Subgroups — C₁₉×#62365 #18068324

Order 4864.

1930 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3397	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3386	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3384	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3373	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3368	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3367	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3366	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3247	C₂	1	4	yes	maximal, complemented
12	C₁₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3180	C₂	1	4	yes	maximal, complemented
15	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
19	C₁₉×#559	C₂²	1	2	yes	—
20	C₁₉×#557	C₂²	1	2	yes	—
21	C₁₉×#556	—	2	2	no	—
22	C₁₉×#556	C₂²	1	2	yes	—
23	C₁₉×#554	C₂²	1	2	yes	—
24	C₁₉×#552	—	2	2	no	—
25	C₁₉×#550	C₂²	1	2	yes	—
26	C₁₉×#550	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
28	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#548	—	2	2	no	—
30	C₁₉×#548	—	2	2	no	—
31	C₁₉×#539	—	2	2	no	—
32	C₁₉×#537	—	2	1	no	—
33	C₁₉×#537	—	2	2	no	—
34	C₁₉×#536	—	2	1	no	—
35	C₁₉×#533	C₂²	1	1	yes	characteristic
36	C₁₉×#532	C₂²	1	1	yes	characteristic
37	C₁₉×#532	C₂²	1	1	yes	characteristic
38	C₁₉×#532	C₂²	1	1	yes	characteristic
39	C₁₉×#532	C₂²	1	4	yes	—
40	C₁₉×#529	C₂²	1	4	yes	—
41	C₁₉×#520	—	2	1	no	—
42	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#501	C₂²	1	4	yes	—
44	C₁₉×#500	C₂²	1	1	yes	characteristic
45	C₁₉×#498	C₂²	1	1	yes	characteristic
46	C₁₉×#496	C₂²	1	4	yes	—
47	C₁₉×#493	C₂²	1	1	yes	characteristic
48	C₁₉×#492	C₂²	1	1	yes	characteristic
49	C₁₉×#490	C₂²	1	4	yes	—
50	C₁₉×#489	C₂²	1	4	yes	—
51	C₁₉×#487	C₂²	1	1	yes	characteristic
52	C₁₉×#486	C₂²	1	1	yes	characteristic
53	C₁₉×#486	C₂²	1	1	yes	characteristic
54	C₁₉×#486	C₂²	1	1	yes	characteristic
55	C₁₉×#478	C₂²	1	4	yes	—
56	C₁₉×#478	C₂²	1	4	yes	—
57	C₁₉×#477	C₂²	1	4	yes	—
58	C₁₉×#476	C₂²	1	2	yes	—
59	C₁₉×#476	C₂²	1	4	yes	—
60	C₁₉×#475	C₂²	1	2	yes	—
61	C₁₉×#474	C₂²	1	2	yes	—
62	C₁₉×#474	C₂²	1	2	yes	—
63	C₁₉×#466	C₂²	1	2	yes	—
64	C₁₉×#466	C₂²	1	2	yes	—
65	C₁₉×#466	C₂²	1	4	yes	—
66	C₁₉×#465	C₂²	1	2	yes	—
67	C₁₉×#465	C₂²	1	2	yes	—
68	C₁₉×#465	C₂²	1	4	yes	—
69	C₁₉×#463	C₂²	1	4	yes	—
70	C₁₉×#463	C₂²	1	4	yes	—
71	C₁₉×#461	C₂²	1	2	yes	—
72	C₁₉×#460	C₂²	1	2	yes	—
73	C₁₉×#460	C₂²	1	4	yes	—
74	C₁₉×#459	C₂²	1	2	yes	—
75	C₁₉×#459	C₂²	1	2	yes	—
76	C₁₉×#459	C₂²	1	4	yes	—
77	C₁₉×#446	C₂²	1	2	yes	—
78	C₁₉×#446	C₂²	1	2	yes	—
79	C₁₉×#446	C₂²	1	2	yes	—
80	C₁₉×#446	C₂²	1	2	yes	—
81	C₁₉×#442	C₂²	1	4	yes	—
82	C₁₉×#442	C₂²	1	4	yes	—
83	C₁₉×#440	C₂²	1	4	yes	—
84	C₁₉×#440	C₂²	1	4	yes	—
85	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₁₉	C₂²	1	2	yes	—
87	C₄×D₈×C₁₉	C₂²	1	2	yes	—
