Subgroups — C₁₉×#11023 #18016982

Order 4864.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₁₉	—	2	2	no	—
11	C₂²×SD₁₆×C₁₉	—	2	2	no	—
12	C₂²×SD₁₆×C₁₉	—	2	2	no	—
13	C₂²×SD₁₆×C₁₉	—	2	2	no	—
14	C₂²×SD₁₆×C₁₉	—	2	2	no	—
15	C₂²×SD₁₆×C₁₉	—	2	2	no	—
16	C₂²×SD₁₆×C₁₉	C₄	1	4	yes	complemented
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	—	2	2	no	—
24	C₂×C₁₉×#103	—	2	2	no	—
25	C₂×C₁₉×#103	—	2	2	no	—
26	C₂×C₁₉×#102	—	2	2	no	—
27	C₂×C₁₉×#102	—	2	2	no	—
28	C₂×C₁₉×#102	—	2	2	no	—
29	C₁₉×#391	—	2	2	no	—
30	C₁₉×#391	—	2	2	no	—
31	C₁₉×#390	—	2	2	no	—
32	C₁₉×#390	—	2	2	no	—
33	C₂×C₁₉×#95	—	2	2	no	—
34	C₁₉×#340	—	2	2	no	—
35	C₁₉×#336	—	2	2	no	—
36	C₂⁵×C₁₉	—	2	1	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
51	C₂²×D₄×C₁₉	—	2	1	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂²×D₄×C₁₉	D₄	1	2	yes	—
64	C₂²×D₄×C₁₉	D₄	1	2	yes	—
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂³×C₄×C₁₉	D₄	1	2	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₉	—	2	8	no	—
71	C₂×SD₁₆×C₁₉	—	2	8	no	—
72	C₂×SD₁₆×C₁₉	—	2	8	no	—
73	C₂×SD₁₆×C₁₉	—	2	8	no	—
74	C₂×SD₁₆×C₁₉	—	2	8	no	—
75	C₂×SD₁₆×C₁₉	—	2	8	no	—
76	C₂×SD₁₆×C₁₉	—	2	8	no	—
77	C₂²×C₈×C₁₉	—	2	1	no	—
78	C₂²×C₈×C₁₉	—	2	1	no	—
79	C₂²×C₈×C₁₉	—	2	1	no	—
80	C₂²×C₈×C₁₉	—	2	1	no	—
81	C₂²×C₈×C₁₉	—	2	1	no	—
82	C₂²×C₈×C₁₉	—	2	1	no	—
83	C₂²×C₈×C₁₉	—	2	1	no	—
84	C₂²×C₈×C₁₉	—	2	1	no	—
85	C₂²×C₈×C₁₉	—	2	1	no	—
86	C₂²×C₈×C₁₉	—	2	1	no	—
87	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₁₉	D₄	1	2	yes	—
89	C₂²×C₈×C₁₉	D₄	1	2	yes	—
90	C₂²×C₈×C₁₉	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₁₉×#103	—	2	8	no	—
113	C₁₉×#102	—	2	8	no	—
114	C₁₉×#95	—	2	8	no	—
115	C₂⁴×C₁₉	—	2	2	no	—
116	C₂⁴×C₁₉	—	2	2	no	—
117	C₂⁴×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	—	4	1	no	—
119	C₂⁴×C₁₉	—	4	1	no	—
120	C₂⁴×C₁₉	—	4	1	no	—
121	C₂⁴×C₁₉	—	4	1	no	—
122	C₂⁴×C₁₉	—	4	2	no	—
123	C₂⁴×C₁₉	—	4	2	no	—
124	C₂⁴×C₁₉	—	4	2	no	—
125	C₂⁴×C₁₉	—	4	2	no	—
126	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	2	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	—	4	1	no	—
144	C₂×Q₈×C₁₉	—	4	1	no	—
145	C₂×Q₈×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	4	1	no	—
147	C₂×Q₈×C₁₉	—	4	1	no	—
148	C₂×Q₈×C₁₉	—	4	1	no	—
149	C₂×Q₈×C₁₉	—	4	1	no	—
150	C₂×Q₈×C₁₉	—	4	1	no	—
151	C₂×Q₈×C₁₉	—	4	1	no	—
152	C₂×Q₈×C₁₉	—	4	1	no	—
153	C₂×Q₈×C₁₉	—	4	1	no	—
154	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	2	2	no	—
168	C₂×D₄×C₁₉	—	2	2	no	—
169	C₂×D₄×C₁₉	—	2	2	no	—
170	C₂×D₄×C₁₉	—	4	1	no	—
171	C₂×D₄×C₁₉	—	4	1	no	—
172	C₂×D₄×C₁₉	—	4	1	no	—
173	C₂×D₄×C₁₉	—	4	1	no	—
174	C₂×D₄×C₁₉	—	4	1	no	—
175	C₂×D₄×C₁₉	—	4	1	no	—
176	C₂×D₄×C₁₉	—	4	1	no	—
177	C₂×D₄×C₁₉	—	4	1	no	—
178	C₂×D₄×C₁₉	—	4	1	no	—
179	C₂×D₄×C₁₉	—	4	1	no	—
