Subgroups — C₁₉×#62406 #18068365

Order 4864.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1056 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×#3555	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3398	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#3390	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#3374	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3261	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3258	C₂	1	2	yes	maximal
17	C₁₉×#3249	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3248	C₂	1	1	yes	maximal, characteristic
19	C₁₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#3178	C₂	1	2	yes	maximal
21	C₁₉×#3177	C₂	1	2	yes	maximal, complemented
22	C₁₉×#3172	C₂	1	1	yes	maximal, characteristic
23	C₁₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#564	—	2	2	no	—
25	C₁₉×#563	—	2	2	no	—
26	Q₈²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#557	—	2	1	no	—
28	C₁₉×#557	—	2	1	no	—
29	C₁₉×#557	C₂²	1	1	yes	characteristic
30	C₁₉×#557	C₂²	1	1	yes	characteristic
31	C₁₉×#557	C₂²	1	1	yes	characteristic
32	C₁₉×#557	C₂²	1	2	yes	—
33	C₁₉×#557	C₂²	1	2	yes	—
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×#556	—	2	1	no	—
38	C₁₉×#556	C₂²	1	1	yes	characteristic
39	C₁₉×#556	C₂²	1	2	yes	—
40	C₁₉×#554	C₂²	1	1	yes	characteristic
41	C₁₉×#552	—	2	1	no	—
42	C₁₉×#544	—	2	1	no	—
43	C₁₉×#542	C₂²	1	2	yes	—
44	C₁₉×#541	—	2	1	no	—
45	C₁₉×#541	—	2	2	no	—
46	C₁₉×#541	—	2	1	no	—
47	C₁₉×#541	—	2	1	no	—
48	C₁₉×#541	—	2	2	no	—
49	C₁₉×#541	C₂²	1	2	yes	—
50	C₁₉×#541	C₂²	1	2	yes	—
51	C₁₉×#541	C₂²	1	2	yes	—
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×#533	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×#499	C₂²	1	2	yes	—
60	C₁₉×#498	C₂²	1	1	yes	characteristic
61	C₁₉×#497	C₂²	1	1	yes	characteristic
62	C₁₉×#497	C₂²	1	2	yes	—
63	C₁₉×#494	C₂²	1	2	yes	—
64	C₁₉×#494	C₂²	1	1	yes	characteristic
65	C₁₉×#491	C₂²	1	1	yes	characteristic
66	C₁₉×#491	C₂²	1	2	yes	—
67	C₁₉×#491	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×#487	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×#479	C₂²	1	2	yes	—
78	C₁₉×#479	C₂²	1	2	yes	—
79	C₁₉×#478	C₂²	1	2	yes	—
80	C₁₉×#477	C₂²	1	1	yes	characteristic
81	C₁₉×#477	C₂²	1	1	yes	characteristic
82	C₁₉×#477	C₂²	1	2	yes	—
83	C₁₉×#477	C₂²	1	2	yes	—
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×#470	C₂²	1	2	yes	—
90	C₁₉×#470	C₂²	1	2	yes	—
91	C₁₉×#468	C₂²	1	1	yes	characteristic
92	C₁₉×#468	C₂²	1	1	yes	characteristic
93	C₁₉×#467	C₂²	1	2	yes	—
94	C₁₉×#467	C₂²	1	2	yes	—
95	C₁₉×#467	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	1	yes	characteristic
102	C₁₉×#462	C₂²	1	1	yes	characteristic
103	C₁₉×#462	C₂²	1	2	yes	—
104	C₁₉×#462	C₂²	1	2	yes	—
105	C₁₉×#462	C₂²	1	2	yes	—
106	C₁₉×#462	C₂²	1	2	yes	—
107	C₁₉×#462	C₂²	1	2	yes	—
108	C₁₉×#462	C₂²	1	2	yes	—
109	C₁₉×#461	C₂²	1	1	yes	characteristic
110	C₁₉×#461	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×#441	C₂²	1	2	yes	—
119	C₁₉×#441	C₂²	1	2	yes	—
120	C₁₉×#441	C₂²	1	2	yes	—
121	C₁₉×#441	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×Q₁₆×C₁₉	C₂²	1	2	yes	—
127	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
128	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
