Subgroups — C₁₉×#24555 #18030514

Order 4864.

1194 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#120	—	2	1	no	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₁₉×#482	—	2	4	no	—
26	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×#386	—	2	1	no	—
40	C₁₉×#386	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#381	—	2	1	no	—
43	C₁₉×#380	C₂²	1	1	yes	characteristic
44	C₁₉×#380	C₂²	1	1	yes	characteristic
45	C₁₉×#380	C₂²	1	1	yes	characteristic
46	C₁₉×#380	C₂²	1	1	yes	characteristic
47	C₁₉×#380	C₂²	1	1	yes	characteristic
48	C₁₉×#380	C₂²	1	1	yes	characteristic
49	C₁₉×#380	C₂²	1	1	yes	characteristic
50	C₁₉×#379	—	2	1	no	—
51	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
56	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
59	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	—	2	1	no	—
63	C₂²×D₄×C₁₉	—	2	1	no	—
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	2	no	—
67	C₂³×C₄×C₁₉	—	2	2	no	—
68	C₂³×C₄×C₁₉	—	2	2	no	—
69	C₂³×C₄×C₁₉	—	2	2	no	—
70	C₂³×C₄×C₁₉	—	4	1	no	—
71	C₂³×C₄×C₁₉	—	4	1	no	—
72	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	—	2	2	no	—
79	C₂²×C₈×C₁₉	—	2	2	no	—
80	C₂²×C₈×C₁₉	—	2	2	no	—
81	C₂²×C₈×C₁₉	—	2	2	no	—
82	C₂²×C₈×C₁₉	—	4	1	no	—
83	C₂²×C₈×C₁₉	—	4	1	no	—
84	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	—	2	2	no	—
90	C₁₉×#121	—	2	2	no	—
91	C₁₉×#121	—	2	2	no	—
92	C₁₉×#121	—	4	1	no	—
93	C₁₉×#121	—	4	1	no	—
94	C₁₉×#120	—	4	4	no	—
95	C₁₉×#117	—	2	2	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	4	1	no	—
98	C₁₉×#117	—	4	1	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	—	2	1	no	—
120	C₁₉×#107	—	2	2	no	—
121	C₁₉×#107	—	4	1	no	—
122	C₁₉×#106	—	2	2	no	—
123	C₁₉×#106	—	4	1	no	—
124	C₁₉×#102	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×#102	—	4	1	no	—
127	C₁₉×#102	—	4	1	no	—
128	C₁₉×C₂²⋊C₈	—	2	2	no	—
129	C₁₉×C₂²⋊C₈	—	2	2	no	—
130	C₁₉×C₂²⋊C₈	—	2	2	no	—
131	C₁₉×C₂²⋊C₈	D₄	1	4	yes	complemented
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	—	2	1	no	—
137	C₁₉×#95	—	2	1	no	—
138	C₁₉×#95	—	2	1	no	—
139	C₂⁴×C₁₉	—	2	2	no	—
140	C₂⁴×C₁₉	—	2	2	no	—
141	C₂⁴×C₁₉	—	2	2	no	—
142	C₂⁴×C₁₉	—	2	2	no	—
143	C₂⁴×C₁₉	—	2	2	no	—
144	C₂⁴×C₁₉	—	2	1	no	—
145	C₂⁴×C₁₉	—	4	1	no	—
146	C₂⁴×C₁₉	—	4	1	no	—
147	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	4	2	no	—
157	C₂×D₄×C₁₉	—	4	2	no	—
158	C₂×D₄×C₁₉	—	4	2	no	—
159	C₂×D₄×C₁₉	—	4	2	no	—
160	C₂×D₄×C₁₉	—	4	2	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	—	4	2	no	—
164	C₂×D₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	1	no	—
172	C₂²×C₄×C₁₉	—	2	1	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	1	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	2	1	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	1	no	—
189	C₂²×C₄×C₁₉	—	2	1	no	—
190	C₂²×C₄×C₁₉	—	2	1	no	—
191	C₂²×C₄×C₁₉	—	2	1	no	—
