Subgroups — C₁₉×#22588 #18028547

Order 4864.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2880	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1938	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1811	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1789	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₁₉×#433	—	2	1	no	—
22	C₁₉×#433	—	2	1	no	—
23	C₁₉×#432	—	2	1	no	—
24	C₁₉×#431	—	2	1	no	—
25	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
33	C₁₉×#419	C₄	1	1	yes	characteristic, complemented
34	C₁₉×#419	C₄	1	1	yes	characteristic, complemented
35	C₁₉×#418	C₄	1	1	yes	characteristic, complemented
36	C₁₉×#418	C₄	1	1	yes	characteristic, complemented
37	C₁₉×#417	C₄	1	1	yes	characteristic, complemented
38	C₁₉×#417	C₄	1	1	yes	characteristic, complemented
39	C₁₉×#417	C₄	1	1	yes	characteristic, complemented
40	C₁₉×#417	C₄	1	1	yes	characteristic, complemented
41	C₁₉×#416	C₂²	1	1	yes	characteristic
42	C₁₉×#416	C₂²	1	1	yes	characteristic
43	C₁₉×#416	C₂²	1	1	yes	characteristic
44	C₁₉×#416	C₂²	1	1	yes	characteristic
45	C₁₉×#408	—	2	1	no	—
46	C₁₉×#408	—	2	1	no	—
47	C₁₉×#408	C₂²	1	1	yes	characteristic
48	C₁₉×#408	C₂²	1	1	yes	characteristic
49	C₁₉×#407	—	2	1	no	—
50	C₁₉×#407	C₂²	1	1	yes	characteristic
51	C₁₉×#407	C₂²	1	1	yes	characteristic
52	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
53	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
59	C₁₉×#341	C₂²	1	1	yes	characteristic, complemented
60	C₁₉×#341	C₂²	1	1	yes	characteristic, complemented
61	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
67	C₂×#41×C₁₉	—	2	1	no	—
68	C₂×#41×C₁₉	—	2	1	no	—
69	C₂×#41×C₁₉	—	2	2	no	—
70	C₂×#41×C₁₉	—	2	2	no	—
71	C₂×#41×C₁₉	—	4	1	no	—
72	C₂×#41×C₁₉	—	4	1	no	—
73	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂²×D₄×C₁₉	—	2	1	no	—
79	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₁₉	—	2	1	no	—
81	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#131	—	2	2	no	—
83	C₁₉×#131	—	2	2	no	—
84	C₁₉×#131	—	4	1	no	—
85	C₁₉×#131	—	4	1	no	—
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	4	1	no	—
89	C₂×M₁₆×C₁₉	—	4	1	no	—
90	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₉	—	2	1	no	—
99	C₂²×C₈×C₁₉	—	2	1	no	—
100	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	—	2	1	no	—
106	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
107	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
108	C₁₉×#117	C₂³	1	1	yes	characteristic
109	C₁₉×#117	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄²×C₁₉	—	2	1	no	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#108	—	4	1	no	—
118	C₁₉×#108	—	4	1	no	—
119	C₁₉×C₄⋊C₈	—	2	1	no	—
120	C₁₉×C₄⋊C₈	—	2	1	no	—
121	C₁₉×C₄⋊C₈	—	2	1	no	—
122	C₁₉×C₄⋊C₈	—	2	1	no	—
123	C₁₉×#104	—	2	2	no	—
124	C₁₉×#104	—	2	2	no	—
125	C₁₉×#104	—	4	1	no	—
126	C₁₉×#104	—	4	1	no	—
127	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
128	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
129	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
130	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
131	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
132	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
133	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
134	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