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×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
137	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₁₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
145	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
148	C₁₉×C₄⋊Q₈	—	2	1	no	—
149	C₁₉×C₄⋊Q₈	—	2	1	no	—
150	C₁₉×C₄⋊Q₈	—	2	2	no	—
151	C₁₉×C₄⋊Q₈	—	2	2	no	—
152	C₁₉×C₄⋊Q₈	—	2	2	no	—
153	C₁₉×C₄⋊Q₈	—	2	1	no	—
154	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₁₉×C₄⋊Q₈	C₂³	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	2	yes	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₉×#126	—	2	2	no	—
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	2	no	—
173	C₁₉×#126	—	2	2	no	—
174	C₁₉×#126	—	2	2	no	—
175	C₁₉×#126	—	2	2	no	—
176	C₁₉×#126	—	2	1	no	—
177	C₁₉×#125	—	2	2	no	—
178	C₁₉×#125	—	2	2	no	—
179	C₁₉×#125	—	2	2	no	—
180	C₁₉×#125	—	2	1	no	—
181	C₁₉×#125	—	2	1	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	2	no	—
190	C₁₉×#125	—	2	2	no	—
191	C₁₉×#125	—	2	2	no	—
192	C₁₉×#125	—	2	2	no	—
193	C₁₉×#125	—	2	2	no	—
194	C₁₉×#125	—	2	2	no	—
195	C₁₉×#125	—	2	2	no	—
196	C₁₉×#125	—	2	2	no	—
197	C₁₉×#125	—	2	1	no	—
198	C₁₉×#125	—	2	1	no	—
199	C₁₉×#125	—	2	1	no	—
200	C₁₉×#125	—	2	1	no	—
201	C₁₉×#125	D₄	1	2	yes	—
202	C₁₉×#125	C₂³	1	2	yes	—
203	C₁₉×#125	C₂³	1	2	yes	—
204	C₁₉×#125	C₂³	1	2	yes	—
205	C₁₉×#125	C₂³	1	1	yes	characteristic
206	C₁₉×#124	—	2	2	no	—
207	C₁₉×#124	C₂³	1	2	yes	—
208	C₁₉×#124	C₂³	1	1	yes	characteristic
209	C₁₉×#123	—	2	1	no	—
210	C₁₉×#123	—	2	2	no	—
211	C₁₉×C₂²⋊Q₈	—	2	1	no	—
212	C₁₉×C₂²⋊Q₈	—	2	1	no	—
213	C₁₉×C₂²⋊Q₈	—	2	2	no	—
214	C₁₉×C₂²⋊Q₈	—	2	1	no	—
215	C₁₉×C₂²⋊Q₈	—	2	1	no	—
216	C₁₉×C₂²⋊Q₈	—	2	1	no	—
217	C₁₉×C₂²⋊Q₈	—	2	2	no	—
218	C₁₉×C₂²⋊Q₈	—	2	2	no	—
219	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
221	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
222	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₁₉×#121	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₁₉	—	2	1	no	—
229	C₄×Q₈×C₁₉	—	2	1	no	—
230	C₄×Q₈×C₁₉	—	2	1	no	—
231	C₄×Q₈×C₁₉	—	2	1	no	—
232	C₄×Q₈×C₁₉	—	2	2	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	1	yes	characteristic
244	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
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	2	yes	—
250	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
251	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
252	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
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	C₁₉×#117	—	2	1	no	—
259	C₁₉×#117	—	2	1	no	—
260	C₁₉×#117	—	2	1	no	—
261	C₁₉×#117	—	2	2	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	1	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	2	yes	—
270	C₁₉×#107	C₂³	1	1	yes	characteristic
271	C₁₉×#107	C₂³	1	2	yes	—
272	C₁₉×#106	C₂³	1	2	yes	—
273	C₁₉×#106	C₂³	1	1	yes	characteristic
274	C₁₉×#106	C₂³	1	1	yes	characteristic
275	C₁₉×#106	C₂³	1	2	yes	—
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	2	yes	—
286	C₁₉×#103	C₂³	1	1	yes	characteristic
287	C₁₉×#103	C₂³	1	1	yes	characteristic
288	C₁₉×#103	C₂³	1	2	yes	—
289	C₁₉×#103	C₂³	1	1	yes	characteristic
290	C₁₉×#103	C₂³	1	2	yes	—
291	C₁₉×#103	C₂³	1	2	yes	—
292	C₁₉×#103	C₂³	1	2	yes	—
293	C₁₉×#103	C₂³	1	1	yes	characteristic
294	C₁₉×#103	C₂³	1	1	yes	characteristic
