉×#126	—	2	1	no	—
173	C₁₉×#125	—	2	2	no	—
174	C₁₉×#125	—	2	1	no	—
175	C₁₉×#125	—	2	1	no	—
176	C₁₉×#125	—	2	2	no	—
177	C₁₉×#125	—	2	2	no	—
178	C₁₉×#125	—	2	2	no	—
179	C₁₉×#125	—	2	2	no	—
180	C₁₉×#125	—	2	2	no	—
181	C₁₉×#125	—	2	2	no	—
182	C₁₉×#125	—	2	2	no	—
183	C₁₉×#125	—	2	2	no	—
184	C₁₉×#125	—	2	2	no	—
185	C₁₉×#125	—	2	2	no	—
186	C₁₉×#125	—	2	2	no	—
187	C₁₉×#125	—	2	2	no	—
188	C₁₉×#125	—	2	2	no	—
189	C₁₉×#125	—	2	1	no	—
190	C₁₉×#125	—	2	1	no	—
191	C₁₉×#125	D₄	1	2	yes	—
192	C₁₉×#125	C₂³	1	2	yes	—
193	C₁₉×#125	C₂³	1	2	yes	—
194	C₁₉×#125	C₂³	1	2	yes	—
195	C₁₉×#125	C₂³	1	1	yes	characteristic
196	C₁₉×#124	—	2	1	no	—
197	C₁₉×#124	—	2	2	no	—
198	C₁₉×#124	—	2	2	no	—
199	C₁₉×#124	—	2	1	no	—
200	C₁₉×#124	C₂³	1	2	yes	—
201	C₁₉×#124	C₂³	1	1	yes	characteristic
202	C₁₉×#123	—	2	1	no	—
203	C₁₉×#123	—	2	2	no	—
204	C₁₉×#123	—	2	2	no	—
205	C₁₉×#123	—	2	2	no	—
206	C₁₉×#123	—	2	2	no	—
207	C₁₉×#123	—	2	2	no	—
208	C₁₉×#123	—	2	2	no	—
209	C₁₉×C₂²⋊Q₈	—	2	2	no	—
210	C₁₉×C₂²⋊Q₈	—	2	1	no	—
211	C₁₉×C₂²⋊Q₈	—	2	1	no	—
212	C₁₉×C₂²⋊Q₈	—	2	2	no	—
213	C₁₉×C₂²⋊Q₈	—	2	2	no	—
214	C₁₉×C₂²⋊Q₈	—	2	2	no	—
215	C₁₉×C₂²⋊Q₈	—	2	2	no	—
216	C₁₉×C₂²⋊Q₈	—	2	1	no	—
217	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
220	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₁₉×#121	—	2	1	no	—
225	C₁₉×#121	—	2	2	no	—
226	C₁₉×#121	—	2	1	no	—
227	C₁₉×#121	—	2	2	no	—
228	C₁₉×#121	—	2	2	no	—
229	C₁₉×#121	C₂³	1	1	yes	characteristic
230	C₁₉×#121	C₂³	1	2	yes	—
231	C₄×Q₈×C₁₉	—	2	1	no	—
232	C₄×Q₈×C₁₉	—	2	1	no	—
233	C₄×Q₈×C₁₉	—	2	2	no	—
234	C₄×Q₈×C₁₉	—	2	1	no	—
235	C₄×Q₈×C₁₉	—	2	1	no	—
236	C₄×Q₈×C₁₉	—	2	2	no	—
237	C₄×Q₈×C₁₉	—	2	1	no	—
238	C₄×Q₈×C₁₉	—	2	1	no	—
239	C₄×Q₈×C₁₉	—	2	1	no	—
240	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
247	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
248	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
249	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
252	C₄×D₄×C₁₉	—	2	1	no	—
253	C₄×D₄×C₁₉	—	2	2	no	—
254	C₄×D₄×C₁₉	—	2	1	no	—
255	C₄×D₄×C₁₉	—	2	1	no	—
256	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₁₉	C₂³	1	2	yes	—
258	C₄×D₄×C₁₉	C₂³	1	2	yes	—
259	C₄×D₄×C₁₉	C₂³	1	2	yes	—
260	C₄×D₄×C₁₉	C₂³	1	2	yes	—
261	C₁₉×#117	—	2	1	no	—
262	C₁₉×#117	—	2	1	no	—
263	C₁₉×#117	—	2	1	no	—
264	C₁₉×#117	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
266	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
267	C₁₉×#107	C₂³	1	1	yes	characteristic
268	C₁₉×#107	C₂³	1	2	yes	—
269	C₁₉×#107	C₂³	1	1	yes	characteristic
270	C₁₉×#107	C₂³	1	2	yes	—
271	C₁₉×#107	C₂³	1	2	yes	—
272	C₁₉×#106	C₂³	1	1	yes	characteristic
273	C₁₉×#106	C₂³	1	2	yes	—
274	C₁₉×#106	C₂³	1	2	yes	—
275	C₁₉×#106	C₂³	1	1	yes	characteristic
