Subgroups — C₁₉×#62391 #18068350

Order 4864.

1600 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3555	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3402	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3398	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3388	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3387	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3377	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3376	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3374	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3369	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3263	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#3261	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3258	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3256	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3181	C₂	1	2	yes	maximal, complemented
16	C₁₉×#3178	C₂	1	2	yes	maximal, complemented
17	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#3173	C₂	1	1	yes	maximal, characteristic
19	C₁₉×#2961	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₉×#563	—	2	2	no	—
21	C₁₉×#563	—	2	2	no	—
22	Q₈²×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#557	C₂²	1	2	yes	—
24	C₁₉×#557	C₂²	1	2	yes	—
25	C₁₉×#557	C₂²	1	2	yes	—
26	C₁₉×#556	—	2	2	no	—
27	C₁₉×#556	C₂²	1	2	yes	—
28	C₁₉×#556	C₂²	1	2	yes	—
29	C₁₉×#556	C₂²	1	2	yes	—
30	C₁₉×#554	C₂²	1	2	yes	—
31	C₁₉×#552	—	2	2	no	—
32	C₁₉×#544	—	2	2	no	—
33	C₁₉×#542	C₂²	1	2	yes	—
34	C₁₉×#542	C₂²	1	2	yes	—
35	C₁₉×#541	—	2	2	no	—
36	C₁₉×#541	—	2	2	no	—
37	C₁₉×#541	—	2	2	no	—
38	C₁₉×#541	C₂²	1	2	yes	—
39	C₁₉×#541	C₂²	1	2	yes	—
40	C₁₉×#533	C₂²	1	2	yes	—
41	C₁₉×#533	C₂²	1	1	yes	characteristic
42	C₁₉×#529	C₂²	1	2	yes	—
43	C₁₉×#501	C₂²	1	2	yes	—
44	C₁₉×#501	C₂²	1	2	yes	—
45	C₁₉×#499	C₂²	1	1	yes	characteristic
46	C₁₉×#498	C₂²	1	1	yes	characteristic
47	C₁₉×#497	C₂²	1	2	yes	—
48	C₁₉×#497	C₂²	1	2	yes	—
49	C₁₉×#495	C₂²	1	1	yes	characteristic
50	C₁₉×#494	C₂²	1	1	yes	characteristic
51	C₁₉×#491	C₂²	1	2	yes	—
52	C₁₉×#491	C₂²	1	2	yes	—
53	C₁₉×#489	C₂²	1	2	yes	—
54	C₁₉×#489	C₂²	1	2	yes	—
55	C₁₉×#488	C₂²	1	2	yes	—
56	C₁₉×#487	C₂²	1	2	yes	—
57	C₁₉×#479	C₂²	1	2	yes	—
58	C₁₉×#479	C₂²	1	2	yes	—
59	C₁₉×#479	C₂²	1	2	yes	—
60	C₁₉×#479	C₂²	1	2	yes	—
61	C₁₉×#478	C₂²	1	2	yes	—
62	C₁₉×#478	C₂²	1	2	yes	—
63	C₁₉×#477	C₂²	1	2	yes	—
64	C₁₉×#476	C₂²	1	2	yes	—
65	C₁₉×#475	C₂²	1	2	yes	—
66	C₁₉×#475	C₂²	1	2	yes	—
67	C₁₉×#475	C₂²	1	2	yes	—
68	C₁₉×#475	C₂²	1	2	yes	—
69	C₁₉×#470	C₂²	1	1	yes	characteristic
70	C₁₉×#470	C₂²	1	1	yes	characteristic
71	C₁₉×#470	C₂²	1	1	yes	characteristic
72	C₁₉×#470	C₂²	1	2	yes	—
73	C₁₉×#469	C₂²	1	1	yes	characteristic
74	C₁₉×#468	C₂²	1	2	yes	—
75	C₁₉×#467	C₂²	1	2	yes	—
76	C₁₉×#467	C₂²	1	2	yes	—
77	C₁₉×#465	C₂²	1	2	yes	—
78	C₁₉×#465	C₂²	1	2	yes	—
79	C₁₉×#464	C₂²	1	2	yes	—
80	C₁₉×#464	C₂²	1	2	yes	—
81	C₁₉×#464	C₂²	1	2	yes	—
82	C₁₉×#464	C₂²	1	2	yes	—
83	C₁₉×#463	C₂²	1	2	yes	—
84	C₁₉×#463	C₂²	1	2	yes	—
85	C₁₉×#462	C₂²	1	2	yes	—
86	C₁₉×#462	C₂²	1	2	yes	—