295	C₁₉×#103	C₂³	1	2	yes	—
296	C₁₉×#103	C₂³	1	2	yes	—
297	C₁₉×#103	C₂³	1	2	yes	—
298	C₁₉×#103	C₂³	1	2	yes	—
299	C₁₉×#103	C₂³	1	2	yes	—
300	C₁₉×#103	C₂³	1	2	yes	—
301	C₁₉×#102	C₂³	1	1	yes	characteristic
302	C₁₉×#102	C₂³	1	2	yes	—
303	C₁₉×#102	C₂³	1	1	yes	characteristic
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	C₂×Q₈×C₁₉	—	2	1	no	—
313	C₂×Q₈×C₁₉	—	2	1	no	—
314	C₂×Q₈×C₁₉	—	2	1	no	—
315	C₂×Q₈×C₁₉	—	2	2	no	—
316	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
317	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
319	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
321	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
322	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
324	C₂×D₄×C₁₉	—	2	1	no	—
325	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₉	—	2	1	no	—
327	C₂²×C₄×C₁₉	—	2	2	no	—
328	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
331	Q₁₆×C₁₉	—	2	2	no	—
332	Q₁₆×C₁₉	—	2	4	no	—
333	Q₁₆×C₁₉	—	4	2	no	—
334	Q₁₆×C₁₉	—	4	2	no	—
335	Q₁₆×C₁₉	—	4	2	no	—
336	Q₁₆×C₁₉	—	4	1	no	—
337	Q₁₆×C₁₉	—	4	2	no	—
338	SD₁₆×C₁₉	—	2	2	no	—
339	SD₁₆×C₁₉	—	4	2	no	—
340	SD₁₆×C₁₉	—	4	1	no	—
341	M₁₆×C₁₉	—	2	2	no	—
342	M₁₆×C₁₉	—	4	1	no	—
343	C₂×C₈×C₁₉	—	4	2	no	—
344	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
345	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
346	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
350	C₄⋊C₄×C₁₉	—	2	1	no	—
351	C₄⋊C₄×C₁₉	—	2	2	no	—
352	C₄⋊C₄×C₁₉	—	2	1	no	—
353	C₄⋊C₄×C₁₉	—	2	2	no	—
354	C₄⋊C₄×C₁₉	—	2	1	no	—
355	C₄⋊C₄×C₁₉	—	2	1	no	—
356	C₄⋊C₄×C₁₉	—	2	1	no	—
357	C₄⋊C₄×C₁₉	—	2	1	no	—
358	C₄⋊C₄×C₁₉	—	2	1	no	—
359	C₄⋊C₄×C₁₉	—	2	1	no	—
360	C₄⋊C₄×C₁₉	—	2	1	no	—
361	C₄⋊C₄×C₁₉	—	2	1	no	—
362	C₄⋊C₄×C₁₉	—	2	1	no	—
363	C₄⋊C₄×C₁₉	—	2	2	no	—
364	C₄⋊C₄×C₁₉	—	2	2	no	—
365	C₄⋊C₄×C₁₉	—	2	1	no	—
366	C₄⋊C₄×C₁₉	—	2	2	no	—
367	C₄⋊C₄×C₁₉	—	2	1	no	—
368	C₄⋊C₄×C₁₉	—	2	1	no	—
369	C₄⋊C₄×C₁₉	—	2	2	no	—
370	C₄⋊C₄×C₁₉	—	2	2	no	—
371	C₄⋊C₄×C₁₉	—	2	2	no	—
372	C₄⋊C₄×C₁₉	—	2	2	no	—
373	C₄⋊C₄×C₁₉	—	2	2	no	—
374	C₄⋊C₄×C₁₉	—	2	2	no	—
375	C₄⋊C₄×C₁₉	—	2	2	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	1	no	—
383	C₄⋊C₄×C₁₉	—	2	1	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	2	no	—
388	C₄⋊C₄×C₁₉	—	2	2	no	—
389	C₄⋊C₄×C₁₉	—	2	2	no	—
390	C₄⋊C₄×C₁₉	—	2	2	no	—
391	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
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	2	yes	—
398	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₁₉	—	2	2	no	—
407	C₂²⋊C₄×C₁₉	—	2	2	no	—
408	C₂²⋊C₄×C₁₉	—	2	1	no	—
409	C₂²⋊C₄×C₁₉	—	2	1	no	—
410	C₂²⋊C₄×C₁₉	—	2	1	no	—
411	C₂²⋊C₄×C₁₉	—	2	1	no	—
412	C₂²⋊C₄×C₁₉	—	2	1	no	—
413	C₂²⋊C₄×C₁₉	—	2	1	no	—
414	C₂²⋊C₄×C₁₉	—	2	2	no	—
415	C₂²⋊C₄×C₁₉	—	2	2	no	—
416	C₂²⋊C₄×C₁₉	—	2	1	no	—
417	C₂²⋊C₄×C₁₉	—	2	2	no	—
418	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
420	C₄²×C₁₉	—	2	2	no	—
421	C₄²×C₁₉	—	2	1	no	—
422	C₄²×C₁₉	—	2	2	no	—
423	C₄²×C₁₉	—	2	1	no	—
424	C₄²×C₁₉	—	2	1	no	—
425	C₄²×C₁₉	—	2	2	no	—
426	C₄²×C₁₉	—	2	2	no	—
427	C₄²×C₁₉	—	2	2	no	—
428	C₄²×C₁₉	—	2	2	no	—
429	C₄²×C₁₉	—	2	2	no	—
430	C₄²×C₁₉	—	2	2	no	—
431	C₄²×C₁₉	—	2	2	no	—
432	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
435	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
436	C₄²×C₁₉	C₂⁴	1	2	yes	—