276	C₁₉×#106	C₂³	1	2	yes	—
277	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₉×#103	C₂³	1	1	yes	characteristic
285	C₁₉×#103	C₂³	1	1	yes	characteristic
286	C₁₉×#103	C₂³	1	2	yes	—
287	C₁₉×#103	C₂³	1	2	yes	—
288	C₁₉×#103	C₂³	1	1	yes	characteristic
289	C₁₉×#103	C₂³	1	1	yes	characteristic
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	1	yes	characteristic
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	2	yes	—
295	C₁₉×#103	C₂³	1	2	yes	—
296	C₁₉×#103	C₂³	1	2	yes	—
297	C₁₉×#102	C₂³	1	1	yes	characteristic
298	C₁₉×#102	C₂³	1	2	yes	—
299	C₁₉×#102	C₂³	1	2	yes	—
300	C₁₉×#102	C₂³	1	1	yes	characteristic
301	C₁₉×#102	C₂³	1	2	yes	—
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	2	yes	—
304	C₁₉×#97	C₂³	1	1	yes	characteristic
305	C₁₉×#97	C₂³	1	1	yes	characteristic
306	C₁₉×#97	C₂³	1	2	yes	—
307	C₁₉×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₉	C₂³	1	2	yes	—
311	C₄×C₈×C₁₉	C₂³	1	2	yes	—
312	#41×C₁₉	—	8	2	no	—
313	#41×C₁₉	—	8	2	no	—
314	C₂×Q₈×C₁₉	—	2	1	no	—
315	C₂×Q₈×C₁₉	—	2	1	no	—
316	C₂×Q₈×C₁₉	—	2	1	no	—
317	C₂×Q₈×C₁₉	—	2	2	no	—
318	C₂×Q₈×C₁₉	—	8	2	no	—
319	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₁₉	—	2	1	no	—
327	C₂×D₄×C₁₉	—	2	2	no	—
328	C₂×D₄×C₁₉	—	2	1	no	—
329	C₂×D₄×C₁₉	—	2	1	no	—
330	C₂×D₄×C₁₉	—	2	2	no	—
331	C₂×D₄×C₁₉	—	2	2	no	—
332	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₁₉	—	2	1	no	—
335	C₂²×C₄×C₁₉	—	2	2	no	—
336	C₂²×C₄×C₁₉	—	2	2	no	—
337	C₂²×C₄×C₁₉	—	2	2	no	—
338	C₂²×C₄×C₁₉	—	2	2	no	—
339	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
342	Q₁₆×C₁₉	—	2	2	no	—
343	Q₁₆×C₁₉	—	4	2	no	—
344	Q₁₆×C₁₉	—	4	1	no	—
345	SD₁₆×C₁₉	—	2	2	no	—
346	SD₁₆×C₁₉	—	2	4	no	—
347	SD₁₆×C₁₉	—	4	2	no	—
348	SD₁₆×C₁₉	—	4	2	no	—
349	SD₁₆×C₁₉	—	4	2	no	—
350	SD₁₆×C₁₉	—	4	2	no	—
351	SD₁₆×C₁₉	—	4	1	no	—
352	M₁₆×C₁₉	—	2	2	no	—
353	M₁₆×C₁₉	—	4	1	no	—
354	C₂×C₈×C₁₉	—	4	2	no	—
355	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
357	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₁₉	—	2	1	no	—
362	C₄⋊C₄×C₁₉	—	2	2	no	—
363	C₄⋊C₄×C₁₉	—	2	2	no	—
364	C₄⋊C₄×C₁₉	—	2	1	no	—
365	C₄⋊C₄×C₁₉	—	2	1	no	—
366	C₄⋊C₄×C₁₉	—	2	1	no	—
367	C₄⋊C₄×C₁₉	—	2	1	no	—
368	C₄⋊C₄×C₁₉	—	2	1	no	—
369	C₄⋊C₄×C₁₉	—	2	1	no	—
370	C₄⋊C₄×C₁₉	—	2	1	no	—
371	C₄⋊C₄×C₁₉	—	2	1	no	—
372	C₄⋊C₄×C₁₉	—	2	1	no	—
373	C₄⋊C₄×C₁₉	—	2	2	no	—
374	C₄⋊C₄×C₁₉	—	2	1	no	—
375	C₄⋊C₄×C₁₉	—	2	1	no	—
376	C₄⋊C₄×C₁₉	—	2	2	no	—
377	C₄⋊C₄×C₁₉	—	2	2	no	—
378	C₄⋊C₄×C₁₉	—	2	2	no	—
379	C₄⋊C₄×C₁₉	—	2	2	no	—
380	C₄⋊C₄×C₁₉	—	2	2	no	—
381	C₄⋊C₄×C₁₉	—	2	2	no	—
382	C₄⋊C₄×C₁₉	—	2	2	no	—
383	C₄⋊C₄×C₁₉	—	2	2	no	—
384	C₄⋊C₄×C₁₉	—	2	2	no	—
385	C₄⋊C₄×C₁₉	—	2	2	no	—
386	C₄⋊C₄×C₁₉	—	2	1	no	—
387	C₄⋊C₄×C₁₉	—	2	1	no	—