180	C₂×D₄×C₁₉	—	4	1	no	—
181	C₂×D₄×C₁₉	—	4	1	no	—
182	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	2	no	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	2	2	no	—
192	C₂²×C₄×C₁₉	—	2	2	no	—
193	C₂²×C₄×C₁₉	—	2	2	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	1	no	—
196	C₂²×C₄×C₁₉	—	4	1	no	—
197	C₂²×C₄×C₁₉	—	4	1	no	—
198	C₂²×C₄×C₁₉	—	4	1	no	—
199	C₂²×C₄×C₁₉	—	4	1	no	—
200	C₂²×C₄×C₁₉	—	4	1	no	—
201	C₂²×C₄×C₁₉	—	4	1	no	—
202	C₂²×C₄×C₁₉	—	4	2	no	—
203	C₂²×C₄×C₁₉	—	4	2	no	—
204	C₂²×C₄×C₁₉	—	4	2	no	—
205	C₂²×C₄×C₁₉	—	4	2	no	—
206	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
207	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
221	SD₁₆×C₁₉	—	2	32	no	—
222	C₂×C₈×C₁₉	—	2	2	no	—
223	C₂×C₈×C₁₉	—	2	2	no	—
224	C₂×C₈×C₁₉	—	2	2	no	—
225	C₂×C₈×C₁₉	—	2	2	no	—
226	C₂×C₈×C₁₉	—	2	2	no	—
227	C₂×C₈×C₁₉	—	2	2	no	—
228	C₂×C₈×C₁₉	—	2	2	no	—
229	C₂×C₈×C₁₉	—	2	2	no	—
230	C₂×C₈×C₁₉	—	2	2	no	—
231	C₂×C₈×C₁₉	—	4	1	no	—
232	C₂×C₈×C₁₉	—	4	1	no	—
233	C₂×C₈×C₁₉	—	4	1	no	—
234	C₂×C₈×C₁₉	—	4	1	no	—
235	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
236	C₄⋊C₄×C₁₉	—	2	2	no	—
237	C₄⋊C₄×C₁₉	—	2	2	no	—
238	C₄⋊C₄×C₁₉	—	2	2	no	—
239	C₄⋊C₄×C₁₉	—	2	2	no	—
240	C₄⋊C₄×C₁₉	—	4	1	no	—
241	C₄⋊C₄×C₁₉	—	4	1	no	—
242	C₄⋊C₄×C₁₉	—	4	1	no	—
243	C₄⋊C₄×C₁₉	—	4	1	no	—
244	C₂²⋊C₄×C₁₉	—	4	16	no	—
245	C₄²×C₁₉	—	4	1	no	—
246	C₄²×C₁₉	—	4	1	no	—
247	C₄²×C₁₉	—	4	1	no	—
248	C₄²×C₁₉	—	4	1	no	—
249	#11023	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	—	2	4	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	4	2	no	—
253	C₂³×C₁₉	—	4	2	no	—
254	C₂³×C₁₉	—	4	2	no	—
255	C₂³×C₁₉	—	4	2	no	—
256	C₂³×C₁₉	—	4	2	no	—
257	C₂³×C₁₉	—	4	4	no	—
258	C₂³×C₁₉	—	4	4	no	—
259	C₂³×C₁₉	—	4	4	no	—
260	C₂³×C₁₉	—	4	4	no	—
261	C₂³×C₁₉	—	4	4	no	—
262	C₂³×C₁₉	—	4	4	no	—
263	C₂³×C₁₉	—	8	2	no	—
264	C₂³×C₁₉	—	8	2	no	—
265	C₂³×C₁₉	—	8	2	no	—
266	C₂³×C₁₉	—	8	2	no	—
267	C₂³×C₁₉	—	8	2	no	—
268	C₂³×C₁₉	—	8	2	no	—
269	C₂³×C₁₉	—	8	1	no	—
270	C₂³×C₁₉	—	8	1	no	—
271	C₂³×C₁₉	—	8	1	no	—
272	C₂³×C₁₉	—	8	1	no	—
273	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
274	C₂³×C₁₉	#120	1	1	yes	characteristic
275	C₂³×C₁₉	#120	1	1	yes	characteristic
276	C₂³×C₁₉	#121	1	1	yes	characteristic
277	C₂³×C₁₉	#121	1	1	yes	characteristic
278	C₂³×C₁₉	#121	1	1	yes	characteristic
279	C₂³×C₁₉	#127	1	1	yes	characteristic
280	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
281	C₂³×C₁₉	#135	1	2	yes	—
282	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
283	C₂³×C₁₉	#137	1	2	yes	—
284	Q₈×C₁₉	—	2	4	no	—
285	Q₈×C₁₉	—	2	4	no	—
286	Q₈×C₁₉	—	4	2	no	—
287	Q₈×C₁₉	—	4	2	no	—
288	Q₈×C₁₉	—	4	2	no	—
289	Q₈×C₁₉	—	4	2	no	—
290	Q₈×C₁₉	—	4	2	no	—
291	Q₈×C₁₉	—	4	2	no	—
292	D₄×C₁₉	—	2	4	no	—
293	D₄×C₁₉	—	2	4	no	—