437	C₄²×C₁₉	C₂⁴	1	2	yes	—
438	#62406	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂³×C₁₉	—	2	1	no	—
440	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₁₉	—	2	2	no	—
442	Q₈×C₁₉	—	2	2	no	—
443	Q₈×C₁₉	—	2	1	no	—
444	Q₈×C₁₉	—	2	1	no	—
445	Q₈×C₁₉	—	2	2	no	—
446	Q₈×C₁₉	—	2	1	no	—
447	Q₈×C₁₉	—	2	2	no	—
448	Q₈×C₁₉	—	2	2	no	—
449	Q₈×C₁₉	—	2	1	no	—
450	Q₈×C₁₉	—	2	2	no	—
451	Q₈×C₁₉	—	2	1	no	—
452	Q₈×C₁₉	—	2	1	no	—
453	Q₈×C₁₉	—	4	2	no	—
454	Q₈×C₁₉	—	4	2	no	—
455	Q₈×C₁₉	—	4	2	no	—
456	Q₈×C₁₉	—	8	1	no	—
457	Q₈×C₁₉	—	8	2	no	—
458	D₄×C₁₉	—	2	1	no	—
459	D₄×C₁₉	—	2	1	no	—
460	D₄×C₁₉	—	8	1	no	—
461	C₂×C₄×C₁₉	—	2	2	no	—
462	C₂×C₄×C₁₉	—	2	1	no	—
463	C₂×C₄×C₁₉	—	2	1	no	—
464	C₂×C₄×C₁₉	—	2	2	no	—
465	C₂×C₄×C₁₉	—	2	1	no	—
466	C₂×C₄×C₁₉	—	2	1	no	—
467	C₂×C₄×C₁₉	—	2	2	no	—
468	C₂×C₄×C₁₉	—	2	1	no	—
469	C₂×C₄×C₁₉	—	2	1	no	—
470	C₂×C₄×C₁₉	—	2	1	no	—
471	C₂×C₄×C₁₉	—	2	2	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	—	4	1	no	—
476	C₂×C₄×C₁₉	—	4	2	no	—
477	C₂×C₄×C₁₉	—	8	2	no	—
478	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
488	C₈×C₁₉	—	2	1	no	—
489	C₈×C₁₉	—	2	2	no	—
490	C₈×C₁₉	—	2	2	no	—
491	C₈×C₁₉	—	2	1	no	—
492	C₈×C₁₉	—	2	1	no	—
493	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
494	#3556	C₂×C₁₉	1	1	yes	characteristic, complemented
495	#3555	C₂×C₁₉	1	1	yes	characteristic
496	#3398	C₂×C₁₉	1	1	yes	characteristic, complemented
497	#3398	C₂×C₁₉	1	2	yes	complemented
498	#3395	C₂×C₁₉	1	1	yes	characteristic, complemented
499	#3390	C₂×C₁₉	1	2	yes	complemented
500	#3387	C₂×C₁₉	1	1	yes	characteristic, complemented
501	#3381	C₂×C₁₉	1	1	yes	characteristic, complemented
502	#3377	C₂×C₁₉	1	2	yes	complemented
503	#3374	C₂×C₁₉	1	1	yes	characteristic, complemented
504	#3374	C₂×C₁₉	1	2	yes	complemented
505	#3372	C₂×C₁₉	1	1	yes	characteristic, complemented
506	#3364	C₂×C₁₉	1	1	yes	characteristic, complemented
507	#3363	C₂×C₁₉	1	1	yes	characteristic, complemented
508	#3261	C₂×C₁₉	1	2	yes	complemented
509	#3258	C₂×C₁₉	1	2	yes	—
510	#3249	C₂×C₁₉	1	1	yes	characteristic, complemented
511	#3248	C₂×C₁₉	1	1	yes	characteristic
512	#3185	C₂×C₁₉	1	1	yes	characteristic, complemented
513	#3178	C₂×C₁₉	1	2	yes	—
514	#3177	C₂×C₁₉	1	2	yes	complemented
515	#3172	C₂×C₁₉	1	1	yes	characteristic
516	#2962	C₂×C₁₉	1	1	yes	characteristic, complemented
517	C₂²×C₁₉	—	2	1	no	—
518	C₂²×C₁₉	—	2	1	no	—
519	C₂²×C₁₉	—	2	1	no	—
520	C₂²×C₁₉	—	4	1	no	—
521	C₂²×C₁₉	—	4	1	no	—
522	C₂²×C₁₉	—	4	1	no	—
523	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₁₉	—	2	1	no	—
525	C₄×C₁₉	—	2	1	no	—
526	C₄×C₁₉	—	2	2	no	—
527	C₄×C₁₉	—	2	2	no	—
528	C₄×C₁₉	—	2	1	no	—
529	C₄×C₁₉	—	2	1	no	—
530	C₄×C₁₉	—	2	2	no	—
531	C₄×C₁₉	—	2	2	no	—
532	C₄×C₁₉	—	4	2	no	—
533	C₄×C₁₉	—	4	1	no	—
534	C₄×C₁₉	—	4	1	no	—
535	C₄×C₁₉	—	4	1	no	—
536	C₄×C₁₉	—	4	2	no	—
537	C₄×C₁₉	—	4	1	no	—
538	C₄×C₁₉	—	4	1	no	—
539	C₄×C₁₉	—	4	2	no	—
540	C₄×C₁₉	—	4	1	no	—
541	C₄×C₁₉	—	4	1	no	—
542	C₄×C₁₉	—	4	2	no	—
543	C₄×C₁₉	#578	1	2	yes	—
544	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
545	C₄×C₁₉	#585	1	1	yes	characteristic
546	#564	—	2	2	no	—
547	#563	—	2	2	no	—
548	Q₈²	C₂²×C₁₉	1	1	yes	characteristic
549	#557	—	2	1	no	—
550	#557	—	2	1	no	—
551	#557	C₂²×C₁₉	1	1	yes	characteristic
552	#557	C₂²×C₁₉	1	1	yes	characteristic
553	#557	C₂²×C₁₉	1	1	yes	characteristic