87	C₁₉×#462	C₂²	1	2	yes	—
88	C₁₉×#462	C₂²	1	2	yes	—
89	C₁₉×#462	C₂²	1	2	yes	—
90	C₁₉×#461	C₂²	1	2	yes	—
91	C₁₉×#446	C₂²	1	2	yes	—
92	C₁₉×#446	C₂²	1	2	yes	—
93	C₁₉×#446	C₂²	1	2	yes	—
94	C₁₉×#446	C₂²	1	2	yes	—
95	C₁₉×#442	C₂²	1	1	yes	characteristic
96	C₁₉×#441	C₂²	1	1	yes	characteristic
97	C₁₉×#441	C₂²	1	1	yes	characteristic
98	C₁₉×#441	C₂²	1	1	yes	characteristic
99	C₁₉×#441	C₂²	1	2	yes	—
100	C₁₉×#441	C₂²	1	2	yes	—
101	C₁₉×#441	C₂²	1	2	yes	—
102	C₁₉×#440	C₂²	1	2	yes	—
103	C₁₉×#440	C₂²	1	2	yes	—
104	C₁₉×#440	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
106	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
109	C₁₉×#424	C₂²	1	1	yes	characteristic
110	C₁₉×#424	C₂²	1	1	yes	characteristic
111	C₁₉×#423	C₂²	1	1	yes	characteristic
112	C₁₉×#405	C₂²	1	1	yes	characteristic
113	C₁₉×#405	C₂²	1	1	yes	characteristic
114	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
115	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
117	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
124	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₁₉×C₄⋊Q₈	—	2	2	no	—
130	C₁₉×C₄⋊Q₈	—	2	2	no	—
131	C₁₉×C₄⋊Q₈	—	2	2	no	—
132	C₁₉×C₄⋊Q₈	—	2	2	no	—
133	C₁₉×C₄⋊Q₈	—	2	2	no	—
134	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
135	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₉×#126	—	2	2	no	—
142	C₁₉×#126	—	2	2	no	—
143	C₁₉×#126	—	2	2	no	—
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×#126	—	2	2	no	—
151	C₁₉×#126	—	2	2	no	—
152	C₁₉×#126	—	2	2	no	—
153	C₁₉×#126	—	2	2	no	—
154	C₁₉×#125	—	2	2	no	—
155	C₁₉×#125	—	2	2	no	—
156	C₁₉×#125	—	2	2	no	—
157	C₁₉×#125	—	2	2	no	—
158	C₁₉×#125	—	2	2	no	—
159	C₁₉×#125	—	2	2	no	—
160	C₁₉×#125	—	2	2	no	—
161	C₁₉×#125	—	2	2	no	—
162	C₁₉×#125	—	2	2	no	—
163	C₁₉×#125	—	2	2	no	—
164	C₁₉×#125	—	2	2	no	—
165	C₁₉×#125	—	2	2	no	—
166	C₁₉×#125	D₄	1	2	yes	—
167	C₁₉×#125	C₂³	1	2	yes	—
168	C₁₉×#125	C₂³	1	2	yes	—
169	C₁₉×#125	C₂³	1	2	yes	—
170	C₁₉×#124	—	2	2	no	—
171	C₁₉×#124	—	2	2	no	—
172	C₁₉×#124	C₂³	1	2	yes	—
173	C₁₉×#124	C₂³	1	2	yes	—
174	C₁₉×#124	C₂³	1	2	yes	—
175	C₁₉×#123	—	2	2	no	—
176	C₁₉×#123	—	2	2	no	—
177	C₁₉×#123	—	2	2	no	—
178	C₁₉×C₂²⋊Q₈	—	2	2	no	—
179	C₁₉×C₂²⋊Q₈	—	2	2	no	—
180	C₁₉×C₂²⋊Q₈	—	2	2	no	—
181	C₁₉×C₂²⋊Q₈	—	2	2	no	—
182	C₁₉×C₂²⋊Q₈	—	2	2	no	—
183	C₁₉×C₂²⋊Q₈	—	2	2	no	—
184	C₁₉×C₂²⋊Q₈	—	2	2	no	—
185	C₁₉×C₂²⋊Q₈	—	2	2	no	—
186	C₁₉×C₂²⋊Q₈	—	2	2	no	—
187	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
188	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₁₉×#121	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₉	—	2	2	no	—
194	C₄×Q₈×C₁₉	—	2	2	no	—
195	C₄×Q₈×C₁₉	—	2	2	no	—
196	C₄×Q₈×C₁₉	—	2	2	no	—
197	C₄×Q₈×C₁₉	—	2	2	no	—
198	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
199	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
200	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
201	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
204	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
205	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