88	C₄×D₈×C₁₉	C₂²	1	2	yes	—
89	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
91	C₂×C₁₉×#97	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
93	C₁₉×2₋¹⁺⁴	—	4	8	no	—
94	C₂×#41×C₁₉	—	2	2	no	—
95	C₂×#41×C₁₉	—	2	2	no	—
96	C₂×#41×C₁₉	—	2	1	no	—
97	C₂×#41×C₁₉	—	2	4	no	—
98	C₂×#41×C₁₉	—	2	1	no	—
99	C₂×#41×C₁₉	—	2	1	no	—
100	C₂²×Q₈×C₁₉	—	2	2	no	—
101	C₂²×Q₈×C₁₉	—	2	2	no	—
102	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₁₉	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
106	C₂×D₈×C₁₉	C₂³	1	2	yes	—
107	C₂×D₈×C₁₉	C₂³	1	2	yes	—
108	C₂×D₈×C₁₉	C₂³	1	4	yes	—
109	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
112	C₁₉×C₄⋊Q₈	—	2	2	no	—
113	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₁₉×#127	C₂³	1	1	yes	characteristic
120	C₁₉×#127	C₂³	1	1	yes	characteristic
121	C₁₉×#127	C₂³	1	4	yes	—
122	C₁₉×#127	C₂³	1	1	yes	characteristic
123	C₁₉×#126	—	2	4	no	—
124	C₁₉×#126	—	2	4	no	—
125	C₁₉×#125	—	2	4	no	—
126	C₁₉×#125	—	2	1	no	—
127	C₁₉×#125	C₂³	1	4	yes	—
128	C₁₉×#124	—	2	2	no	—
129	C₁₉×#124	—	2	4	no	—
130	C₁₉×#124	—	2	1	no	—
131	C₁₉×#124	—	2	1	no	—
132	C₁₉×#124	—	2	1	no	—
133	C₁₉×#124	C₂³	1	4	yes	—
134	C₁₉×#123	—	2	4	no	—
135	C₁₉×#123	—	2	4	no	—
136	C₁₉×C₂²⋊Q₈	—	2	2	no	—
137	C₁₉×C₂²⋊Q₈	—	2	2	no	—
138	C₁₉×C₂²⋊Q₈	—	2	1	no	—
139	C₁₉×C₂²⋊Q₈	—	2	2	no	—
140	C₁₉×C₂²⋊Q₈	—	2	2	no	—
141	C₁₉×C₂²⋊Q₈	—	2	4	no	—
142	C₁₉×C₂²⋊Q₈	—	2	4	no	—
143	C₁₉×C₂²⋊Q₈	—	2	4	no	—
144	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₉×#121	—	2	4	no	—
146	C₁₉×#121	—	2	1	no	—
147	C₁₉×#121	—	2	1	no	—
148	C₁₉×#121	—	2	1	no	—
149	C₁₉×#121	—	2	2	no	—
150	C₁₉×#121	—	2	2	no	—
151	C₁₉×#121	—	2	4	no	—
152	C₁₉×#121	—	2	4	no	—
153	C₁₉×#121	C₂³	1	2	yes	—
154	C₁₉×#121	C₂³	1	2	yes	—
155	C₁₉×#121	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₉	—	2	2	no	—
157	C₄×Q₈×C₁₉	—	2	1	no	—
158	C₄×Q₈×C₁₉	D₄	1	2	yes	—
159	C₄×Q₈×C₁₉	D₄	1	2	yes	—
160	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
163	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
164	C₄×D₄×C₁₉	—	2	4	no	—
165	C₄×D₄×C₁₉	—	2	2	no	—
166	C₄×D₄×C₁₉	—	2	4	no	—
167	C₄×D₄×C₁₉	—	2	1	no	—
168	C₄×D₄×C₁₉	—	2	1	no	—
169	C₄×D₄×C₁₉	—	2	1	no	—
170	C₄×D₄×C₁₉	C₂³	1	2	yes	—
171	C₄×D₄×C₁₉	C₂³	1	2	yes	—
172	C₄×D₄×C₁₉	C₂³	1	2	yes	—
173	C₄×D₄×C₁₉	C₂³	1	4	yes	—
174	C₄×D₄×C₁₉	C₂³	1	4	yes	—
175	C₄×D₄×C₁₉	C₂³	1	4	yes	—
176	C₁₉×#117	—	2	1	no	—
177	C₁₉×#117	—	2	2	no	—
178	C₁₉×#117	—	2	4	no	—
179	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
182	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
184	C₁₉×#107	C₂³	1	2	yes	—
185	C₁₉×#107	C₂³	1	2	yes	—
186	C₁₉×#107	C₂³	1	4	yes	—
187	C₁₉×#106	C₂³	1	2	yes	—
188	C₁₉×#106	C₂³	1	2	yes	—
189	C₁₉×#106	C₂³	1	4	yes	—
190	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