554	#557	C₂²×C₁₉	1	2	yes	—
555	#557	C₂²×C₁₉	1	1	yes	characteristic
556	#557	C₂²×C₁₉	1	1	yes	characteristic
557	#557	C₂²×C₁₉	1	2	yes	—
558	#557	C₂²×C₁₉	1	2	yes	—
559	#556	—	2	1	no	—
560	#556	C₂²×C₁₉	1	1	yes	characteristic
561	#556	C₂²×C₁₉	1	2	yes	—
562	#554	C₂²×C₁₉	1	1	yes	characteristic
563	#552	—	2	1	no	—
564	#544	—	2	1	no	—
565	#542	C₂²×C₁₉	1	2	yes	—
566	#541	—	2	1	no	—
567	#541	—	2	2	no	—
568	#541	—	2	1	no	—
569	#541	—	2	1	no	—
570	#541	—	2	2	no	—
571	#541	C₂²×C₁₉	1	2	yes	—
572	#541	C₂²×C₁₉	1	2	yes	—
573	#541	C₂²×C₁₉	1	2	yes	—
574	#533	C₂²×C₁₉	1	1	yes	characteristic
575	#533	C₂²×C₁₉	1	1	yes	characteristic
576	#533	C₂²×C₁₉	1	1	yes	characteristic
577	#533	C₂²×C₁₉	1	1	yes	characteristic
578	#529	C₂²×C₁₉	1	1	yes	characteristic
579	#501	C₂²×C₁₉	1	2	yes	—
580	#501	C₂²×C₁₉	1	1	yes	characteristic
581	#499	C₂²×C₁₉	1	2	yes	—
582	#498	C₂²×C₁₉	1	1	yes	characteristic
583	#497	C₂²×C₁₉	1	1	yes	characteristic
584	#497	C₂²×C₁₉	1	2	yes	—
585	#494	C₂²×C₁₉	1	2	yes	—
586	#494	C₂²×C₁₉	1	1	yes	characteristic
587	#491	C₂²×C₁₉	1	2	yes	—
588	#491	C₂²×C₁₉	1	1	yes	characteristic
589	#491	C₂²×C₁₉	1	2	yes	—
590	#489	C₂²×C₁₉	1	1	yes	characteristic
591	#488	C₂²×C₁₉	1	2	yes	—
592	#487	C₂²×C₁₉	1	1	yes	characteristic
593	#487	C₂²×C₁₉	1	2	yes	—
594	#487	C₂²×C₁₉	1	1	yes	characteristic
595	#479	C₂²×C₁₉	1	2	yes	—
596	#479	C₂²×C₁₉	1	2	yes	—
597	#479	C₂²×C₁₉	1	2	yes	—
598	#479	C₂²×C₁₉	1	2	yes	—
599	#479	C₂²×C₁₉	1	2	yes	—
600	#479	C₂²×C₁₉	1	2	yes	—
601	#478	C₂²×C₁₉	1	2	yes	—
602	#477	C₂²×C₁₉	1	1	yes	characteristic
603	#477	C₂²×C₁₉	1	2	yes	—
604	#477	C₂²×C₁₉	1	1	yes	characteristic
605	#477	C₂²×C₁₉	1	2	yes	—
606	#475	C₂²×C₁₉	1	1	yes	characteristic
607	#475	C₂²×C₁₉	1	2	yes	—
608	#474	C₂²×C₁₉	1	1	yes	characteristic
609	#470	C₂²×C₁₉	1	1	yes	characteristic
610	#470	C₂²×C₁₉	1	1	yes	characteristic
611	#470	C₂²×C₁₉	1	2	yes	—
612	#470	C₂²×C₁₉	1	2	yes	—
613	#468	C₂²×C₁₉	1	1	yes	characteristic
614	#468	C₂²×C₁₉	1	1	yes	characteristic
615	#467	C₂²×C₁₉	1	2	yes	—
616	#467	C₂²×C₁₉	1	2	yes	—
617	#467	C₂²×C₁₉	1	2	yes	—
618	#465	C₂²×C₁₉	1	2	yes	—
619	#464	C₂²×C₁₉	1	2	yes	—
620	#464	C₂²×C₁₉	1	2	yes	—
621	#464	C₂²×C₁₉	1	2	yes	—
622	#462	C₂²×C₁₉	1	1	yes	characteristic
623	#462	C₂²×C₁₉	1	2	yes	—
624	#462	C₂²×C₁₉	1	1	yes	characteristic
625	#462	C₂²×C₁₉	1	2	yes	—
626	#462	C₂²×C₁₉	1	2	yes	—
627	#462	C₂²×C₁₉	1	1	yes	characteristic
628	#462	C₂²×C₁₉	1	2	yes	—
629	#462	C₂²×C₁₉	1	2	yes	—
630	#462	C₂²×C₁₉	1	2	yes	—
631	#461	C₂²×C₁₉	1	1	yes	characteristic
632	#461	C₂²×C₁₉	1	2	yes	—
633	#446	C₂²×C₁₉	1	1	yes	characteristic
634	#446	C₂²×C₁₉	1	2	yes	—
635	#446	C₂²×C₁₉	1	1	yes	characteristic
636	#446	C₂²×C₁₉	1	2	yes	—
637	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
638	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
639	#441	C₂²×C₁₉	1	2	yes	—
640	#441	C₂²×C₁₉	1	2	yes	—
641	#441	C₂²×C₁₉	1	2	yes	—
642	#441	C₂²×C₁₉	1	2	yes	—
643	#441	C₂²×C₁₉	1	2	yes	—
644	#440	C₂²×C₁₉	1	2	yes	—
645	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
646	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
647	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
648	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
649	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
650	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