388	C₄⋊C₄×C₁₉	—	2	2	no	—
389	C₄⋊C₄×C₁₉	—	2	1	no	—
390	C₄⋊C₄×C₁₉	—	2	2	no	—
391	C₄⋊C₄×C₁₉	—	2	2	no	—
392	C₄⋊C₄×C₁₉	—	2	2	no	—
393	C₄⋊C₄×C₁₉	—	2	2	no	—
394	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
409	C₂²⋊C₄×C₁₉	—	2	1	no	—
410	C₂²⋊C₄×C₁₉	—	2	1	no	—
411	C₂²⋊C₄×C₁₉	—	2	2	no	—
412	C₂²⋊C₄×C₁₉	—	2	1	no	—
413	C₂²⋊C₄×C₁₉	—	2	1	no	—
414	C₂²⋊C₄×C₁₉	—	2	1	no	—
415	C₂²⋊C₄×C₁₉	—	2	1	no	—
416	C₂²⋊C₄×C₁₉	—	2	2	no	—
417	C₂²⋊C₄×C₁₉	—	2	2	no	—
418	C₂²⋊C₄×C₁₉	—	2	2	no	—
419	C₂²⋊C₄×C₁₉	—	2	1	no	—
420	C₂²⋊C₄×C₁₉	—	2	2	no	—
421	C₂²⋊C₄×C₁₉	—	2	2	no	—
422	C₂²⋊C₄×C₁₉	—	2	2	no	—
423	C₂²⋊C₄×C₁₉	—	2	2	no	—
424	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
426	C₄²×C₁₉	—	2	1	no	—
427	C₄²×C₁₉	—	2	2	no	—
428	C₄²×C₁₉	—	2	1	no	—
429	C₄²×C₁₉	—	2	1	no	—
430	C₄²×C₁₉	—	2	2	no	—
431	C₄²×C₁₉	—	2	2	no	—
432	C₄²×C₁₉	—	2	2	no	—
433	C₄²×C₁₉	—	2	2	no	—
434	C₄²×C₁₉	—	2	2	no	—
435	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
438	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₁₉	C₂⁴	1	2	yes	—
440	C₄²×C₁₉	C₂⁴	1	2	yes	—
441	#62402	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₁₉	—	2	2	no	—
443	C₂³×C₁₉	—	2	1	no	—
444	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₁₉	—	2	2	no	—
446	Q₈×C₁₉	—	2	2	no	—
447	Q₈×C₁₉	—	2	1	no	—
448	Q₈×C₁₉	—	2	2	no	—
449	Q₈×C₁₉	—	2	1	no	—
450	Q₈×C₁₉	—	2	1	no	—
451	Q₈×C₁₉	—	2	1	no	—
452	Q₈×C₁₉	—	2	1	no	—
453	Q₈×C₁₉	—	2	2	no	—
454	Q₈×C₁₉	—	2	1	no	—
455	Q₈×C₁₉	—	4	2	no	—
456	Q₈×C₁₉	—	4	2	no	—
457	Q₈×C₁₉	—	4	2	no	—
458	Q₈×C₁₉	—	4	2	no	—
459	Q₈×C₁₉	—	8	2	no	—
460	D₄×C₁₉	—	2	1	no	—
461	D₄×C₁₉	—	2	2	no	—
462	D₄×C₁₉	—	2	1	no	—
463	D₄×C₁₉	—	2	2	no	—
464	D₄×C₁₉	—	4	2	no	—
465	D₄×C₁₉	—	8	1	no	—
466	D₄×C₁₉	—	8	2	no	—
467	D₄×C₁₉	—	8	2	no	—
468	D₄×C₁₉	—	8	1	no	—
469	D₄×C₁₉	—	8	2	no	—
470	C₂×C₄×C₁₉	—	2	2	no	—
471	C₂×C₄×C₁₉	—	2	1	no	—
472	C₂×C₄×C₁₉	—	2	1	no	—
473	C₂×C₄×C₁₉	—	2	1	no	—
474	C₂×C₄×C₁₉	—	2	2	no	—
475	C₂×C₄×C₁₉	—	2	1	no	—
476	C₂×C₄×C₁₉	—	2	1	no	—
477	C₂×C₄×C₁₉	—	2	1	no	—
478	C₂×C₄×C₁₉	—	2	1	no	—
479	C₂×C₄×C₁₉	—	2	2	no	—
480	C₂×C₄×C₁₉	—	2	1	no	—
481	C₂×C₄×C₁₉	—	2	2	no	—
482	C₂×C₄×C₁₉	—	2	1	no	—
483	C₂×C₄×C₁₉	—	4	1	no	—
484	C₂×C₄×C₁₉	—	4	2	no	—
485	C₂×C₄×C₁₉	—	8	2	no	—
486	C₂×C₄×C₁₉	—	8	2	no	—
487	C₂×C₄×C₁₉	—	8	2	no	—
488	C₂×C₄×C₁₉	—	8	2	no	—
489	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
499	C₈×C₁₉	—	2	1	no	—
500	C₈×C₁₉	—	2	2	no	—
501	C₈×C₁₉	—	2	2	no	—
502	C₈×C₁₉	—	2	1	no	—
503	C₈×C₁₉	—	2	1	no	—
504	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
505	#3556	C₂×C₁₉	1	1	yes	characteristic, complemented
506	#3554	C₂×C₁₉	1	1	yes	characteristic
507	#3400	C₂×C₁₉	1	1	yes	characteristic, complemented
508	#3400	C₂×C₁₉	1	2	yes	complemented