192	C₂²×C₄×C₁₉	—	4	1	no	—
193	C₂²×C₄×C₁₉	—	4	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	4	no	—
196	C₂²×C₄×C₁₉	—	4	4	no	—
197	C₂²×C₄×C₁₉	—	4	4	no	—
198	C₂²×C₄×C₁₉	—	4	4	no	—
199	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	#41	1	2	yes	—
204	C₂²×C₄×C₁₉	#41	1	2	yes	—
205	C₂²×C₄×C₁₉	#41	1	2	yes	—
206	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
207	C₂×C₈×C₁₉	—	2	1	no	—
208	C₂×C₈×C₁₉	—	2	1	no	—
209	C₂×C₈×C₁₉	—	2	1	no	—
210	C₂×C₈×C₁₉	—	2	1	no	—
211	C₂×C₈×C₁₉	—	2	1	no	—
212	C₂×C₈×C₁₉	—	2	1	no	—
213	C₂×C₈×C₁₉	—	2	1	no	—
214	C₂×C₈×C₁₉	—	2	1	no	—
215	C₂×C₈×C₁₉	—	2	1	no	—
216	C₂×C₈×C₁₉	—	2	1	no	—
217	C₂×C₈×C₁₉	—	4	4	no	—
218	C₂×C₈×C₁₉	—	4	4	no	—
219	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
220	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
221	C₄⋊C₄×C₁₉	—	2	1	no	—
222	C₄⋊C₄×C₁₉	—	2	1	no	—
223	C₄⋊C₄×C₁₉	—	2	1	no	—
224	C₄⋊C₄×C₁₉	—	2	1	no	—
225	C₄⋊C₄×C₁₉	—	2	1	no	—
226	C₄⋊C₄×C₁₉	—	2	1	no	—
227	C₄⋊C₄×C₁₉	—	2	1	no	—
228	C₄⋊C₄×C₁₉	—	2	1	no	—
229	C₄⋊C₄×C₁₉	—	2	1	no	—
230	C₄⋊C₄×C₁₉	—	2	1	no	—
231	C₄⋊C₄×C₁₉	—	2	1	no	—
232	C₄⋊C₄×C₁₉	—	2	1	no	—
233	C₄⋊C₄×C₁₉	—	2	1	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₂²⋊C₄×C₁₉	—	4	2	no	—
236	C₂²⋊C₄×C₁₉	—	4	2	no	—
237	C₂²⋊C₄×C₁₉	—	4	2	no	—
238	C₂²⋊C₄×C₁₉	—	4	2	no	—
239	C₂²⋊C₄×C₁₉	—	4	2	no	—
240	C₂²⋊C₄×C₁₉	—	4	2	no	—
241	C₂²⋊C₄×C₁₉	—	4	2	no	—
242	C₂²⋊C₄×C₁₉	—	4	2	no	—
243	C₂²⋊C₄×C₁₉	—	4	2	no	—
244	C₂²⋊C₄×C₁₉	—	4	2	no	—
245	C₂²⋊C₄×C₁₉	—	4	2	no	—
246	C₂²⋊C₄×C₁₉	—	4	2	no	—
247	C₄²×C₁₉	—	4	2	no	—
248	C₄²×C₁₉	—	4	2	no	—
249	#24555	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	—	2	1	no	—
251	C₂³×C₁₉	—	2	1	no	—
252	C₂³×C₁₉	—	2	1	no	—
253	C₂³×C₁₉	—	2	1	no	—
254	C₂³×C₁₉	—	2	8	no	—
255	C₂³×C₁₉	—	2	1	no	—
256	C₂³×C₁₉	—	2	1	no	—
257	C₂³×C₁₉	—	2	1	no	—
258	C₂³×C₁₉	—	2	1	no	—
259	C₂³×C₁₉	—	2	1	no	—
260	C₂³×C₁₉	—	2	1	no	—
261	C₂³×C₁₉	—	2	1	no	—
262	C₂³×C₁₉	—	2	1	no	—
263	C₂³×C₁₉	—	2	1	no	—
264	C₂³×C₁₉	—	2	1	no	—
265	C₂³×C₁₉	—	2	1	no	—
266	C₂³×C₁₉	—	2	1	no	—
267	C₂³×C₁₉	—	4	4	no	—
268	C₂³×C₁₉	—	4	4	no	—
269	C₂³×C₁₉	—	4	4	no	—
270	C₂³×C₁₉	—	4	4	no	—
271	C₂³×C₁₉	—	4	4	no	—
272	C₂³×C₁₉	—	4	4	no	—
273	C₂³×C₁₉	—	4	1	no	—
274	C₂³×C₁₉	—	4	1	no	—
275	C₂³×C₁₉	—	4	1	no	—
276	C₂³×C₁₉	—	4	1	no	—
277	C₂³×C₁₉	—	4	1	no	—
278	C₂³×C₁₉	—	4	1	no	—
279	C₂³×C₁₉	—	4	1	no	—
280	C₂³×C₁₉	#121	1	2	yes	—
281	C₂³×C₁₉	#123	1	2	yes	—
282	C₂³×C₁₉	#135	1	2	yes	—
283	C₂³×C₁₉	#135	1	2	yes	—
284	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
285	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
286	D₄×C₁₉	—	4	1	no	—
287	D₄×C₁₉	—	4	1	no	—
288	D₄×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	4	1	no	—
290	D₄×C₁₉	—	8	4	no	—
291	D₄×C₁₉	—	8	4	no	—
292	D₄×C₁₉	—	8	4	no	—