206	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
208	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
209	C₄×D₄×C₁₉	—	2	2	no	—
210	C₄×D₄×C₁₉	C₂³	1	2	yes	—
211	C₄×D₄×C₁₉	C₂³	1	2	yes	—
212	C₄×D₄×C₁₉	C₂³	1	2	yes	—
213	C₁₉×#117	—	2	2	no	—
214	C₁₉×#117	—	2	2	no	—
215	C₁₉×#117	—	2	2	no	—
216	C₁₉×#117	—	2	2	no	—
217	C₁₉×#117	—	2	2	no	—
218	C₁₉×#117	C₂³	1	1	yes	characteristic
219	C₁₉×#117	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
221	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
222	C₁₉×#107	C₂³	1	2	yes	—
223	C₁₉×#107	C₂³	1	2	yes	—
224	C₁₉×#107	C₂³	1	2	yes	—
225	C₁₉×#106	C₂³	1	2	yes	—
226	C₁₉×#106	C₂³	1	2	yes	—
227	C₁₉×#106	C₂³	1	2	yes	—
228	C₁₉×#106	C₂³	1	1	yes	characteristic
229	C₁₉×#106	C₂³	1	1	yes	characteristic
230	C₁₉×#106	C₂³	1	1	yes	characteristic
231	C₁₉×#106	C₂³	1	1	yes	characteristic
232	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
233	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
234	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₉×#103	C₂³	1	2	yes	—
239	C₁₉×#103	C₂³	1	2	yes	—
240	C₁₉×#103	C₂³	1	2	yes	—
241	C₁₉×#103	C₂³	1	2	yes	—
242	C₁₉×#103	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×#102	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×#97	C₂³	1	2	yes	—
255	C₁₉×#97	C₂³	1	2	yes	—
256	C₁₉×#97	C₂³	1	2	yes	—
257	C₁₉×#97	C₂³	1	1	yes	characteristic
258	C₁₉×#97	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₁₉	C₂³	1	2	yes	—
261	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
262	C₂×Q₈×C₁₉	—	2	2	no	—
263	C₂×Q₈×C₁₉	—	2	2	no	—
264	C₂×Q₈×C₁₉	—	2	2	no	—
265	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
266	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
267	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
269	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
270	C₂×D₄×C₁₉	—	2	2	no	—
271	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₉	—	2	2	no	—
273	C₂²×C₄×C₁₉	—	2	2	no	—
274	C₂²×C₄×C₁₉	—	2	2	no	—
275	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₁₉	—	2	4	no	—
278	Q₁₆×C₁₉	—	4	2	no	—
279	Q₁₆×C₁₉	—	4	1	no	—
280	Q₁₆×C₁₉	—	4	2	no	—
281	Q₁₆×C₁₉	—	4	1	no	—
282	Q₁₆×C₁₉	—	4	1	no	—
283	SD₁₆×C₁₉	—	2	4	no	—
284	SD₁₆×C₁₉	—	4	2	no	—
285	SD₁₆×C₁₉	—	4	2	no	—
286	D₈×C₁₉	—	4	1	no	—
287	M₁₆×C₁₉	—	4	1	no	—
288	M₁₆×C₁₉	—	4	1	no	—
289	C₂×C₈×C₁₉	—	2	2	no	—
290	C₂×C₈×C₁₉	—	4	1	no	—
291	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
292	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
293	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
294	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
295	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
296	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₁₉	—	2	2	no	—
298	C₄⋊C₄×C₁₉	—	2	2	no	—
299	C₄⋊C₄×C₁₉	—	2	2	no	—
300	C₄⋊C₄×C₁₉	—	2	2	no	—
301	C₄⋊C₄×C₁₉	—	2	2	no	—
302	C₄⋊C₄×C₁₉	—	2	2	no	—
303	C₄⋊C₄×C₁₉	—	2	2	no	—
304	C₄⋊C₄×C₁₉	—	2	2	no	—
305	C₄⋊C₄×C₁₉	—	2	2	no	—
306	C₄⋊C₄×C₁₉	—	2	2	no	—
307	C₄⋊C₄×C₁₉	—	2	2	no	—
308	C₄⋊C₄×C₁₉	—	2	2	no	—
309	C₄⋊C₄×C₁₉	—	2	2	no	—