135	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
136	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
137	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
138	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
139	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
140	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
141	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
142	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×C₂²⋊C₈	—	2	1	no	—
145	C₁₉×C₂²⋊C₈	—	2	1	no	—
146	C₁₉×C₂²⋊C₈	—	2	1	no	—
147	C₁₉×C₂²⋊C₈	—	2	1	no	—
148	C₁₉×C₂²⋊C₈	—	2	1	no	—
149	C₁₉×C₂²⋊C₈	—	2	1	no	—
150	C₁₉×C₂²⋊C₈	—	2	1	no	—
151	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
152	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
153	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
154	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
155	C₁₉×#97	—	2	1	no	—
156	C₁₉×#97	—	2	1	no	—
157	C₁₉×#97	—	4	1	no	—
158	C₄×C₈×C₁₉	—	2	1	no	—
159	C₄×C₈×C₁₉	—	2	1	no	—
160	C₄×C₈×C₁₉	—	4	1	no	—
161	C₁₉×#95	—	2	1	no	—
162	C₂⁴×C₁₉	—	2	1	no	—
163	C₂⁴×C₁₉	#41	1	1	yes	characteristic
164	#41×C₁₉	—	2	1	no	—
165	#41×C₁₉	—	2	1	no	—
166	#41×C₁₉	—	2	2	no	—
167	#41×C₁₉	—	2	2	no	—
168	#41×C₁₉	—	2	1	no	—
169	#41×C₁₉	—	2	1	no	—
170	#41×C₁₉	—	2	1	no	—
171	#41×C₁₉	—	2	1	no	—
172	#41×C₁₉	—	4	2	no	—
173	#41×C₁₉	—	4	2	no	—
174	#41×C₁₉	—	4	1	no	—
175	#41×C₁₉	—	4	1	no	—
176	#41×C₁₉	—	4	2	no	—
177	#41×C₁₉	—	4	2	no	—
178	#41×C₁₉	#41	1	2	yes	—
179	#41×C₁₉	#41	1	2	yes	—
180	C₂×Q₈×C₁₉	—	2	1	no	—
181	C₂×Q₈×C₁₉	—	2	2	no	—
182	C₂×Q₈×C₁₉	—	4	1	no	—
183	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	2	no	—
187	C₂×D₄×C₁₉	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	2	1	no	—
191	C₂×D₄×C₁₉	—	4	1	no	—
192	C₂×D₄×C₁₉	—	4	2	no	—
193	C₂×D₄×C₁₉	—	4	2	no	—
194	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
195	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	1	no	—
202	C₂²×C₄×C₁₉	—	2	1	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	1	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	4	2	no	—
210	C₂²×C₄×C₁₉	—	4	2	no	—
211	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂²×C₄	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	#41	1	1	yes	characteristic
216	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
217	M₁₆×C₁₉	—	2	1	no	—
218	M₁₆×C₁₉	—	2	1	no	—
219	M₁₆×C₁₉	—	2	1	no	—
220	M₁₆×C₁₉	—	2	1	no	—
221	M₁₆×C₁₉	—	2	1	no	—
222	M₁₆×C₁₉	—	2	1	no	—
223	M₁₆×C₁₉	—	2	1	no	—
224	M₁₆×C₁₉	—	2	1	no	—
225	M₁₆×C₁₉	—	4	1	no	—
226	M₁₆×C₁₉	—	4	1	no	—
227	M₁₆×C₁₉	—	4	1	no	—
228	M₁₆×C₁₉	—	4	1	no	—
229	M₁₆×C₁₉	—	4	2	no	—
230	M₁₆×C₁₉	—	4	2	no	—
231	C₂×C₈×C₁₉	—	2	1	no	—
232	C₂×C₈×C₁₉	—	2	1	no	—
233	C₂×C₈×C₁₉	—	2	1	no	—
234	C₂×C₈×C₁₉	—	2	1	no	—
235	C₂×C₈×C₁₉	—	2	1	no	—
236	C₂×C₈×C₁₉	—	2	1	no	—
237	C₂×C₈×C₁₉	—	2	1	no	—
238	C₂×C₈×C₁₉	—	2	1	no	—
239	C₂×C₈×C₁₉	—	2	1	no	—
240	C₂×C₈×C₁₉	—	2	1	no	—
241	C₂×C₈×C₁₉	—	2	1	no	—
242	C₂×C₈×C₁₉	—	2	1	no	—
243	C₂×C₈×C₁₉	—	4	2	no	—
244	C₂×C₈×C₁₉	—	4	2	no	—
245	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
248	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
249	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₄⋊C₄×C₁₉	—	2	1	no	—
254	C₄⋊C₄×C₁₉	—	2	1	no	—
255	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
256	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