651	C₄×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
652	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
653	#424	C₂²×C₁₉	1	2	yes	—
654	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
655	#405	C₂²×C₁₉	1	2	yes	—
656	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
657	C₂×C₁₉	—	4	1	no	—
658	C₂×C₁₉	—	8	1	no	—
659	C₂×C₁₉	#3497	1	1	yes	characteristic
660	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
661	C₂×C₁₉	#3586	1	1	yes	characteristic
662	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
663	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
665	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
666	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
667	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
668	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
670	C₂×SD₁₆	C₂³×C₁₉	1	1	yes	characteristic
671	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
672	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
673	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
674	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
675	C₄⋊Q₈	—	2	1	no	—
676	C₄⋊Q₈	—	2	1	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	—	2	2	no	—
679	C₄⋊Q₈	—	2	2	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
682	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
683	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
684	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
687	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
689	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	1	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	1	no	—
708	#125	—	2	1	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	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	1	no	—
725	#125	—	2	1	no	—
726	#125	—	2	1	no	—
727	#125	—	2	1	no	—
728	#125	D₄×C₁₉	1	2	yes	—
729	#125	C₂³×C₁₉	1	1	yes	characteristic
730	#125	C₂³×C₁₉	1	2	yes	—
731	#125	C₂³×C₁₉	1	2	yes	—
732	#125	C₂³×C₁₉	1	2	yes	—
733	#124	—	2	2	no	—
734	#124	C₂³×C₁₉	1	1	yes	characteristic
735	#124	C₂³×C₁₉	1	2	yes	—
736	#123	—	2	1	no	—
737	#123	—	2	2	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
747	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
748	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
750	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
751	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
752	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
753	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
754	#121	C₂³×C₁₉	1	1	yes	characteristic
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	2	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
769	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
772	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
773	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
774	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
775	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
776	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
777	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
778	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
779	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