310	C₄⋊C₄×C₁₉	—	2	2	no	—
311	C₄⋊C₄×C₁₉	—	2	2	no	—
312	C₄⋊C₄×C₁₉	—	2	2	no	—
313	C₄⋊C₄×C₁₉	—	2	2	no	—
314	C₄⋊C₄×C₁₉	—	2	2	no	—
315	C₄⋊C₄×C₁₉	—	2	2	no	—
316	C₄⋊C₄×C₁₉	—	2	2	no	—
317	C₄⋊C₄×C₁₉	—	2	2	no	—
318	C₄⋊C₄×C₁₉	—	2	2	no	—
319	C₄⋊C₄×C₁₉	—	2	2	no	—
320	C₄⋊C₄×C₁₉	—	2	2	no	—
321	C₄⋊C₄×C₁₉	—	2	2	no	—
322	C₄⋊C₄×C₁₉	—	2	2	no	—
323	C₄⋊C₄×C₁₉	—	2	2	no	—
324	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
326	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
327	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
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	—	2	2	no	—
340	C₂²⋊C₄×C₁₉	—	2	2	no	—
341	C₂²⋊C₄×C₁₉	—	2	2	no	—
342	C₂²⋊C₄×C₁₉	—	2	2	no	—
343	C₂²⋊C₄×C₁₉	—	2	2	no	—
344	C₂²⋊C₄×C₁₉	—	2	2	no	—
345	C₂²⋊C₄×C₁₉	—	2	2	no	—
346	C₂²⋊C₄×C₁₉	—	2	2	no	—
347	C₂²⋊C₄×C₁₉	—	2	2	no	—
348	C₂²⋊C₄×C₁₉	—	2	2	no	—
349	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
350	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
351	C₂²⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₁₉	—	2	2	no	—
353	C₄²×C₁₉	—	2	2	no	—
354	C₄²×C₁₉	—	2	2	no	—
355	C₄²×C₁₉	—	2	2	no	—
356	C₄²×C₁₉	—	2	2	no	—
357	C₄²×C₁₉	—	2	2	no	—
358	C₄²×C₁₉	—	2	2	no	—
359	C₄²×C₁₉	—	2	2	no	—
360	C₄²×C₁₉	—	2	2	no	—
361	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₁₉	C₂⁴	1	2	yes	—
364	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
365	C₄²×C₁₉	C₂⁴	1	2	yes	—
366	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
367	#62391	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂³×C₁₉	—	2	2	no	—
369	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
370	Q₈×C₁₉	—	2	2	no	—
371	Q₈×C₁₉	—	2	2	no	—
372	Q₈×C₁₉	—	2	2	no	—
373	Q₈×C₁₉	—	2	2	no	—
374	Q₈×C₁₉	—	2	2	no	—
375	Q₈×C₁₉	—	2	2	no	—
376	Q₈×C₁₉	—	4	2	no	—
377	Q₈×C₁₉	—	4	2	no	—
378	Q₈×C₁₉	—	8	2	no	—
379	Q₈×C₁₉	—	8	2	no	—
380	Q₈×C₁₉	—	8	2	no	—
381	D₄×C₁₉	—	2	2	no	—
382	D₄×C₁₉	—	2	2	no	—
383	D₄×C₁₉	—	8	2	no	—
384	C₂×C₄×C₁₉	—	2	1	no	—
385	C₂×C₄×C₁₉	—	2	1	no	—
386	C₂×C₄×C₁₉	—	2	2	no	—
387	C₂×C₄×C₁₉	—	2	2	no	—
388	C₂×C₄×C₁₉	—	2	2	no	—
389	C₂×C₄×C₁₉	—	2	2	no	—
390	C₂×C₄×C₁₉	—	2	2	no	—
391	C₂×C₄×C₁₉	—	2	2	no	—
392	C₂×C₄×C₁₉	—	2	2	no	—
393	C₂×C₄×C₁₉	—	4	2	no	—
394	C₂×C₄×C₁₉	—	4	4	no	—
395	C₂×C₄×C₁₉	—	8	2	no	—
396	C₂×C₄×C₁₉	—	8	2	no	—
397	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
405	C₈×C₁₉	—	2	1	no	—
406	C₈×C₁₉	—	2	2	no	—
407	C₈×C₁₉	—	2	1	no	—
408	C₈×C₁₉	—	2	2	no	—
409	C₈×C₁₉	—	2	1	no	—
410	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
411	#3555	C₂×C₁₉	1	2	yes	complemented
412	#3402	C₂×C₁₉	1	2	yes	complemented
413	#3398	C₂×C₁₉	1	2	yes	complemented
414	#3388	C₂×C₁₉	1	2	yes	complemented
415	#3387	C₂×C₁₉	1	2	yes	complemented
416	#3377	C₂×C₁₉	1	2	yes	complemented
417	#3376	C₂×C₁₉	1	2	yes	complemented
418	#3374	C₂×C₁₉	1	2	yes	complemented
419	#3369	C₂×C₁₉	1	2	yes	complemented
420	#3263	C₂×C₁₉	1	1	yes	characteristic
421	#3261	C₂×C₁₉	1	1	yes	characteristic, complemented
422	#3258	C₂×C₁₉	1	2	yes	complemented
423	#3256	C₂×C₁₉	1	1	yes	characteristic
424	#3255	C₂×C₁₉	1	1	yes	characteristic, complemented