257	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
258	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
259	C₂²⋊C₄×C₁₉	—	2	1	no	—
260	C₂²⋊C₄×C₁₉	—	2	1	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂²⋊C₄×C₁₉	—	4	2	no	—
264	C₄²×C₁₉	—	2	1	no	—
265	C₄²×C₁₉	—	2	1	no	—
266	C₄²×C₁₉	—	2	1	no	—
267	C₄²×C₁₉	—	2	1	no	—
268	C₄²×C₁₉	—	2	1	no	—
269	C₄²×C₁₉	—	2	1	no	—
270	C₄²×C₁₉	—	2	1	no	—
271	C₄²×C₁₉	—	2	1	no	—
272	#22588	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂³×C₁₉	—	2	1	no	—
274	C₂³×C₁₉	—	2	1	no	—
275	C₂³×C₁₉	—	2	1	no	—
276	C₂³×C₁₉	—	2	1	no	—
277	C₂³×C₁₉	—	4	1	no	—
278	C₂³×C₁₉	—	4	1	no	—
279	C₂³×C₁₉	—	4	2	no	—
280	C₂³×C₁₉	—	4	2	no	—
281	C₂³×C₁₉	—	8	1	no	—
282	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
283	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
284	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
285	Q₈×C₁₉	—	2	1	no	—
286	Q₈×C₁₉	—	2	1	no	—
287	Q₈×C₁₉	—	2	1	no	—
288	Q₈×C₁₉	—	4	2	no	—
289	Q₈×C₁₉	#117	1	2	yes	—
290	D₄×C₁₉	—	2	2	no	—
291	D₄×C₁₉	—	2	2	no	—
292	D₄×C₁₉	—	2	1	no	—
293	D₄×C₁₉	—	2	1	no	—
294	D₄×C₁₉	—	2	1	no	—
295	D₄×C₁₉	—	4	2	no	—
296	D₄×C₁₉	—	4	2	no	—
297	D₄×C₁₉	—	4	2	no	—
298	D₄×C₁₉	—	4	1	no	—
299	D₄×C₁₉	—	4	1	no	—
300	D₄×C₁₉	#117	1	2	yes	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	1	no	—
304	C₂×C₄×C₁₉	—	2	1	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	—	2	2	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	1	no	—
312	C₂×C₄×C₁₉	—	2	1	no	—
313	C₂×C₄×C₁₉	—	2	1	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	1	no	—
318	C₂×C₄×C₁₉	—	2	1	no	—
319	C₂×C₄×C₁₉	—	2	1	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	4	2	no	—
322	C₂×C₄×C₁₉	—	4	2	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	2	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	—	8	1	no	—
332	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
333	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
334	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
335	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
340	C₈×C₁₉	—	2	1	no	—
341	C₈×C₁₉	—	2	1	no	—
342	C₈×C₁₉	—	2	1	no	—
343	C₈×C₁₉	—	2	1	no	—
344	C₈×C₁₉	—	2	1	no	—
345	C₈×C₁₉	—	2	1	no	—
346	C₈×C₁₉	—	2	1	no	—
347	C₈×C₁₉	—	2	1	no	—
348	C₈×C₁₉	—	4	1	no	—
349	C₈×C₁₉	—	4	1	no	—
350	C₈×C₁₉	—	4	1	no	—
351	C₈×C₁₉	—	4	1	no	—
352	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#2896	C₂×C₁₉	1	1	yes	characteristic
354	#2880	C₂×C₁₉	1	1	yes	characteristic
355	#1938	C₂×C₁₉	1	1	yes	characteristic, complemented
356	#1937	C₂×C₁₉	1	1	yes	characteristic, complemented
357	#1929	C₂×C₁₉	1	1	yes	characteristic, complemented
358	#1929	C₂×C₁₉	1	1	yes	characteristic, complemented
359	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
360	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
361	#1826	C₂×C₁₉	1	1	yes	characteristic, complemented
362	#1811	C₂×C₁₉	1	1	yes	characteristic, complemented
363	#1789	C₂×C₁₉	1	1	yes	characteristic
364	#1765	C₂×C₁₉	1	1	yes	characteristic, complemented
365	#1764	C₂×C₁₉	1	1	yes	characteristic, complemented
366	#1753	C₂×C₁₉	1	1	yes	characteristic, complemented
367	C₂²×C₁₉	—	2	1	no	—
368	C₂²×C₁₉	—	2	1	no	—
369	C₂²×C₁₉	—	2	1	no	—
370	C₂²×C₁₉	—	2	1	no	—
371	C₂²×C₁₉	—	2	2	no	—
372	C₂²×C₁₉	—	2	1	no	—
373	C₂²×C₁₉	—	2	1	no	—
374	C₂²×C₁₉	—	2	1	no	—