191	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
192	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
193	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
194	C₁₉×#103	C₂³	1	2	yes	—
195	C₁₉×#103	C₂³	1	2	yes	—
196	C₁₉×#103	C₂³	1	4	yes	—
197	C₁₉×#102	C₂³	1	2	yes	—
198	C₁₉×#102	C₂³	1	2	yes	—
199	C₁₉×#102	C₂³	1	2	yes	—
200	C₁₉×#102	C₂³	1	2	yes	—
201	C₁₉×#102	C₂³	1	2	yes	—
202	C₁₉×#102	C₂³	1	2	yes	—
203	C₁₉×#102	C₂³	1	4	yes	—
204	C₁₉×#102	C₂³	1	4	yes	—
205	C₁₉×#102	C₂³	1	4	yes	—
206	C₁₉×#97	C₂³	1	4	yes	—
207	C₁₉×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
212	#41×C₁₉	—	4	16	no	—
213	#41×C₁₉	—	4	8	no	—
214	#41×C₁₉	—	4	8	no	—
215	#41×C₁₉	—	4	4	no	—
216	#41×C₁₉	—	4	4	no	—
217	#41×C₁₉	—	4	4	no	—
218	C₂×Q₈×C₁₉	—	2	4	no	—
219	C₂×Q₈×C₁₉	—	2	1	no	—
220	C₂×Q₈×C₁₉	—	2	4	no	—
221	C₂×Q₈×C₁₉	—	2	1	no	—
222	C₂×Q₈×C₁₉	—	2	1	no	—
223	C₂×Q₈×C₁₉	—	2	1	no	—
224	C₂×Q₈×C₁₉	—	4	8	no	—
225	C₂×Q₈×C₁₉	—	4	8	no	—
226	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₉	—	2	2	no	—
230	C₂×D₄×C₁₉	—	2	2	no	—
231	C₂×D₄×C₁₉	—	2	2	no	—
232	C₂×D₄×C₁₉	—	2	1	no	—
233	C₂×D₄×C₁₉	—	2	4	no	—
234	C₂×D₄×C₁₉	—	2	1	no	—
235	C₂×D₄×C₁₉	—	2	1	no	—
236	C₂×D₄×C₁₉	—	2	4	no	—
237	C₂×D₄×C₁₉	—	2	1	no	—
238	C₂×D₄×C₁₉	—	2	1	no	—
239	C₂×D₄×C₁₉	—	2	1	no	—
240	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₉	—	2	2	no	—
244	C₂²×C₄×C₁₉	—	2	4	no	—
245	C₂²×C₄×C₁₉	—	2	4	no	—
246	C₂²×C₄×C₁₉	—	2	2	no	—
247	C₂²×C₄×C₁₉	—	2	2	no	—
248	C₂²×C₄×C₁₉	—	2	4	no	—
249	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₁₉	—	2	4	no	—
255	SD₁₆×C₁₉	—	4	4	no	—
256	SD₁₆×C₁₉	—	4	2	no	—
257	D₈×C₁₉	—	2	4	no	—
258	D₈×C₁₉	—	4	2	no	—
259	D₈×C₁₉	—	4	4	no	—
260	C₂×C₈×C₁₉	—	2	2	no	—
261	C₂×C₈×C₁₉	—	4	1	no	—
262	C₂×C₈×C₁₉	—	4	2	no	—
263	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
265	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
266	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
267	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
268	C₄⋊C₄×C₁₉	—	2	1	no	—
269	C₄⋊C₄×C₁₉	—	2	4	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
271	C₄⋊C₄×C₁₉	—	2	2	no	—
272	C₄⋊C₄×C₁₉	—	2	4	no	—
273	C₄⋊C₄×C₁₉	—	2	4	no	—
274	C₄⋊C₄×C₁₉	—	2	1	no	—
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	—	2	1	no	—
278	C₄⋊C₄×C₁₉	—	2	2	no	—
279	C₄⋊C₄×C₁₉	—	2	4	no	—
280	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
284	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₁₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₉	—	2	2	no	—
290	C₂²⋊C₄×C₁₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₉	—	2	2	no	—
293	C₂²⋊C₄×C₁₉	—	2	2	no	—
294	C₂²⋊C₄×C₁₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	2	no	—
297	C₂²⋊C₄×C₁₉	—	2	2	no	—
298	C₂²⋊C₄×C₁₉	—	2	2	no	—
299	C₂²⋊C₄×C₁₉	—	2	4	no	—