781	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₁₉	1	2	yes	—
785	#117	—	2	1	no	—
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	—	2	2	no	—
789	#117	—	2	1	no	—
790	#117	—	2	1	no	—
791	#117	C₂³×C₁₉	1	2	yes	—
792	C₂×C₄⋊C₄	—	2	1	no	—
793	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
794	#107	C₂³×C₁₉	1	1	yes	characteristic
795	#107	C₂³×C₁₉	1	2	yes	—
796	#107	C₂³×C₁₉	1	2	yes	—
797	#107	C₂³×C₁₉	1	1	yes	characteristic
798	#107	C₂³×C₁₉	1	2	yes	—
799	#106	C₂³×C₁₉	1	2	yes	—
800	#106	C₂³×C₁₉	1	1	yes	characteristic
801	#106	C₂³×C₁₉	1	1	yes	characteristic
802	#106	C₂³×C₁₉	1	2	yes	—
803	#106	C₂³×C₁₉	1	2	yes	—
804	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
807	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
808	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
809	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
810	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
811	#103	C₂³×C₁₉	1	1	yes	characteristic
812	#103	C₂³×C₁₉	1	2	yes	—
813	#103	C₂³×C₁₉	1	1	yes	characteristic
814	#103	C₂³×C₁₉	1	1	yes	characteristic
815	#103	C₂³×C₁₉	1	2	yes	—
816	#103	C₂³×C₁₉	1	1	yes	characteristic
817	#103	C₂³×C₁₉	1	2	yes	—
818	#103	C₂³×C₁₉	1	2	yes	—
819	#103	C₂³×C₁₉	1	2	yes	—
820	#103	C₂³×C₁₉	1	1	yes	characteristic
821	#103	C₂³×C₁₉	1	1	yes	characteristic
822	#103	C₂³×C₁₉	1	2	yes	—
823	#103	C₂³×C₁₉	1	2	yes	—
824	#103	C₂³×C₁₉	1	2	yes	—
825	#103	C₂³×C₁₉	1	2	yes	—
826	#103	C₂³×C₁₉	1	2	yes	—
827	#103	C₂³×C₁₉	1	2	yes	—
828	#102	C₂³×C₁₉	1	1	yes	characteristic
829	#102	C₂³×C₁₉	1	2	yes	—
830	#102	C₂³×C₁₉	1	1	yes	characteristic
831	#97	C₂³×C₁₉	1	1	yes	characteristic
832	#97	C₂³×C₁₉	1	1	yes	characteristic
833	#97	C₂³×C₁₉	1	2	yes	—
834	#97	C₂³×C₁₉	1	2	yes	—
835	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
836	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
837	C₄×C₈	C₂³×C₁₉	1	2	yes	—
838	C₄×C₈	C₂³×C₁₉	1	2	yes	—
839	C₁₉	#62406	1	1	yes	characteristic, direct product factor, Sylow
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
845	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
846	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
847	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
848	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
849	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
850	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
851	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
857	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
859	Q₁₆	—	2	2	no	—
860	Q₁₆	—	2	4	no	—
861	Q₁₆	—	4	2	no	—
862	Q₁₆	—	4	2	no	—
863	Q₁₆	—	4	2	no	—
864	Q₁₆	—	4	1	no	—
865	Q₁₆	—	4	2	no	—
866	SD₁₆	—	2	2	no	—
867	SD₁₆	—	4	2	no	—
868	SD₁₆	—	4	1	no	—
869	M₁₆	—	2	2	no	—
870	M₁₆	—	4	1	no	—
871	C₂×C₈	—	4	2	no	—
872	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
874	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
875	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
876	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
877	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
922	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
923	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
924	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
928	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