425	#3181	C₂×C₁₉	1	2	yes	complemented
426	#3178	C₂×C₁₉	1	2	yes	complemented
427	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
428	#3173	C₂×C₁₉	1	1	yes	characteristic
429	#2961	C₂×C₁₉	1	1	yes	characteristic, complemented
430	C₂²×C₁₉	—	2	2	no	—
431	C₂²×C₁₉	—	2	1	no	—
432	C₂²×C₁₉	—	4	2	no	—
433	C₂²×C₁₉	—	4	2	no	—
434	C₂²×C₁₉	—	4	2	no	—
435	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
436	C₄×C₁₉	—	2	2	no	—
437	C₄×C₁₉	—	2	2	no	—
438	C₄×C₁₉	—	2	2	no	—
439	C₄×C₁₉	—	2	2	no	—
440	C₄×C₁₉	—	2	2	no	—
441	C₄×C₁₉	—	2	2	no	—
442	C₄×C₁₉	—	2	1	no	—
443	C₄×C₁₉	—	4	2	no	—
444	C₄×C₁₉	—	4	2	no	—
445	C₄×C₁₉	—	4	2	no	—
446	C₄×C₁₉	—	4	2	no	—
447	C₄×C₁₉	—	4	2	no	—
448	C₄×C₁₉	—	4	2	no	—
449	C₄×C₁₉	—	4	2	no	—
450	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₄×C₁₉	#585	1	1	yes	characteristic
452	#563	—	2	2	no	—
453	#563	—	2	2	no	—
454	Q₈²	C₂²×C₁₉	1	2	yes	—
455	#557	C₂²×C₁₉	1	2	yes	—
456	#557	C₂²×C₁₉	1	2	yes	—
457	#557	C₂²×C₁₉	1	2	yes	—
458	#556	—	2	2	no	—
459	#556	C₂²×C₁₉	1	2	yes	—
460	#556	C₂²×C₁₉	1	2	yes	—
461	#556	C₂²×C₁₉	1	2	yes	—
462	#554	C₂²×C₁₉	1	2	yes	—
463	#552	—	2	2	no	—
464	#544	—	2	2	no	—
465	#542	C₂²×C₁₉	1	2	yes	—
466	#542	C₂²×C₁₉	1	2	yes	—
467	#541	—	2	2	no	—
468	#541	—	2	2	no	—
469	#541	—	2	2	no	—
470	#541	C₂²×C₁₉	1	2	yes	—
471	#541	C₂²×C₁₉	1	2	yes	—
472	#533	C₂²×C₁₉	1	2	yes	—
473	#533	C₂²×C₁₉	1	1	yes	characteristic
474	#529	C₂²×C₁₉	1	2	yes	—
475	#501	C₂²×C₁₉	1	2	yes	—
476	#501	C₂²×C₁₉	1	2	yes	—
477	#499	C₂²×C₁₉	1	1	yes	characteristic
478	#498	C₂²×C₁₉	1	1	yes	characteristic
479	#497	C₂²×C₁₉	1	2	yes	—
480	#497	C₂²×C₁₉	1	2	yes	—
481	#495	C₂²×C₁₉	1	1	yes	characteristic
482	#494	C₂²×C₁₉	1	1	yes	characteristic
483	#491	C₂²×C₁₉	1	2	yes	—
484	#491	C₂²×C₁₉	1	2	yes	—
485	#489	C₂²×C₁₉	1	2	yes	—
486	#489	C₂²×C₁₉	1	2	yes	—
487	#488	C₂²×C₁₉	1	2	yes	—
488	#487	C₂²×C₁₉	1	2	yes	—
489	#479	C₂²×C₁₉	1	2	yes	—
490	#479	C₂²×C₁₉	1	2	yes	—
491	#479	C₂²×C₁₉	1	2	yes	—
492	#479	C₂²×C₁₉	1	2	yes	—
493	#478	C₂²×C₁₉	1	2	yes	—
494	#478	C₂²×C₁₉	1	2	yes	—
495	#477	C₂²×C₁₉	1	2	yes	—
496	#476	C₂²×C₁₉	1	2	yes	—
497	#475	C₂²×C₁₉	1	2	yes	—
498	#475	C₂²×C₁₉	1	2	yes	—
499	#475	C₂²×C₁₉	1	2	yes	—
500	#475	C₂²×C₁₉	1	2	yes	—
501	#470	C₂²×C₁₉	1	1	yes	characteristic
502	#470	C₂²×C₁₉	1	1	yes	characteristic
503	#470	C₂²×C₁₉	1	1	yes	characteristic
504	#470	C₂²×C₁₉	1	2	yes	—
505	#469	C₂²×C₁₉	1	1	yes	characteristic
506	#468	C₂²×C₁₉	1	2	yes	—
507	#467	C₂²×C₁₉	1	2	yes	—
508	#467	C₂²×C₁₉	1	2	yes	—
509	#465	C₂²×C₁₉	1	2	yes	—
510	#465	C₂²×C₁₉	1	2	yes	—
511	#464	C₂²×C₁₉	1	2	yes	—
512	#464	C₂²×C₁₉	1	2	yes	—
513	#464	C₂²×C₁₉	1	2	yes	—
514	#464	C₂²×C₁₉	1	2	yes	—
515	#463	C₂²×C₁₉	1	2	yes	—
516	#463	C₂²×C₁₉	1	2	yes	—
517	#462	C₂²×C₁₉	1	2	yes	—
518	#462	C₂²×C₁₉	1	2	yes	—
519	#462	C₂²×C₁₉	1	2	yes	—
520	#462	C₂²×C₁₉	1	2	yes	—
521	#462	C₂²×C₁₉	1	2	yes	—
522	#461	C₂²×C₁₉	1	2	yes	—
523	#446	C₂²×C₁₉	1	2	yes	—
524	#446	C₂²×C₁₉	1	2	yes	—
525	#446	C₂²×C₁₉	1	2	yes	—
526	#446	C₂²×C₁₉	1	2	yes	—
527	#442	C₂²×C₁₉	1	1	yes	characteristic
528	#441	C₂²×C₁₉	1	1	yes	characteristic