509	#3392	C₂×C₁₉	1	1	yes	characteristic, complemented
510	#3388	C₂×C₁₉	1	2	yes	complemented
511	#3386	C₂×C₁₉	1	1	yes	characteristic, complemented
512	#3383	C₂×C₁₉	1	1	yes	characteristic, complemented
513	#3374	C₂×C₁₉	1	1	yes	characteristic, complemented
514	#3372	C₂×C₁₉	1	2	yes	complemented
515	#3371	C₂×C₁₉	1	2	yes	complemented
516	#3368	C₂×C₁₉	1	1	yes	characteristic, complemented
517	#3365	C₂×C₁₉	1	1	yes	characteristic, complemented
518	#3359	C₂×C₁₉	1	1	yes	characteristic, complemented
519	#3260	C₂×C₁₉	1	2	yes	complemented
520	#3258	C₂×C₁₉	1	2	yes	complemented
521	#3248	C₂×C₁₉	1	1	yes	characteristic, complemented
522	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
523	#3182	C₂×C₁₉	1	1	yes	characteristic, complemented
524	#3178	C₂×C₁₉	1	2	yes	complemented
525	#3174	C₂×C₁₉	1	2	yes	complemented
526	#3172	C₂×C₁₉	1	1	yes	characteristic, complemented
527	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
528	C₂²×C₁₉	—	2	1	no	—
529	C₂²×C₁₉	—	2	1	no	—
530	C₂²×C₁₉	—	2	1	no	—
531	C₂²×C₁₉	—	4	2	no	—
532	C₂²×C₁₉	—	4	1	no	—
533	C₂²×C₁₉	—	4	2	no	—
534	C₂²×C₁₉	—	4	1	no	—
535	C₂²×C₁₉	—	4	1	no	—
536	C₂²×C₁₉	—	4	2	no	—
537	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
538	C₄×C₁₉	—	2	1	no	—
539	C₄×C₁₉	—	2	1	no	—
540	C₄×C₁₉	—	2	2	no	—
541	C₄×C₁₉	—	2	2	no	—
542	C₄×C₁₉	—	2	1	no	—
543	C₄×C₁₉	—	2	1	no	—
544	C₄×C₁₉	—	2	2	no	—
545	C₄×C₁₉	—	2	2	no	—
546	C₄×C₁₉	—	4	1	no	—
547	C₄×C₁₉	—	4	1	no	—
548	C₄×C₁₉	—	4	1	no	—
549	C₄×C₁₉	—	4	1	no	—
550	C₄×C₁₉	—	4	2	no	—
551	C₄×C₁₉	—	4	1	no	—
552	C₄×C₁₉	—	4	1	no	—
553	C₄×C₁₉	—	4	1	no	—
554	C₄×C₁₉	—	4	2	no	—
555	C₄×C₁₉	—	4	2	no	—
556	C₄×C₁₉	#577	1	2	yes	—
557	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
558	C₄×C₁₉	#585	1	1	yes	characteristic
559	#564	—	2	2	no	—
560	#562	—	2	2	no	—
561	#559	C₂²×C₁₉	1	1	yes	characteristic
562	#559	C₂²×C₁₉	1	2	yes	—
563	#557	—	2	1	no	—
564	#557	—	2	1	no	—
565	#557	C₂²×C₁₉	1	1	yes	characteristic
566	#557	C₂²×C₁₉	1	2	yes	—
567	#557	C₂²×C₁₉	1	1	yes	characteristic
568	#557	C₂²×C₁₉	1	1	yes	characteristic
569	#557	C₂²×C₁₉	1	1	yes	characteristic
570	#557	C₂²×C₁₉	1	2	yes	—
571	#557	C₂²×C₁₉	1	1	yes	characteristic
572	#554	C₂²×C₁₉	1	2	yes	—
573	#550	C₂²×C₁₉	1	1	yes	characteristic
574	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
575	#548	—	2	1	no	—
576	#547	—	2	1	no	—
577	#542	—	2	1	no	—
578	#542	C₂²×C₁₉	1	2	yes	—
579	#541	—	2	1	no	—
580	#541	—	2	1	no	—
581	#541	—	2	2	no	—
582	#541	C₂²×C₁₉	1	2	yes	—
583	#541	C₂²×C₁₉	1	2	yes	—
584	#540	C₂²×C₁₉	1	2	yes	—
585	#539	—	2	2	no	—
586	#536	—	2	1	no	—
587	#533	C₂²×C₁₉	1	1	yes	characteristic
588	#533	C₂²×C₁₉	1	1	yes	characteristic
589	#533	C₂²×C₁₉	1	1	yes	characteristic