300	C₄²×C₁₉	—	2	4	no	—
301	C₄²×C₁₉	—	2	2	no	—
302	C₄²×C₁₉	C₂×D₄	1	4	yes	—
303	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
306	C₄²×C₁₉	C₂⁴	1	4	yes	—
307	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
308	#62365	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₁₉	—	2	2	no	—
310	C₂³×C₁₉	—	2	2	no	—
311	C₂³×C₁₉	—	2	2	no	—
312	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₁₉	—	2	4	no	—
314	Q₈×C₁₉	—	2	4	no	—
315	Q₈×C₁₉	—	2	2	no	—
316	Q₈×C₁₉	—	2	2	no	—
317	Q₈×C₁₉	—	4	8	no	—
318	Q₈×C₁₉	—	4	2	no	—
319	Q₈×C₁₉	—	4	2	no	—
320	Q₈×C₁₉	—	4	2	no	—
321	Q₈×C₁₉	—	8	1	no	—
322	D₄×C₁₉	—	2	2	no	—
323	D₄×C₁₉	—	2	2	no	—
324	D₄×C₁₉	—	2	2	no	—
325	D₄×C₁₉	—	2	2	no	—
326	D₄×C₁₉	—	2	2	no	—
327	D₄×C₁₉	—	2	2	no	—
328	D₄×C₁₉	—	4	8	no	—
329	D₄×C₁₉	—	4	4	no	—
330	D₄×C₁₉	—	4	4	no	—
331	D₄×C₁₉	—	4	4	no	—
332	D₄×C₁₉	—	4	2	no	—
333	D₄×C₁₉	—	4	2	no	—
334	D₄×C₁₉	—	4	2	no	—
335	D₄×C₁₉	—	8	4	no	—
336	D₄×C₁₉	—	8	1	no	—
337	D₄×C₁₉	—	8	1	no	—
338	D₄×C₁₉	—	8	1	no	—
339	C₂×C₄×C₁₉	—	2	4	no	—
340	C₂×C₄×C₁₉	—	2	1	no	—
341	C₂×C₄×C₁₉	—	2	1	no	—
342	C₂×C₄×C₁₉	—	2	2	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	2	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
347	C₂×C₄×C₁₉	—	4	2	no	—
348	C₂×C₄×C₁₉	—	4	1	no	—
349	C₂×C₄×C₁₉	—	4	8	no	—
350	C₂×C₄×C₁₉	—	4	8	no	—
351	C₂×C₄×C₁₉	—	4	4	no	—
352	C₂×C₄×C₁₉	—	4	4	no	—
353	C₂×C₄×C₁₉	—	4	4	no	—
354	C₂×C₄×C₁₉	—	8	4	no	—
355	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
356	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
364	C₈×C₁₉	—	2	1	no	—
365	C₈×C₁₉	—	2	1	no	—
366	C₈×C₁₉	—	2	4	no	—
367	C₈×C₁₉	—	2	1	no	—
368	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	complemented
369	#3507	C₂×C₁₉	1	1	yes	characteristic, complemented
370	#3497	C₂×C₁₉	1	1	yes	characteristic, complemented
371	#3399	C₂×C₁₉	1	2	yes	complemented
372	#3397	C₂×C₁₉	1	2	yes	complemented
373	#3386	C₂×C₁₉	1	2	yes	complemented
374	#3384	C₂×C₁₉	1	2	yes	complemented
375	#3373	C₂×C₁₉	1	2	yes	complemented
376	#3368	C₂×C₁₉	1	2	yes	complemented
377	#3367	C₂×C₁₉	1	2	yes	complemented
378	#3366	C₂×C₁₉	1	2	yes	complemented
379	#3247	C₂×C₁₉	1	4	yes	complemented
380	#3246	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#3245	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#3180	C₂×C₁₉	1	4	yes	complemented
383	#3169	C₂×C₁₉	1	1	yes	characteristic, complemented
384	#3167	C₂×C₁₉	1	1	yes	characteristic, complemented
385	C₂×#446	C₂×C₁₉	1	1	yes	characteristic, complemented
386	C₂²×C₁₉	—	2	1	no	—
387	C₂²×C₁₉	—	2	1	no	—
388	C₂²×C₁₉	—	4	2	no	—
389	C₂²×C₁₉	—	4	2	no	—
390	C₂²×C₁₉	—	4	2	no	—
391	C₂²×C₁₉	—	4	2	no	—
392	C₂²×C₁₉	—	4	2	no	—
393	C₂²×C₁₉	—	4	2	no	—
394	C₂²×C₁₉	—	4	2	no	—
395	C₂²×C₁₉	—	4	2	no	—
396	C₂²×C₁₉	—	4	2	no	—
397	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