529	#441	C₂²×C₁₉	1	2	yes	—
530	#441	C₂²×C₁₉	1	1	yes	characteristic
531	#441	C₂²×C₁₉	1	1	yes	characteristic
532	#441	C₂²×C₁₉	1	2	yes	—
533	#441	C₂²×C₁₉	1	2	yes	—
534	#440	C₂²×C₁₉	1	2	yes	—
535	#440	C₂²×C₁₉	1	2	yes	—
536	#440	C₂²×C₁₉	1	2	yes	—
537	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
538	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
539	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
540	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
541	#424	C₂²×C₁₉	1	1	yes	characteristic
542	#424	C₂²×C₁₉	1	1	yes	characteristic
543	#423	C₂²×C₁₉	1	1	yes	characteristic
544	#405	C₂²×C₁₉	1	1	yes	characteristic
545	#405	C₂²×C₁₉	1	1	yes	characteristic
546	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
547	C₂×C₁₉	—	4	1	no	—
548	C₂×C₁₉	—	8	2	no	—
549	C₂×C₁₉	#3497	1	1	yes	characteristic
550	C₂×C₁₉	#3586	1	2	yes	—
551	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
552	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
553	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
554	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
555	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
556	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
557	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
558	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
560	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
561	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
562	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
565	C₄⋊Q₈	—	2	2	no	—
566	C₄⋊Q₈	—	2	2	no	—
567	C₄⋊Q₈	—	2	2	no	—
568	C₄⋊Q₈	—	2	2	no	—
569	C₄⋊Q₈	—	2	2	no	—
570	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
571	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
572	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
573	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
576	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#126	—	2	2	no	—
581	#126	—	2	2	no	—
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#126	—	2	2	no	—
590	#125	—	2	2	no	—
591	#125	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	—	2	2	no	—
594	#125	—	2	2	no	—
595	#125	—	2	2	no	—
596	#125	—	2	2	no	—
597	#125	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	D₄×C₁₉	1	2	yes	—
603	#125	C₂³×C₁₉	1	2	yes	—
604	#125	C₂³×C₁₉	1	2	yes	—
605	#125	C₂³×C₁₉	1	2	yes	—
606	#124	—	2	2	no	—
607	#124	—	2	2	no	—
608	#124	C₂³×C₁₉	1	2	yes	—
609	#124	C₂³×C₁₉	1	2	yes	—
610	#124	C₂³×C₁₉	1	2	yes	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
624	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
627	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
628	#121	C₂³×C₁₉	1	2	yes	—
629	C₄×Q₈	—	2	2	no	—
630	C₄×Q₈	—	2	2	no	—
631	C₄×Q₈	—	2	2	no	—
632	C₄×Q₈	—	2	2	no	—
633	C₄×Q₈	—	2	2	no	—
634	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
635	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
636	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
637	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