294	D₄×C₁₉	—	4	2	no	—
295	D₄×C₁₉	—	4	2	no	—
296	D₄×C₁₉	—	4	2	no	—
297	D₄×C₁₉	—	4	2	no	—
298	D₄×C₁₉	—	4	2	no	—
299	D₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	2	4	no	—
301	C₂×C₄×C₁₉	—	2	4	no	—
302	C₂×C₄×C₁₉	—	2	4	no	—
303	C₂×C₄×C₁₉	—	2	4	no	—
304	C₂×C₄×C₁₉	—	4	2	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	4	2	no	—
307	C₂×C₄×C₁₉	—	4	2	no	—
308	C₂×C₄×C₁₉	—	4	2	no	—
309	C₂×C₄×C₁₉	—	4	2	no	—
310	C₂×C₄×C₁₉	—	4	2	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	4	2	no	—
313	C₂×C₄×C₁₉	—	4	2	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	4	2	no	—
316	C₂×C₄×C₁₉	—	4	4	no	—
317	C₂×C₄×C₁₉	—	4	4	no	—
318	C₂×C₄×C₁₉	—	8	2	no	—
319	C₂×C₄×C₁₉	—	8	2	no	—
320	C₂×C₄×C₁₉	—	8	1	no	—
321	C₂×C₄×C₁₉	—	8	1	no	—
322	C₂×C₄×C₁₉	—	8	1	no	—
323	C₂×C₄×C₁₉	—	8	1	no	—
324	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
332	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
333	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
334	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
335	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
336	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
337	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
338	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
339	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
341	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
342	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
343	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
344	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
345	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
346	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
347	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
348	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
349	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
350	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
351	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
352	C₈×C₁₉	—	2	4	no	—
353	C₈×C₁₉	—	4	2	no	—
354	C₂³×SD₁₆	C₂×C₁₉	1	1	yes	characteristic
355	C₂²×#103	C₂×C₁₉	1	1	yes	characteristic, complemented
356	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic
357	C₂×#391	C₂×C₁₉	1	1	yes	characteristic, complemented
358	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
359	C₂×#340	C₂×C₁₉	1	1	yes	characteristic, complemented
360	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
361	C₂²×C₁₉	—	4	8	no	—
362	C₂²×C₁₉	—	4	4	no	—
363	C₂²×C₁₉	—	8	4	no	—
364	C₂²×C₁₉	—	8	4	no	—
365	C₂²×C₁₉	—	8	2	no	—
366	C₂²×C₁₉	—	8	2	no	—
367	C₂²×C₁₉	—	8	4	no	—
368	C₂²×C₁₉	—	8	2	no	—
369	C₂²×C₁₉	—	8	2	no	—
370	C₂²×C₁₉	—	8	2	no	—
371	C₂²×C₁₉	—	8	2	no	—
372	C₂²×C₁₉	#386	1	1	yes	characteristic