293	C₂×C₄×C₁₉	—	2	1	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	2	1	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	2	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	2	no	—
303	C₂×C₄×C₁₉	—	2	2	no	—
304	C₂×C₄×C₁₉	—	2	2	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	1	no	—
308	C₂×C₄×C₁₉	—	4	4	no	—
309	C₂×C₄×C₁₉	—	4	4	no	—
310	C₂×C₄×C₁₉	—	4	4	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	1	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	1	no	—
325	C₂×C₄×C₁₉	—	4	1	no	—
326	C₂×C₄×C₁₉	—	4	1	no	—
327	C₂×C₄×C₁₉	—	4	1	no	—
328	C₂×C₄×C₁₉	—	4	1	no	—
329	C₂×C₄×C₁₉	—	4	1	no	—
330	C₂×C₄×C₁₉	—	4	1	no	—
331	C₂×C₄×C₁₉	—	4	1	no	—
332	C₂×C₄×C₁₉	—	4	1	no	—
333	C₂×C₄×C₁₉	—	4	1	no	—
334	C₂×C₄×C₁₉	—	4	1	no	—
335	C₂×C₄×C₁₉	—	4	1	no	—
336	C₂×C₄×C₁₉	#121	1	2	yes	—
337	C₂×C₄×C₁₉	#123	1	2	yes	—
338	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
344	C₈×C₁₉	—	2	2	no	—
345	C₈×C₁₉	—	2	2	no	—
346	C₈×C₁₉	—	4	1	no	—
347	C₈×C₁₉	—	4	1	no	—
348	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
349	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#2847	C₂×C₁₉	1	1	yes	characteristic
351	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#2077	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#2076	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#2034	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#2033	C₂×C₁₉	1	1	yes	characteristic, complemented
356	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
357	#1893	C₂×C₁₉	1	1	yes	characteristic, complemented
358	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
359	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
360	#1825	C₂×C₁₉	1	1	yes	characteristic, complemented
361	#1808	C₂×C₁₉	1	1	yes	characteristic, complemented
362	#1807	C₂×C₁₉	1	1	yes	characteristic, complemented
363	C₂²×C₁₉	—	2	2	no	—
364	C₂²×C₁₉	—	2	2	no	—
365	C₂²×C₁₉	—	2	2	no	—
366	C₂²×C₁₉	—	2	2	no	—
367	C₂²×C₁₉	—	2	2	no	—
368	C₂²×C₁₉	—	2	2	no	—
369	C₂²×C₁₉	—	2	2	no	—
370	C₂²×C₁₉	—	2	2	no	—
371	C₂²×C₁₉	—	2	2	no	—
372	C₂²×C₁₉	—	2	2	no	—
373	C₂²×C₁₉	—	2	2	no	—
374	C₂²×C₁₉	—	2	2	no	—
375	C₂²×C₁₉	—	4	16	no	—
376	C₂²×C₁₉	—	4	1	no	—
377	C₂²×C₁₉	—	4	1	no	—
378	C₂²×C₁₉	—	4	1	no	—
379	C₂²×C₁₉	—	4	1	no	—
380	C₂²×C₁₉	—	4	1	no	—
381	C₂²×C₁₉	—	4	1	no	—
382	C₂²×C₁₉	—	4	1	no	—
383	C₂²×C₁₉	—	4	1	no	—
384	C₂²×C₁₉	—	8	1	no	—
385	C₂²×C₁₉	—	8	1	no	—
386	C₂²×C₁₉	—	8	1	no	—
387	C₂²×C₁₉	—	8	1	no	—
388	C₂²×C₁₉	—	8	1	no	—
389	C₂²×C₁₉	—	8	1	no	—
390	C₂²×C₁₉	—	8	1	no	—
391	C₂²×C₁₉	#482	1	4	yes	complemented
392	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
393	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
394	C₂²×C₁₉	#534	1	1	yes	characteristic
395	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
396	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
397	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₂²×C₁₉	#575	1	1	yes	characteristic