638	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
639	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
640	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
641	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
642	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
643	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
644	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	C₂³×C₁₉	1	2	yes	—
647	C₄×D₄	C₂³×C₁₉	1	2	yes	—
648	C₄×D₄	C₂³×C₁₉	1	2	yes	—
649	#117	—	2	2	no	—
650	#117	—	2	2	no	—
651	#117	—	2	2	no	—
652	#117	—	2	2	no	—
653	#117	—	2	2	no	—
654	#117	C₂³×C₁₉	1	1	yes	characteristic
655	#117	C₂³×C₁₉	1	1	yes	characteristic
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
658	#107	C₂³×C₁₉	1	2	yes	—
659	#107	C₂³×C₁₉	1	2	yes	—
660	#107	C₂³×C₁₉	1	2	yes	—
661	#106	C₂³×C₁₉	1	2	yes	—
662	#106	C₂³×C₁₉	1	2	yes	—
663	#106	C₂³×C₁₉	1	2	yes	—
664	#106	C₂³×C₁₉	1	1	yes	characteristic
665	#106	C₂³×C₁₉	1	1	yes	characteristic
666	#106	C₂³×C₁₉	1	1	yes	characteristic
667	#106	C₂³×C₁₉	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
669	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
670	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
671	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
672	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
673	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
674	#103	C₂³×C₁₉	1	2	yes	—
675	#103	C₂³×C₁₉	1	2	yes	—
676	#103	C₂³×C₁₉	1	2	yes	—
677	#103	C₂³×C₁₉	1	2	yes	—
678	#103	C₂³×C₁₉	1	2	yes	—
679	#103	C₂³×C₁₉	1	2	yes	—
680	#103	C₂³×C₁₉	1	2	yes	—
681	#103	C₂³×C₁₉	1	2	yes	—
682	#103	C₂³×C₁₉	1	2	yes	—
683	#103	C₂³×C₁₉	1	2	yes	—
684	#103	C₂³×C₁₉	1	2	yes	—
685	#103	C₂³×C₁₉	1	2	yes	—
686	#102	C₂³×C₁₉	1	2	yes	—
687	#102	C₂³×C₁₉	1	2	yes	—
688	#102	C₂³×C₁₉	1	2	yes	—
689	#102	C₂³×C₁₉	1	2	yes	—
690	#97	C₂³×C₁₉	1	2	yes	—
691	#97	C₂³×C₁₉	1	2	yes	—
692	#97	C₂³×C₁₉	1	2	yes	—
693	#97	C₂³×C₁₉	1	1	yes	characteristic
694	#97	C₂³×C₁₉	1	1	yes	characteristic
695	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
696	C₄×C₈	C₂³×C₁₉	1	2	yes	—
697	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
698	C₁₉	#62391	1	1	yes	characteristic, direct product factor, Sylow
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
703	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
704	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
705	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
706	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
714	Q₁₆	—	2	4	no	—
715	Q₁₆	—	4	2	no	—
716	Q₁₆	—	4	1	no	—
717	Q₁₆	—	4	2	no	—
718	Q₁₆	—	4	1	no	—
719	Q₁₆	—	4	1	no	—
720	SD₁₆	—	2	4	no	—
721	SD₁₆	—	4	2	no	—
722	SD₁₆	—	4	2	no	—
723	D₈	—	4	1	no	—
724	M₁₆	—	4	1	no	—
725	M₁₆	—	4	1	no	—
726	C₂×C₈	—	2	2	no	—
727	C₂×C₈	—	4	1	no	—
728	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
729	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
730	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
731	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
732	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