373	C₂²×C₁₉	#386	1	1	yes	characteristic
374	C₂²×C₁₉	#390	1	1	yes	characteristic
375	C₂²×C₁₉	#392	1	1	yes	characteristic
376	C₂²×C₁₉	#392	1	1	yes	characteristic
377	C₂²×C₁₉	#392	1	1	yes	characteristic
378	C₂²×C₁₉	#394	1	1	yes	characteristic
379	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
380	C₂²×C₁₉	#440	1	2	yes	—
381	C₂²×C₁₉	#448	1	2	yes	—
382	C₂²×C₁₉	#449	1	2	yes	—
383	C₂²×C₁₉	#450	1	2	yes	—
384	C₂²×C₁₉	#452	1	2	yes	—
385	C₂²×C₁₉	#460	1	2	yes	—
386	C₂²×C₁₉	#461	1	2	yes	—
387	C₂²×C₁₉	#463	1	2	yes	—
388	C₂²×C₁₉	#464	1	2	yes	—
389	C₂²×C₁₉	#465	1	2	yes	—
390	C₂²×C₁₉	#468	1	2	yes	—
391	C₂²×C₁₉	#492	1	1	yes	characteristic
392	C₂²×C₁₉	#495	1	1	yes	characteristic
393	C₂²×C₁₉	#496	1	1	yes	characteristic
394	C₂²×C₁₉	#497	1	1	yes	characteristic
395	C₄×C₁₉	—	4	4	no	—
396	C₄×C₁₉	—	4	4	no	—
397	C₄×C₁₉	—	8	2	no	—
398	C₄×C₁₉	—	8	2	no	—
399	C₄×C₁₉	#379	1	1	yes	characteristic
400	C₄×C₁₉	#386	1	1	yes	characteristic
401	C₄×C₁₉	#386	1	1	yes	characteristic
402	C₄×C₁₉	#390	1	1	yes	characteristic
403	C₄×C₁₉	#392	1	1	yes	characteristic
404	C₄×C₁₉	#394	1	1	yes	characteristic
405	C₄×C₁₉	#394	1	1	yes	characteristic
406	C₄×C₁₉	#394	1	1	yes	characteristic
407	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
408	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
409	C₂²×SD₁₆	—	2	2	no	—
410	C₂²×SD₁₆	—	2	2	no	—
411	C₂²×SD₁₆	—	2	2	no	—
412	C₂²×SD₁₆	—	2	2	no	—
413	C₂²×SD₁₆	—	2	2	no	—
414	C₂²×SD₁₆	—	2	2	no	—
415	C₂²×SD₁₆	C₄×C₁₉	1	4	yes	complemented
416	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
417	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
420	C₂²×C₂²⋊C₄	—	2	2	no	—
421	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
422	C₂×#103	—	2	2	no	—
423	C₂×#103	—	2	2	no	—
424	C₂×#103	—	2	2	no	—
425	C₂×#102	—	2	2	no	—
426	C₂×#102	—	2	2	no	—
427	C₂×#102	—	2	2	no	—
428	#391	—	2	2	no	—
429	#391	—	2	2	no	—
430	#390	—	2	2	no	—
431	#390	—	2	2	no	—
432	C₂×#95	—	2	2	no	—
433	#340	—	2	2	no	—
434	#336	—	2	2	no	—
435	C₂×C₁₉	—	8	4	no	—
436	C₂×C₁₉	#1438	1	1	yes	characteristic
437	C₂×C₁₉	#1877	1	2	yes	—
438	C₂×C₁₉	#1880	1	2	yes	—
439	C₂×C₁₉	#1968	1	1	yes	characteristic
440	C₂×C₁₉	#1973	1	1	yes	characteristic
441	C₂×C₁₉	#2000	1	2	yes	—
442	C₂×C₁₉	#2012	1	1	yes	characteristic
443	C₂×C₁₉	#2013	1	1	yes	characteristic
444	C₂×C₁₉	#2014	1	1	yes	characteristic
445	C₂×C₁₉	#2015	1	1	yes	characteristic
446	C₂×C₁₉	#2055	1	2	yes	—
447	C₂⁵	—	2	1	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	—	2	1	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×Q₈	—	2	1	no	—
452	C₂²×Q₈	—	2	1	no	—
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	—	2	1	no	—
456	C₂²×Q₈	—	2	1	no	—
457	C₂²×Q₈	—	2	1	no	—
458	C₂²×Q₈	—	2	1	no	—