399	C₄×C₁₉	—	2	2	no	—
400	C₄×C₁₉	—	2	2	no	—
401	C₄×C₁₉	—	4	1	no	—
402	C₄×C₁₉	—	8	1	no	—
403	C₄×C₁₉	—	8	1	no	—
404	C₄×C₁₉	—	8	1	no	—
405	C₄×C₁₉	—	8	1	no	—
406	C₄×C₁₉	—	8	1	no	—
407	C₄×C₁₉	—	8	1	no	—
408	C₄×C₁₉	—	8	1	no	—
409	C₄×C₁₉	#546	1	1	yes	characteristic
410	C₄×C₁₉	#546	1	1	yes	characteristic
411	C₄×C₁₉	#551	1	1	yes	characteristic
412	C₄×C₁₉	#551	1	1	yes	characteristic
413	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
414	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
415	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
416	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
418	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
419	C₂×#120	—	2	1	no	—
420	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
422	#482	—	2	4	no	—
423	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
425	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
426	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
427	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
428	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
429	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
430	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
431	C₂×C₂²⋊C₈	—	2	4	no	—
432	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
433	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
436	#386	—	2	1	no	—
437	#386	—	2	1	no	—
438	#386	—	2	1	no	—
439	#381	—	2	1	no	—
440	#380	C₂²×C₁₉	1	1	yes	characteristic
441	#380	C₂²×C₁₉	1	1	yes	characteristic
442	#380	C₂²×C₁₉	1	1	yes	characteristic
443	#380	C₂²×C₁₉	1	1	yes	characteristic
444	#380	C₂²×C₁₉	1	1	yes	characteristic
445	#380	C₂²×C₁₉	1	1	yes	characteristic
446	#380	C₂²×C₁₉	1	1	yes	characteristic
447	#379	—	2	1	no	—
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
452	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
453	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
454	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
455	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
457	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
458	C₂×C₁₉	—	2	4	no	—
459	C₂×C₁₉	—	4	2	no	—
460	C₂×C₁₉	—	4	2	no	—
461	C₂×C₁₉	—	16	1	no	—
462	C₂×C₁₉	#2412	1	1	yes	characteristic
463	C₂×C₁₉	#3050	1	1	yes	characteristic
464	C₂×C₁₉	#3055	1	1	yes	characteristic
465	C₂×C₁₉	C₂×#482	1	1	yes	characteristic
466	C₂×C₁₉	#3091	1	1	yes	characteristic
467	C₂×C₁₉	#3188	1	1	yes	characteristic
468	C₂×C₁₉	#3191	1	1	yes	characteristic
469	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
474	C₂³×C₄	—	2	2	no	—
475	C₂³×C₄	—	2	2	no	—
476	C₂³×C₄	—	2	2	no	—
477	C₂³×C₄	—	2	2	no	—
478	C₂³×C₄	—	4	1	no	—
479	C₂³×C₄	—	4	1	no	—
480	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
481	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
482	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