733	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
762	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
765	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
766	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
767	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
771	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
772	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
787	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
799	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
800	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
801	C₄²	C₂⁴×C₁₉	1	2	yes	—
802	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
803	C₄²	C₂⁴×C₁₉	1	2	yes	—
804	C₂³	—	2	2	no	—
805	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
806	Q₈	—	2	2	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	4	2	no	—
813	Q₈	—	4	2	no	—
814	Q₈	—	8	2	no	—
815	Q₈	—	8	2	no	—
816	Q₈	—	8	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	2	no	—
819	D₄	—	8	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	—	8	2	no	—
833	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
840	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
841	C₈	—	2	1	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	1	no	—
844	C₈	—	2	2	no	—
845	C₈	—	2	1	no	—
846	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
853	C₄	—	2	1	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
868	C₄	C₁₉×#585	1	1	yes	characteristic
869	C₂	—	4	1	no	—
870	C₂	—	8	2	no	—
871	C₂	C₁₉×#3497	1	1	yes	characteristic
872	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#469	C₂²
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×#3555	C₂	semidirect
2. C₁₉×#3402	C₂	semidirect
3. C₁₉×#3398	C₂	semidirect
4. C₁₉×#3388	C₂	semidirect
5. C₁₉×#3387	C₂	semidirect
6. C₁₉×#3377	C₂	semidirect
7. C₁₉×#3376	C₂	semidirect
8. C₁₉×#3374	C₂	semidirect
9. C₁₉×#3369	C₂	semidirect
11. C₁₉×#3261	C₂	semidirect
12. C₁₉×#3258	C₂	semidirect
14. C₁₉×#3255	C₂	semidirect
15. C₁₉×#3181	C₂	semidirect
16. C₁₉×#3178	C₂	semidirect
17. C₁₉×#3177	C₂	semidirect
19. C₁₉×#2961	C₂	semidirect
367. #62391	C₁₉	direct (N × H)
411. #3555	C₂×C₁₉	semidirect
412. #3402	C₂×C₁₉	semidirect
413. #3398	C₂×C₁₉	semidirect
414. #3388	C₂×C₁₉	semidirect
415. #3387	C₂×C₁₉	semidirect
416. #3377	C₂×C₁₉	semidirect
417. #3376	C₂×C₁₉	semidirect
418. #3374	C₂×C₁₉	semidirect
419. #3369	C₂×C₁₉	semidirect
421. #3261	C₂×C₁₉	semidirect
422. #3258	C₂×C₁₉	semidirect
424. #3255	C₂×C₁₉	semidirect
425. #3181	C₂×C₁₉	semidirect
426. #3178	C₂×C₁₉	semidirect
427. #3177	C₂×C₁₉	semidirect
429. #2961	C₂×C₁₉	semidirect
698. C₁₉	#62391	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×#3555	2
C₁₉×#3402	2
C₁₉×#3398	2
C₁₉×#3388	2
C₁₉×#3387	2
C₁₉×#3377	2
C₁₉×#3376	2
C₁₉×#3374	2
C₁₉×#3369	2
C₁₉×#3263	2
C₁₉×#3261	2
C₁₉×#3258	2
C₁₉×#3256	2
C₁₉×#3255	2
C₁₉×#3181	2
C₁₉×#3178	2
C₁₉×#3177	2
C₁₉×#3173	2
C₁₉×#2961	2
#62391	19

Subgroups — C19×#62391 #18068350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62391 #18068350