590	#532	C₂²×C₁₉	1	1	yes	characteristic
591	#529	C₂²×C₁₉	1	1	yes	characteristic
592	#501	C₂²×C₁₉	1	2	yes	—
593	#501	C₂²×C₁₉	1	1	yes	characteristic
594	#500	C₂²×C₁₉	1	1	yes	characteristic
595	#499	C₂²×C₁₉	1	2	yes	—
596	#497	C₂²×C₁₉	1	1	yes	characteristic
597	#497	C₂²×C₁₉	1	2	yes	—
598	#492	C₂²×C₁₉	1	2	yes	—
599	#492	C₂²×C₁₉	1	1	yes	characteristic
600	#491	C₂²×C₁₉	1	1	yes	characteristic
601	#491	C₂²×C₁₉	1	2	yes	—
602	#490	C₂²×C₁₉	1	2	yes	—
603	#489	C₂²×C₁₉	1	1	yes	characteristic
604	#488	C₂²×C₁₉	1	2	yes	—
605	#487	C₂²×C₁₉	1	2	yes	—
606	#487	C₂²×C₁₉	1	1	yes	characteristic
607	#486	C₂²×C₁₉	1	1	yes	characteristic
608	#479	C₂²×C₁₉	1	2	yes	—
609	#479	C₂²×C₁₉	1	2	yes	—
610	#479	C₂²×C₁₉	1	2	yes	—
611	#479	C₂²×C₁₉	1	2	yes	—
612	#478	C₂²×C₁₉	1	2	yes	—
613	#478	C₂²×C₁₉	1	2	yes	—
614	#478	C₂²×C₁₉	1	2	yes	—
615	#477	C₂²×C₁₉	1	2	yes	—
616	#476	C₂²×C₁₉	1	2	yes	—
617	#475	C₂²×C₁₉	1	1	yes	characteristic
618	#475	C₂²×C₁₉	1	2	yes	—
619	#475	C₂²×C₁₉	1	1	yes	characteristic
620	#475	C₂²×C₁₉	1	1	yes	characteristic
621	#474	C₂²×C₁₉	1	1	yes	characteristic
622	#470	C₂²×C₁₉	1	1	yes	characteristic
623	#470	C₂²×C₁₉	1	1	yes	characteristic
624	#468	C₂²×C₁₉	1	1	yes	characteristic
625	#468	C₂²×C₁₉	1	1	yes	characteristic
626	#468	C₂²×C₁₉	1	2	yes	—
627	#468	C₂²×C₁₉	1	2	yes	—
628	#467	C₂²×C₁₉	1	2	yes	—
629	#465	C₂²×C₁₉	1	2	yes	—
630	#465	C₂²×C₁₉	1	2	yes	—
631	#465	C₂²×C₁₉	1	2	yes	—
632	#464	C₂²×C₁₉	1	2	yes	—
633	#464	C₂²×C₁₉	1	2	yes	—
634	#464	C₂²×C₁₉	1	2	yes	—
635	#462	C₂²×C₁₉	1	1	yes	characteristic
636	#462	C₂²×C₁₉	1	2	yes	—
637	#461	C₂²×C₁₉	1	1	yes	characteristic
638	#461	C₂²×C₁₉	1	2	yes	—
639	#461	C₂²×C₁₉	1	2	yes	—
640	#461	C₂²×C₁₉	1	2	yes	—
641	#461	C₂²×C₁₉	1	2	yes	—
642	#460	C₂²×C₁₉	1	1	yes	characteristic
643	#460	C₂²×C₁₉	1	1	yes	characteristic
644	#460	C₂²×C₁₉	1	2	yes	—
645	#460	C₂²×C₁₉	1	2	yes	—
646	#446	C₂²×C₁₉	1	1	yes	characteristic
647	#446	C₂²×C₁₉	1	2	yes	—
648	#446	C₂²×C₁₉	1	1	yes	characteristic
649	#446	C₂²×C₁₉	1	2	yes	—
650	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
651	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
652	#441	C₂²×C₁₉	1	2	yes	—
653	#440	C₂²×C₁₉	1	2	yes	—
654	#440	C₂²×C₁₉	1	2	yes	—
655	#440	C₂²×C₁₉	1	2	yes	—
656	#440	C₂²×C₁₉	1	2	yes	—
657	#440	C₂²×C₁₉	1	2	yes	—
658	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
659	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
660	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
663	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
665	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
666	#424	C₂²×C₁₉	1	2	yes	—
667	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
668	#405	C₂²×C₁₉	1	2	yes	—