398	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
399	C₄×C₁₉	—	2	4	no	—
400	C₄×C₁₉	—	2	1	no	—
401	C₄×C₁₉	—	2	1	no	—
402	C₄×C₁₉	—	2	1	no	—
403	C₄×C₁₉	—	2	4	no	—
404	C₄×C₁₉	—	4	2	no	—
405	C₄×C₁₉	—	4	2	no	—
406	C₄×C₁₉	—	4	2	no	—
407	C₄×C₁₉	—	4	2	no	—
408	C₄×C₁₉	—	4	2	no	—
409	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
410	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
411	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
412	C₄×C₁₉	#585	1	1	yes	characteristic
413	C₂×2₋¹⁺⁴	—	2	1	no	—
414	#559	C₂²×C₁₉	1	2	yes	—
415	#557	C₂²×C₁₉	1	2	yes	—
416	#556	—	2	2	no	—
417	#556	C₂²×C₁₉	1	2	yes	—
418	#554	C₂²×C₁₉	1	2	yes	—
419	#552	—	2	2	no	—
420	#550	C₂²×C₁₉	1	2	yes	—
421	#550	C₂²×C₁₉	1	2	yes	—
422	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
423	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
424	#548	—	2	2	no	—
425	#548	—	2	2	no	—
426	#539	—	2	2	no	—
427	#537	—	2	1	no	—
428	#537	—	2	2	no	—
429	#536	—	2	1	no	—
430	#533	C₂²×C₁₉	1	1	yes	characteristic
431	#532	C₂²×C₁₉	1	1	yes	characteristic
432	#532	C₂²×C₁₉	1	1	yes	characteristic
433	#532	C₂²×C₁₉	1	1	yes	characteristic
434	#532	C₂²×C₁₉	1	4	yes	—
435	#529	C₂²×C₁₉	1	4	yes	—
436	#520	—	2	1	no	—
437	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
438	#501	C₂²×C₁₉	1	4	yes	—
439	#500	C₂²×C₁₉	1	1	yes	characteristic
440	#498	C₂²×C₁₉	1	1	yes	characteristic
441	#496	C₂²×C₁₉	1	4	yes	—
442	#493	C₂²×C₁₉	1	1	yes	characteristic
443	#492	C₂²×C₁₉	1	1	yes	characteristic
444	#490	C₂²×C₁₉	1	4	yes	—
445	#489	C₂²×C₁₉	1	4	yes	—
446	#487	C₂²×C₁₉	1	1	yes	characteristic
447	#486	C₂²×C₁₉	1	1	yes	characteristic
448	#486	C₂²×C₁₉	1	1	yes	characteristic
449	#486	C₂²×C₁₉	1	1	yes	characteristic
450	#478	C₂²×C₁₉	1	4	yes	—
451	#478	C₂²×C₁₉	1	4	yes	—
452	#477	C₂²×C₁₉	1	4	yes	—
453	#476	C₂²×C₁₉	1	2	yes	—
454	#476	C₂²×C₁₉	1	4	yes	—
455	#475	C₂²×C₁₉	1	2	yes	—
456	#474	C₂²×C₁₉	1	2	yes	—
457	#474	C₂²×C₁₉	1	2	yes	—
458	#466	C₂²×C₁₉	1	2	yes	—
459	#466	C₂²×C₁₉	1	2	yes	—
460	#466	C₂²×C₁₉	1	4	yes	—
461	#465	C₂²×C₁₉	1	2	yes	—
462	#465	C₂²×C₁₉	1	2	yes	—
463	#465	C₂²×C₁₉	1	4	yes	—
464	#463	C₂²×C₁₉	1	4	yes	—
465	#463	C₂²×C₁₉	1	4	yes	—
466	#461	C₂²×C₁₉	1	2	yes	—
467	#460	C₂²×C₁₉	1	4	yes	—
468	#460	C₂²×C₁₉	1	2	yes	—
469	#459	C₂²×C₁₉	1	2	yes	—
470	#459	C₂²×C₁₉	1	4	yes	—
471	#459	C₂²×C₁₉	1	2	yes	—
472	#446	C₂²×C₁₉	1	2	yes	—
473	#446	C₂²×C₁₉	1	2	yes	—
474	#446	C₂²×C₁₉	1	2	yes	—
475	#446	C₂²×C₁₉	1	2	yes	—
476	#442	C₂²×C₁₉	1	4	yes	—
477	#442	C₂²×C₁₉	1	4	yes	—
478	#440	C₂²×C₁₉	1	4	yes	—
479	#440	C₂²×C₁₉	1	4	yes	—
480	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
481	C₄×SD₁₆	C₂²×C₁₉	1	2	yes	—
482	C₄×D₈	C₂²×C₁₉	1	2	yes	—
483	C₄×D₈	C₂²×C₁₉	1	2	yes	—
484	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