375	C₂²×C₁₉	—	2	1	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	—	8	1	no	—
382	C₂²×C₁₉	—	8	1	no	—
383	C₂²×C₁₉	—	8	4	no	—
384	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
385	C₂²×C₁₉	#551	1	1	yes	characteristic
386	C₂²×C₁₉	#551	1	1	yes	characteristic
387	C₄×C₁₉	—	2	1	no	—
388	C₄×C₁₉	—	2	1	no	—
389	C₄×C₁₉	—	2	2	no	—
390	C₄×C₁₉	—	4	2	no	—
391	C₄×C₁₉	—	4	1	no	—
392	C₄×C₁₉	—	4	1	no	—
393	C₄×C₁₉	—	4	1	no	—
394	C₄×C₁₉	—	4	1	no	—
395	C₄×C₁₉	—	4	1	no	—
396	C₄×C₁₉	—	8	1	no	—
397	C₄×C₁₉	C₂×#117	1	1	yes	characteristic
398	C₄×C₁₉	#518	1	1	yes	characteristic
399	C₄×C₁₉	#546	1	1	yes	characteristic
400	C₄×C₁₉	#546	1	1	yes	characteristic
401	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
402	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
403	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
404	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
406	#433	—	2	1	no	—
407	#433	—	2	1	no	—
408	#432	—	2	1	no	—
409	#431	—	2	1	no	—
410	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
411	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
412	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
413	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
414	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
415	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
416	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
418	#419	C₄×C₁₉	1	1	yes	characteristic, complemented
419	#419	C₄×C₁₉	1	1	yes	characteristic, complemented
420	#418	C₄×C₁₉	1	1	yes	characteristic, complemented
421	#418	C₄×C₁₉	1	1	yes	characteristic, complemented
422	#417	C₄×C₁₉	1	1	yes	characteristic, complemented
423	#417	C₄×C₁₉	1	1	yes	characteristic, complemented
424	#417	C₄×C₁₉	1	1	yes	characteristic, complemented
425	#417	C₄×C₁₉	1	1	yes	characteristic, complemented
426	#416	C₂²×C₁₉	1	1	yes	characteristic
427	#416	C₂²×C₁₉	1	1	yes	characteristic
428	#416	C₂²×C₁₉	1	1	yes	characteristic
429	#416	C₂²×C₁₉	1	1	yes	characteristic
430	#408	—	2	1	no	—
431	#408	—	2	1	no	—
432	#408	C₂²×C₁₉	1	1	yes	characteristic
433	#408	C₂²×C₁₉	1	1	yes	characteristic
434	#407	—	2	1	no	—
435	#407	C₂²×C₁₉	1	1	yes	characteristic
436	#407	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	—	2	1	no	—
438	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
439	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
440	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
441	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
442	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
443	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
444	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
445	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
446	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
447	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
448	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
449	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
450	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
452	C₂×C₁₉	—	2	1	no	—
453	C₂×C₁₉	—	2	1	no	—
454	C₂×C₁₉	—	4	1	no	—
455	C₂×C₁₉	—	4	1	no	—
456	C₂×C₁₉	—	4	2	no	—
457	C₂×C₁₉	—	8	1	no	—
458	C₂×C₁₉	#2342	1	1	yes	characteristic
459	C₂×C₁₉	#2955	1	1	yes	characteristic
460	C₂×C₁₉	#2956	1	1	yes	characteristic
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	4	1	no	—