933	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	1	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
961	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
962	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
963	C₄²	C₂⁴×C₁₉	1	2	yes	—
964	C₄²	C₂⁴×C₁₉	1	2	yes	—
965	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
966	C₂³	—	2	1	no	—
967	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
968	Q₈	—	2	2	no	—
969	Q₈	—	2	2	no	—
970	Q₈	—	2	1	no	—
971	Q₈	—	2	1	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	2	1	no	—
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	4	2	no	—
981	Q₈	—	4	2	no	—
982	Q₈	—	4	2	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	2	no	—
985	D₄	—	2	1	no	—
986	D₄	—	2	1	no	—
987	D₄	—	8	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	4	1	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	8	2	no	—
1005	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1008	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1009	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1010	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1012	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
1014	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
1015	C₈	—	2	1	no	—
1016	C₈	—	2	2	no	—
1017	C₈	—	2	2	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
1028	C₄	—	2	1	no	—
1029	C₄	—	2	1	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	C₁₉×#578	1	2	yes	—
1048	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
1049	C₄	C₁₉×#585	1	1	yes	characteristic
1050	C₂	—	4	1	no	—
1051	C₂	—	8	1	no	—
1052	C₂	C₁₉×#3497	1	1	yes	characteristic
1053	C₂	C₂×C₁₉×#578	1	1	yes	characteristic
1054	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×#121	C₂³
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×#3398	C₂	semidirect
4. C₁₉×#3398	C₂	semidirect
5. C₁₉×#3395	C₂	semidirect
6. C₁₉×#3390	C₂	semidirect
7. C₁₉×#3387	C₂	semidirect
8. C₁₉×#3381	C₂	semidirect
9. C₁₉×#3377	C₂	semidirect
10. C₁₉×#3374	C₂	semidirect
11. C₁₉×#3374	C₂	semidirect
12. C₁₉×#3372	C₂	semidirect
13. C₁₉×#3364	C₂	semidirect
14. C₁₉×#3363	C₂	semidirect
15. C₁₉×#3261	C₂	semidirect
17. C₁₉×#3249	C₂	semidirect
19. C₁₉×#3185	C₂	semidirect
21. C₁₉×#3177	C₂	semidirect
23. C₁₉×#2962	C₂	semidirect
438. #62406	C₁₉	direct (N × H)
494. #3556	C₂×C₁₉	semidirect
496. #3398	C₂×C₁₉	semidirect
497. #3398	C₂×C₁₉	semidirect
498. #3395	C₂×C₁₉	semidirect
499. #3390	C₂×C₁₉	semidirect
500. #3387	C₂×C₁₉	semidirect
501. #3381	C₂×C₁₉	semidirect
502. #3377	C₂×C₁₉	semidirect
503. #3374	C₂×C₁₉	semidirect
504. #3374	C₂×C₁₉	semidirect
505. #3372	C₂×C₁₉	semidirect
506. #3364	C₂×C₁₉	semidirect
507. #3363	C₂×C₁₉	semidirect
508. #3261	C₂×C₁₉	semidirect
510. #3249	C₂×C₁₉	semidirect
512. #3185	C₂×C₁₉	semidirect
514. #3177	C₂×C₁₉	semidirect
516. #2962	C₂×C₁₉	semidirect
839. C₁₉	#62406	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×#3555	2
C₁₉×#3398	2
C₁₉×#3395	2
C₁₉×#3390	2
C₁₉×#3387	2
C₁₉×#3381	2
C₁₉×#3377	2
C₁₉×#3374	2
C₁₉×#3372	2
C₁₉×#3364	2
C₁₉×#3363	2
C₁₉×#3261	2
C₁₉×#3258	2
C₁₉×#3249	2
C₁₉×#3248	2
C₁₉×#3185	2
C₁₉×#3178	2
C₁₉×#3177	2
C₁₉×#3172	2
C₁₉×#2962	2
#62406	19

Subgroups — C19×#62406 #18068365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62406 #18068365