486	C₂²×C₈	—	2	2	no	—
487	C₂²×C₈	—	2	2	no	—
488	C₂²×C₈	—	2	2	no	—
489	C₂²×C₈	—	2	2	no	—
490	C₂²×C₈	—	4	1	no	—
491	C₂²×C₈	—	4	1	no	—
492	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	4	1	no	—
501	#121	—	4	1	no	—
502	#120	—	4	4	no	—
503	#117	—	2	2	no	—
504	#117	—	2	2	no	—
505	#117	—	4	1	no	—
506	#117	—	4	1	no	—
507	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	#107	—	2	2	no	—
529	#107	—	4	1	no	—
530	#106	—	2	2	no	—
531	#106	—	4	1	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	4	1	no	—
535	#102	—	4	1	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	—	2	2	no	—
538	C₂²⋊C₈	—	2	2	no	—
539	C₂²⋊C₈	D₄×C₁₉	1	4	yes	complemented
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	C₁₉	#24555	1	1	yes	characteristic, direct product factor, Sylow
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	—	4	1	no	—
556	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
557	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
611	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
612	C₂²×C₄	#41×C₁₉	1	2	yes	—
613	C₂²×C₄	#41×C₁₉	1	2	yes	—
614	C₂²×C₄	#41×C₁₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	4	4	no	—
627	C₂×C₈	—	4	4	no	—
628	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
629	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	4	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	4	no	—
678	C₂³	—	4	4	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	C₁₉×#121	1	2	yes	—
689	C₂³	C₁₉×#123	1	2	yes	—
690	C₂³	C₁₉×#135	1	2	yes	—
691	C₂³	C₁₉×#135	1	2	yes	—
692	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
693	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	8	4	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	C₁₉×#121	1	2	yes	—
745	C₂×C₄	C₁₉×#123	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
748	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
749	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
750	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	4	1	no	—
755	C₈	—	4	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	16	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	C₁₉×#482	1	4	yes	complemented
785	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
786	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
787	C₂²	C₁₉×#534	1	1	yes	characteristic
788	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
789	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
790	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
791	C₂²	C₁₉×#575	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	8	1	no	—
796	C₄	—	8	1	no	—
797	C₄	—	8	1	no	—
798	C₄	—	8	1	no	—
799	C₄	—	8	1	no	—
800	C₄	—	8	1	no	—
801	C₄	—	8	1	no	—
802	C₄	C₁₉×#546	1	1	yes	characteristic
803	C₄	C₁₉×#546	1	1	yes	characteristic
804	C₄	C₁₉×#551	1	1	yes	characteristic