669	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
670	C₂×C₁₉	—	4	1	no	—
671	C₂×C₁₉	—	8	2	no	—
672	C₂×C₁₉	—	8	1	no	—
673	C₂×C₁₉	#3497	1	1	yes	characteristic
674	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
675	C₂×C₁₉	#3586	1	1	yes	characteristic
676	C₂×#41	—	2	1	no	—
677	C₂×#41	—	2	1	no	—
678	C₂²×Q₈	—	2	1	no	—
679	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
680	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
681	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
683	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
685	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
689	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
697	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
706	#127	C₂³×C₁₉	1	1	yes	characteristic
707	#127	C₂³×C₁₉	1	2	yes	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	1	no	—
716	#125	—	2	1	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	1	no	—
732	#125	D₄×C₁₉	1	2	yes	—
733	#125	C₂³×C₁₉	1	1	yes	characteristic
734	#125	C₂³×C₁₉	1	2	yes	—
735	#125	C₂³×C₁₉	1	2	yes	—
736	#125	C₂³×C₁₉	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	C₂³×C₁₉	1	1	yes	characteristic
742	#124	C₂³×C₁₉	1	2	yes	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
759	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
760	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	C₂³×C₁₉	1	1	yes	characteristic
771	#121	C₂³×C₁₉	1	2	yes	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	2	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	2	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
787	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
789	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
790	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₁₉	1	2	yes	—
799	C₄×D₄	C₂³×C₁₉	1	2	yes	—
800	C₄×D₄	C₂³×C₁₉	1	2	yes	—
801	C₄×D₄	C₂³×C₁₉	1	2	yes	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₁₉	1	2	yes	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
808	#107	C₂³×C₁₉	1	1	yes	characteristic
809	#107	C₂³×C₁₉	1	2	yes	—
810	#107	C₂³×C₁₉	1	1	yes	characteristic
811	#107	C₂³×C₁₉	1	2	yes	—
812	#107	C₂³×C₁₉	1	2	yes	—
813	#106	C₂³×C₁₉	1	1	yes	characteristic
814	#106	C₂³×C₁₉	1	2	yes	—
815	#106	C₂³×C₁₉	1	2	yes	—
816	#106	C₂³×C₁₉	1	1	yes	characteristic
817	#106	C₂³×C₁₉	1	2	yes	—
818	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
821	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
822	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
823	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
824	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
825	#103	C₂³×C₁₉	1	1	yes	characteristic
826	#103	C₂³×C₁₉	1	1	yes	characteristic