485	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
486	C₂×#97	C₂²×C₁₉	1	2	yes	—
487	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
488	C₂×C₁₉	—	2	2	no	—
489	C₂×C₁₉	—	8	2	no	—
490	C₂×C₁₉	—	8	2	no	—
491	C₂×C₁₉	—	8	2	no	—
492	C₂×C₁₉	#3497	1	1	yes	characteristic
493	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₂×C₁₉	#3584	1	1	yes	characteristic
495	2₋¹⁺⁴	—	4	8	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	1	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	2	1	no	—
501	C₂×#41	—	2	1	no	—
502	C₂²×Q₈	—	2	2	no	—
503	C₂²×Q₈	—	2	2	no	—
504	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
505	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
506	C₂×SD₁₆	C₂³×C₁₉	1	2	yes	—
507	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
508	C₂×D₈	C₂³×C₁₉	1	2	yes	—
509	C₂×D₈	C₂³×C₁₉	1	2	yes	—
510	C₂×D₈	C₂³×C₁₉	1	4	yes	—
511	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
512	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
514	C₄⋊Q₈	—	2	2	no	—
515	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
519	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
521	#127	C₂³×C₁₉	1	1	yes	characteristic
522	#127	C₂³×C₁₉	1	4	yes	—
523	#127	C₂³×C₁₉	1	1	yes	characteristic
524	#127	C₂³×C₁₉	1	1	yes	characteristic
525	#126	—	2	4	no	—
526	#126	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	—	2	1	no	—
529	#125	C₂³×C₁₉	1	4	yes	—
530	#124	—	2	2	no	—
531	#124	—	2	4	no	—
532	#124	—	2	1	no	—
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	C₂³×C₁₉	1	4	yes	—
536	#123	—	2	4	no	—
537	#123	—	2	4	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	—	2	4	no	—
546	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
547	#121	—	2	4	no	—
548	#121	—	2	1	no	—
549	#121	—	2	1	no	—
550	#121	—	2	1	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	4	no	—
554	#121	—	2	4	no	—
555	#121	C₂³×C₁₉	1	2	yes	—
556	#121	C₂³×C₁₉	1	2	yes	—
557	#121	C₂³×C₁₉	1	2	yes	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	D₄×C₁₉	1	2	yes	—
561	C₄×Q₈	D₄×C₁₉	1	2	yes	—
562	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
563	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
564	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
565	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
566	C₄×D₄	—	2	4	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	4	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	C₂³×C₁₉	1	4	yes	—
573	C₄×D₄	C₂³×C₁₉	1	2	yes	—
574	C₄×D₄	C₂³×C₁₉	1	2	yes	—
575	C₄×D₄	C₂³×C₁₉	1	4	yes	—
576	C₄×D₄	C₂³×C₁₉	1	4	yes	—
577	C₄×D₄	C₂³×C₁₉	1	2	yes	—
578	#117	—	2	1	no	—
579	#117	—	2	2	no	—
580	#117	—	2	4	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
584	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