459	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
460	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
461	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
474	C₂²×D₄	D₄×C₁₉	1	2	yes	—
475	C₂²×D₄	D₄×C₁₉	1	2	yes	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	D₄×C₁₉	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
481	C₂×SD₁₆	—	2	8	no	—
482	C₂×SD₁₆	—	2	8	no	—
483	C₂×SD₁₆	—	2	8	no	—
484	C₂×SD₁₆	—	2	8	no	—
485	C₂×SD₁₆	—	2	8	no	—
486	C₂×SD₁₆	—	2	8	no	—
487	C₂×SD₁₆	—	2	8	no	—
488	C₂²×C₈	—	2	1	no	—
489	C₂²×C₈	—	2	1	no	—
490	C₂²×C₈	—	2	1	no	—
491	C₂²×C₈	—	2	1	no	—
492	C₂²×C₈	—	2	1	no	—
493	C₂²×C₈	—	2	1	no	—
494	C₂²×C₈	—	2	1	no	—
495	C₂²×C₈	—	2	1	no	—
496	C₂²×C₈	—	2	1	no	—
497	C₂²×C₈	—	2	1	no	—
498	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
499	C₂²×C₈	D₄×C₁₉	1	2	yes	—
500	C₂²×C₈	D₄×C₁₉	1	2	yes	—
501	C₂²×C₈	D₄×C₁₉	1	2	yes	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
513	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
514	C₂×C₂²⋊C₄	—	2	8	no	—
515	C₂×C₂²⋊C₄	—	4	4	no	—
516	C₂×C₂²⋊C₄	—	4	4	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	—	2	1	no	—
521	C₂×C₄²	—	2	1	no	—
522	C₂×C₄²	—	2	1	no	—
523	#103	—	2	8	no	—
524	#102	—	2	8	no	—
525	#95	—	2	8	no	—
526	C₁₉	#11023	1	1	yes	characteristic, direct product factor, Sylow
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	—	4	1	no	—
533	C₂⁴	—	4	1	no	—
534	C₂⁴	—	4	2	no	—
535	C₂⁴	—	4	2	no	—
536	C₂⁴	—	4	2	no	—
537	C₂⁴	—	4	2	no	—
538	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	—	4	1	no	—
556	C₂×Q₈	—	4	1	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×Q₈	—	4	1	no	—
559	C₂×Q₈	—	4	1	no	—
560	C₂×Q₈	—	4	1	no	—
561	C₂×Q₈	—	4	1	no	—
562	C₂×Q₈	—	4	1	no	—
563	C₂×Q₈	—	4	1	no	—
564	C₂×Q₈	—	4	1	no	—
565	C₂×Q₈	—	4	1	no	—
566	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	1	no	—
610	C₂²×C₄	—	4	1	no	—
611	C₂²×C₄	—	4	1	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
619	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
630	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
631	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
632	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
633	SD₁₆	—	2	32	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	—	2	2	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	4	1	no	—
644	C₂×C₈	—	4	1	no	—
645	C₂×C₈	—	4	1	no	—
646	C₂×C₈	—	4	1	no	—
647	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	—	4	1	no	—
655	C₄⋊C₄	—	4	1	no	—
656	C₂²⋊C₄	—	4	16	no	—
657	C₄²	—	4	1	no	—
658	C₄²	—	4	1	no	—
659	C₄²	—	4	1	no	—
660	C₄²	—	4	1	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	4	4	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	8	2	no	—
675	C₂³	—	8	2	no	—