827	#103	C₂³×C₁₉	1	2	yes	—
828	#103	C₂³×C₁₉	1	2	yes	—
829	#103	C₂³×C₁₉	1	1	yes	characteristic
830	#103	C₂³×C₁₉	1	1	yes	characteristic
831	#103	C₂³×C₁₉	1	2	yes	—
832	#103	C₂³×C₁₉	1	1	yes	characteristic
833	#103	C₂³×C₁₉	1	2	yes	—
834	#103	C₂³×C₁₉	1	1	yes	characteristic
835	#103	C₂³×C₁₉	1	2	yes	—
836	#103	C₂³×C₁₉	1	2	yes	—
837	#103	C₂³×C₁₉	1	2	yes	—
838	#102	C₂³×C₁₉	1	1	yes	characteristic
839	#102	C₂³×C₁₉	1	2	yes	—
840	#102	C₂³×C₁₉	1	2	yes	—
841	#102	C₂³×C₁₉	1	1	yes	characteristic
842	#102	C₂³×C₁₉	1	2	yes	—
843	#102	C₂³×C₁₉	1	2	yes	—
844	#102	C₂³×C₁₉	1	2	yes	—
845	#97	C₂³×C₁₉	1	1	yes	characteristic
846	#97	C₂³×C₁₉	1	1	yes	characteristic
847	#97	C₂³×C₁₉	1	2	yes	—
848	#97	C₂³×C₁₉	1	2	yes	—
849	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₁₉	1	2	yes	—
852	C₄×C₈	C₂³×C₁₉	1	2	yes	—
853	C₁₉	#62402	1	1	yes	characteristic, direct product factor, Sylow
854	#41	—	8	2	no	—
855	#41	—	8	2	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	8	2	no	—
861	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
862	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
863	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
864	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
865	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
866	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
867	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
875	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
882	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
884	Q₁₆	—	2	2	no	—
885	Q₁₆	—	4	2	no	—
886	Q₁₆	—	4	1	no	—
887	SD₁₆	—	2	2	no	—
888	SD₁₆	—	2	4	no	—
889	SD₁₆	—	4	2	no	—
890	SD₁₆	—	4	2	no	—
891	SD₁₆	—	4	2	no	—
892	SD₁₆	—	4	2	no	—
893	SD₁₆	—	4	1	no	—
894	M₁₆	—	2	2	no	—
895	M₁₆	—	4	1	no	—
896	C₂×C₈	—	4	2	no	—
897	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
899	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
902	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
937	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
967	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
978	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
979	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
980	C₄²	C₂⁴×C₁₉	1	2	yes	—
981	C₄²	C₂⁴×C₁₉	1	2	yes	—
982	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
983	C₂³	—	2	1	no	—
984	C₂³	—	2	2	no	—
985	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
986	Q₈	—	2	2	no	—
987	Q₈	—	2	2	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	2	2	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	4	2	no	—
999	Q₈	—	4	2	no	—
1000	Q₈	—	8	2	no	—
1001	D₄	—	2	1	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	4	2	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	1	no	—