805	C₄	C₁₉×#551	1	1	yes	characteristic
806	C₂	—	2	4	no	—
807	C₂	—	4	2	no	—
808	C₂	—	4	2	no	—
809	C₂	—	16	1	no	—
810	C₂	C₁₉×#2412	1	1	yes	characteristic
811	C₂	C₁₉×#3050	1	1	yes	characteristic
812	C₂	C₁₉×#3055	1	1	yes	characteristic
813	C₂	C₂×C₁₉×#482	1	1	yes	characteristic
814	C₂	C₁₉×#3091	1	1	yes	characteristic
815	C₂	C₁₉×#3188	1	1	yes	characteristic
816	C₂	C₁₉×#3191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#482	C₂	semidirect
2. C₂²×C₁₉×C₂²⋊C₈	C₂	semidirect
4. C₁₉×#2280	C₂	semidirect
5. C₁₉×#2077	C₂	semidirect
6. C₁₉×#2076	C₂	semidirect
7. C₁₉×#2034	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#1893	C₂	semidirect
10. C₁₉×#1893	C₂	semidirect
11. C₁₉×#1875	C₂	semidirect
12. C₁₉×#1854	C₂	semidirect
13. C₁₉×#1825	C₂	semidirect
14. C₁₉×#1808	C₂	semidirect
15. C₁₉×#1807	C₂	semidirect
26. C₂×C₁₉×#107	C₂²	semidirect
27. C₂×C₁₉×#107	C₂²	semidirect
28. C₂×C₁₉×#106	C₂²	semidirect
29. C₂×C₁₉×#106	C₂²	semidirect
30. C₂×C₁₉×#102	C₂²	semidirect
31. C₂×C₁₉×#102	C₂²	semidirect
32. C₂×C₁₉×#102	C₂²	semidirect
33. C₂×C₁₉×#102	C₂²	semidirect
53. C₁₉×#340	C₂²	semidirect
54. C₁₉×#340	C₂²	semidirect
55. C₁₉×#340	C₂²	semidirect
56. C₁₉×#340	C₂²	semidirect
57. C₁₉×#340	C₂²	semidirect
58. C₁₉×#340	C₂²	semidirect
59. C₁₉×#340	C₂²	semidirect
60. C₁₉×#340	C₂²	semidirect
131. C₁₉×C₂²⋊C₈	D₄	semidirect
249. #24555	C₁₉	direct (N × H)
348. C₂×#482	C₂×C₁₉	semidirect
349. C₂²×C₂²⋊C₈	C₂×C₁₉	semidirect
351. #2280	C₂×C₁₉	semidirect
352. #2077	C₂×C₁₉	semidirect
353. #2076	C₂×C₁₉	semidirect
354. #2034	C₂×C₁₉	semidirect
355. #2033	C₂×C₁₉	semidirect
356. #1893	C₂×C₁₉	semidirect
357. #1893	C₂×C₁₉	semidirect
358. #1875	C₂×C₁₉	semidirect
359. #1854	C₂×C₁₉	semidirect
360. #1825	C₂×C₁₉	semidirect
361. #1808	C₂×C₁₉	semidirect
362. #1807	C₂×C₁₉	semidirect
391. C₂²×C₁₉	#482	semidirect
423. C₂×#107	C₂²×C₁₉	semidirect
424. C₂×#107	C₂²×C₁₉	semidirect
425. C₂×#106	C₂²×C₁₉	semidirect
426. C₂×#106	C₂²×C₁₉	semidirect
427. C₂×#102	C₂²×C₁₉	semidirect
428. C₂×#102	C₂²×C₁₉	semidirect
429. C₂×#102	C₂²×C₁₉	semidirect
430. C₂×#102	C₂²×C₁₉	semidirect
450. #340	C₂²×C₁₉	semidirect
451. #340	C₂²×C₁₉	semidirect
452. #340	C₂²×C₁₉	semidirect
453. #340	C₂²×C₁₉	semidirect
454. #340	C₂²×C₁₉	semidirect
455. #340	C₂²×C₁₉	semidirect
456. #340	C₂²×C₁₉	semidirect
457. #340	C₂²×C₁₉	semidirect
539. C₂²⋊C₈	D₄×C₁₉	semidirect
547. C₁₉	#24555	direct (N × H)
784. C₂²	C₁₉×#482	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#482	2
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#2847	2
C₁₉×#2280	2
C₁₉×#2077	2
C₁₉×#2076	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#1893	2
C₁₉×#1875	2
C₁₉×#1854	2
C₁₉×#1825	2
C₁₉×#1808	2
C₁₉×#1807	2
#24555	19

Subgroups — C19×#24555 #18030514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24555 #18030514