676	C₂³	—	8	2	no	—
677	C₂³	—	8	2	no	—
678	C₂³	—	8	2	no	—
679	C₂³	—	8	2	no	—
680	C₂³	—	8	1	no	—
681	C₂³	—	8	1	no	—
682	C₂³	—	8	1	no	—
683	C₂³	—	8	1	no	—
684	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
685	C₂³	C₁₉×#120	1	1	yes	characteristic
686	C₂³	C₁₉×#120	1	1	yes	characteristic
687	C₂³	C₁₉×#121	1	1	yes	characteristic
688	C₂³	C₁₉×#121	1	1	yes	characteristic
689	C₂³	C₁₉×#121	1	1	yes	characteristic
690	C₂³	C₁₉×#127	1	1	yes	characteristic
691	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
692	C₂³	C₁₉×#135	1	2	yes	—
693	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
694	C₂³	C₁₉×#137	1	2	yes	—
695	Q₈	—	2	4	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	4	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	2	no	—
702	Q₈	—	4	2	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	8	2	no	—
730	C₂×C₄	—	8	2	no	—
731	C₂×C₄	—	8	1	no	—
732	C₂×C₄	—	8	1	no	—
733	C₂×C₄	—	8	1	no	—
734	C₂×C₄	—	8	1	no	—
735	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
736	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
737	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
738	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
739	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
740	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
741	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
742	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
743	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
744	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
745	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
746	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
747	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
748	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
749	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
750	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
751	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
752	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
753	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
754	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
755	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
756	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
757	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
758	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
759	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
760	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
761	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
762	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
763	C₈	—	2	4	no	—
764	C₈	—	4	2	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	8	no	—
767	C₂²	—	8	2	no	—