586	#107	C₂³×C₁₉	1	2	yes	—
587	#107	C₂³×C₁₉	1	2	yes	—
588	#107	C₂³×C₁₉	1	4	yes	—
589	#106	C₂³×C₁₉	1	2	yes	—
590	#106	C₂³×C₁₉	1	2	yes	—
591	#106	C₂³×C₁₉	1	4	yes	—
592	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
593	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
594	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
595	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
596	#103	C₂³×C₁₉	1	2	yes	—
597	#103	C₂³×C₁₉	1	2	yes	—
598	#103	C₂³×C₁₉	1	4	yes	—
599	#102	C₂³×C₁₉	1	2	yes	—
600	#102	C₂³×C₁₉	1	2	yes	—
601	#102	C₂³×C₁₉	1	2	yes	—
602	#102	C₂³×C₁₉	1	2	yes	—
603	#102	C₂³×C₁₉	1	2	yes	—
604	#102	C₂³×C₁₉	1	2	yes	—
605	#102	C₂³×C₁₉	1	4	yes	—
606	#102	C₂³×C₁₉	1	4	yes	—
607	#102	C₂³×C₁₉	1	4	yes	—
608	#97	C₂³×C₁₉	1	4	yes	—
609	#97	C₂³×C₁₉	1	4	yes	—
610	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
611	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
612	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
613	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
614	C₁₉	#62365	1	1	yes	characteristic, direct product factor, Sylow
615	#41	—	4	16	no	—
616	#41	—	4	8	no	—
617	#41	—	4	8	no	—
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	#41	—	4	4	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	4	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	4	8	no	—
628	C₂×Q₈	—	4	8	no	—
629	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
630	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
644	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
645	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
653	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
654	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
657	SD₁₆	—	2	4	no	—
658	SD₁₆	—	4	4	no	—
659	SD₁₆	—	4	2	no	—
660	D₈	—	2	4	no	—
661	D₈	—	4	2	no	—
662	D₈	—	4	4	no	—
663	C₂×C₈	—	2	2	no	—
664	C₂×C₈	—	4	1	no	—
665	C₂×C₈	—	4	2	no	—
666	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
667	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
668	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
669	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
670	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
686	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
687	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
688	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
689	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	2	no	—
705	C₄²	C₂×D₄×C₁₉	1	4	yes	—
706	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
707	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
708	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
709	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
710	C₄²	C₂⁴×C₁₉	1	4	yes	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