1008	D₄	—	8	2	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	8	2	no	—
1027	C₂×C₄	—	8	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1031	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1034	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1035	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1039	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1040	C₈	—	2	1	no	—
1041	C₈	—	2	2	no	—
1042	C₈	—	2	2	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	C₁₉×#577	1	2	yes	—
1075	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1076	C₄	C₁₉×#585	1	1	yes	characteristic
1077	C₂	—	4	1	no	—
1078	C₂	—	8	1	no	—
1079	C₂	—	8	2	no	—
1080	C₂	C₁₉×#3497	1	1	yes	characteristic
1081	C₂	C₂×C₁₉×#577	1	1	yes	characteristic
1082	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3554	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3556	C₂	semidirect
3. C₁₉×#3400	C₂	semidirect
4. C₁₉×#3400	C₂	semidirect
5. C₁₉×#3392	C₂	semidirect
6. C₁₉×#3388	C₂	semidirect
7. C₁₉×#3386	C₂	semidirect
8. C₁₉×#3383	C₂	semidirect
9. C₁₉×#3374	C₂	semidirect
10. C₁₉×#3372	C₂	semidirect
11. C₁₉×#3371	C₂	semidirect
12. C₁₉×#3368	C₂	semidirect
13. C₁₉×#3365	C₂	semidirect
14. C₁₉×#3359	C₂	semidirect
15. C₁₉×#3260	C₂	semidirect
16. C₁₉×#3258	C₂	semidirect
17. C₁₉×#3248	C₂	semidirect
18. C₁₉×#3246	C₂	semidirect
19. C₁₉×#3182	C₂	semidirect
20. C₁₉×#3178	C₂	semidirect
21. C₁₉×#3174	C₂	semidirect
22. C₁₉×#3172	C₂	semidirect
23. C₁₉×#2962	C₂	semidirect
441. #62402	C₁₉	direct (N × H)
505. #3556	C₂×C₁₉	semidirect
507. #3400	C₂×C₁₉	semidirect
508. #3400	C₂×C₁₉	semidirect
509. #3392	C₂×C₁₉	semidirect
510. #3388	C₂×C₁₉	semidirect
511. #3386	C₂×C₁₉	semidirect
512. #3383	C₂×C₁₉	semidirect
513. #3374	C₂×C₁₉	semidirect
514. #3372	C₂×C₁₉	semidirect
515. #3371	C₂×C₁₉	semidirect
516. #3368	C₂×C₁₉	semidirect
517. #3365	C₂×C₁₉	semidirect
518. #3359	C₂×C₁₉	semidirect
519. #3260	C₂×C₁₉	semidirect
520. #3258	C₂×C₁₉	semidirect
521. #3248	C₂×C₁₉	semidirect
522. #3246	C₂×C₁₉	semidirect
523. #3182	C₂×C₁₉	semidirect
524. #3178	C₂×C₁₉	semidirect
525. #3174	C₂×C₁₉	semidirect
526. #3172	C₂×C₁₉	semidirect
527. #2962	C₂×C₁₉	semidirect
853. C₁₉	#62402	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×#3556	2
C₁₉×#3554	2
C₁₉×#3400	2
C₁₉×#3392	2
C₁₉×#3388	2
C₁₉×#3386	2
C₁₉×#3383	2
C₁₉×#3374	2
C₁₉×#3372	2
C₁₉×#3371	2
C₁₉×#3368	2
C₁₉×#3365	2
C₁₉×#3359	2
C₁₉×#3260	2
C₁₉×#3258	2
C₁₉×#3248	2
C₁₉×#3246	2
C₁₉×#3182	2
C₁₉×#3178	2
C₁₉×#3174	2
C₁₉×#3172	2
C₁₉×#2962	2
#62402	19

Subgroups — C19×#62402 #18068361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62402 #18068361