768	C₂²	—	8	2	no	—
769	C₂²	—	8	4	no	—
770	C₂²	—	8	2	no	—
771	C₂²	—	8	2	no	—
772	C₂²	—	8	2	no	—
773	C₂²	—	8	2	no	—
774	C₂²	—	8	4	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₁₉×#386	1	1	yes	characteristic
777	C₂²	C₁₉×#386	1	1	yes	characteristic
778	C₂²	C₁₉×#390	1	1	yes	characteristic
779	C₂²	C₁₉×#392	1	1	yes	characteristic
780	C₂²	C₁₉×#392	1	1	yes	characteristic
781	C₂²	C₁₉×#392	1	1	yes	characteristic
782	C₂²	C₁₉×#394	1	1	yes	characteristic
783	C₂²	C₄×SD₁₆×C₁₉	1	2	yes	—
784	C₂²	C₁₉×#440	1	2	yes	—
785	C₂²	C₁₉×#448	1	2	yes	—
786	C₂²	C₁₉×#449	1	2	yes	—
787	C₂²	C₁₉×#450	1	2	yes	—
788	C₂²	C₁₉×#452	1	2	yes	—
789	C₂²	C₁₉×#460	1	2	yes	—
790	C₂²	C₁₉×#461	1	2	yes	—
791	C₂²	C₁₉×#463	1	2	yes	—
792	C₂²	C₁₉×#464	1	2	yes	—
793	C₂²	C₁₉×#465	1	2	yes	—
794	C₂²	C₁₉×#468	1	2	yes	—
795	C₂²	C₁₉×#492	1	1	yes	characteristic
796	C₂²	C₁₉×#495	1	1	yes	characteristic
797	C₂²	C₁₉×#496	1	1	yes	characteristic
798	C₂²	C₁₉×#497	1	1	yes	characteristic
799	C₄	—	4	4	no	—
800	C₄	—	4	4	no	—
801	C₄	—	8	2	no	—
802	C₄	—	8	2	no	—
803	C₄	C₁₉×#379	1	1	yes	characteristic
804	C₄	C₁₉×#386	1	1	yes	characteristic
805	C₄	C₁₉×#386	1	1	yes	characteristic
806	C₄	C₁₉×#390	1	1	yes	characteristic
807	C₄	C₁₉×#392	1	1	yes	characteristic
808	C₄	C₁₉×#394	1	1	yes	characteristic
809	C₄	C₁₉×#394	1	1	yes	characteristic
810	C₄	C₁₉×#394	1	1	yes	characteristic
811	C₂	—	8	4	no	—
812	C₂	C₁₉×#1438	1	1	yes	characteristic
813	C₂	C₁₉×#1877	1	2	yes	—
814	C₂	C₁₉×#1880	1	2	yes	—
815	C₂	C₁₉×#1968	1	1	yes	characteristic
816	C₂	C₁₉×#1973	1	1	yes	characteristic
817	C₂	C₁₉×#2000	1	2	yes	—
818	C₂	C₁₉×#2012	1	1	yes	characteristic
819	C₂	C₁₉×#2013	1	1	yes	characteristic
820	C₂	C₁₉×#2014	1	1	yes	characteristic
821	C₂	C₁₉×#2015	1	1	yes	characteristic
822	C₂	C₁₉×#2055	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#103	C₂	semidirect
4. C₂×C₁₉×#391	C₂	semidirect
6. C₂×C₁₉×#340	C₂	semidirect
7. C₂×C₁₉×#336	C₂	semidirect
16. C₂²×SD₁₆×C₁₉	C₄	semidirect
154. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
206. C₂²×C₄×C₁₉	SD₁₆	semidirect
235. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
249. #11023	C₁₉	direct (N × H)
355. C₂²×#103	C₂×C₁₉	semidirect
357. C₂×#391	C₂×C₁₉	semidirect
359. C₂×#340	C₂×C₁₉	semidirect
360. C₂×#336	C₂×C₁₉	semidirect
415. C₂²×SD₁₆	C₄×C₁₉	semidirect
526. C₁₉	#11023	direct (N × H)
566. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
618. C₂²×C₄	SD₁₆×C₁₉	semidirect
647. C₂×C₈	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₁₉	2
C₂²×C₁₉×#103	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#391	2
C₂×C₁₉×#390	2
C₂×C₁₉×#340	2
C₂×C₁₉×#336	2
#11023	19

Subgroups — C19×#11023 #18016982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11023 #18016982