715	Q₈	—	2	4	no	—
716	Q₈	—	2	4	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	4	8	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	8	1	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	1	no	—
739	D₄	—	8	1	no	—
740	D₄	—	8	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	8	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
758	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
759	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
765	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
766	C₈	—	2	1	no	—
767	C₈	—	2	1	no	—
768	C₈	—	2	4	no	—
769	C₈	—	2	1	no	—
770	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	complemented
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
783	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
784	C₄	—	2	1	no	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
795	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
796	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
797	C₄	C₁₉×#585	1	1	yes	characteristic
798	C₂	—	2	2	no	—
799	C₂	—	8	2	no	—
800	C₂	—	8	2	no	—
801	C₂	—	8	2	no	—
802	C₂	C₁₉×#3497	1	1	yes	characteristic
803	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
804	C₂	C₁₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3507	C₂	semidirect
2. C₁₉×#3497	C₂	semidirect
3. C₁₉×#3399	C₂	semidirect
4. C₁₉×#3397	C₂	semidirect
5. C₁₉×#3386	C₂	semidirect
6. C₁₉×#3384	C₂	semidirect
7. C₁₉×#3373	C₂	semidirect
8. C₁₉×#3368	C₂	semidirect
9. C₁₉×#3367	C₂	semidirect
10. C₁₉×#3366	C₂	semidirect
11. C₁₉×#3247	C₂	semidirect
12. C₁₉×#3246	C₂	semidirect
13. C₁₉×#3245	C₂	semidirect
14. C₁₉×#3180	C₂	semidirect
15. C₁₉×#3169	C₂	semidirect
16. C₁₉×#3167	C₂	semidirect
17. C₂×C₁₉×#446	C₂	semidirect
308. #62365	C₁₉	direct (N × H)
368. C₈×C₁₉	2₋¹⁺⁴	semidirect
369. #3507	C₂×C₁₉	semidirect
370. #3497	C₂×C₁₉	semidirect
371. #3399	C₂×C₁₉	semidirect
372. #3397	C₂×C₁₉	semidirect
373. #3386	C₂×C₁₉	semidirect
374. #3384	C₂×C₁₉	semidirect
375. #3373	C₂×C₁₉	semidirect
376. #3368	C₂×C₁₉	semidirect
377. #3367	C₂×C₁₉	semidirect
378. #3366	C₂×C₁₉	semidirect
379. #3247	C₂×C₁₉	semidirect
380. #3246	C₂×C₁₉	semidirect
381. #3245	C₂×C₁₉	semidirect
382. #3180	C₂×C₁₉	semidirect
383. #3169	C₂×C₁₉	semidirect
384. #3167	C₂×C₁₉	semidirect
385. C₂×#446	C₂×C₁₉	semidirect
614. C₁₉	#62365	direct (N × H)
770. C₈	C₁₉×2₋¹⁺⁴	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3507	2
C₁₉×#3497	2
C₁₉×#3399	2
C₁₉×#3397	2
C₁₉×#3386	2
C₁₉×#3384	2
C₁₉×#3373	2
C₁₉×#3368	2
C₁₉×#3367	2
C₁₉×#3366	2
C₁₉×#3247	2
C₁₉×#3246	2
C₁₉×#3245	2
C₁₉×#3180	2
C₁₉×#3169	2
C₁₉×#3167	2
C₂×C₁₉×#446	2
#62365	19

Subgroups — C19×#62365 #18068324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62365 #18068324