466	C₂×#41	—	4	1	no	—
467	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
468	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
469	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
470	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
471	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
476	#131	—	2	2	no	—
477	#131	—	2	2	no	—
478	#131	—	4	1	no	—
479	#131	—	4	1	no	—
480	C₂×M₁₆	—	2	1	no	—
481	C₂×M₁₆	—	2	1	no	—
482	C₂×M₁₆	—	4	1	no	—
483	C₂×M₁₆	—	4	1	no	—
484	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
485	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
486	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
487	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
490	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
491	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
492	C₂²×C₈	—	2	1	no	—
493	C₂²×C₈	—	2	1	no	—
494	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
498	#117	—	2	1	no	—
499	#117	—	2	1	no	—
500	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
501	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
502	#117	C₂³×C₁₉	1	1	yes	characteristic
503	#117	C₂³×C₁₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₄²	—	2	1	no	—
509	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
511	#108	—	4	1	no	—
512	#108	—	4	1	no	—
513	C₄⋊C₈	—	2	1	no	—
514	C₄⋊C₈	—	2	1	no	—
515	C₄⋊C₈	—	2	1	no	—
516	C₄⋊C₈	—	2	1	no	—
517	#104	—	2	2	no	—
518	#104	—	2	2	no	—
519	#104	—	4	1	no	—
520	#104	—	4	1	no	—
521	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
522	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
523	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
524	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
525	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
526	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
527	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
528	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
529	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
530	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
531	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
532	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
533	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
534	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
535	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
536	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
537	C₂²⋊C₈	—	2	1	no	—
538	C₂²⋊C₈	—	2	1	no	—
539	C₂²⋊C₈	—	2	1	no	—
540	C₂²⋊C₈	—	2	1	no	—
541	C₂²⋊C₈	—	2	1	no	—
542	C₂²⋊C₈	—	2	1	no	—
543	C₂²⋊C₈	—	2	1	no	—
544	C₂²⋊C₈	—	2	1	no	—
545	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
546	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
547	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
548	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
549	#97	—	2	1	no	—
550	#97	—	2	1	no	—
551	#97	—	4	1	no	—
552	C₄×C₈	—	2	1	no	—
553	C₄×C₈	—	2	1	no	—
554	C₄×C₈	—	4	1	no	—
555	#95	—	2	1	no	—
556	C₁₉	#22588	1	1	yes	characteristic, direct product factor, Sylow
557	C₂⁴	—	2	1	no	—
558	C₂⁴	#41×C₁₉	1	1	yes	characteristic
559	#41	—	2	1	no	—
560	#41	—	2	1	no	—
561	#41	—	2	2	no	—
562	#41	—	2	2	no	—
563	#41	—	2	1	no	—
564	#41	—	2	1	no	—
565	#41	—	2	1	no	—
566	#41	—	2	1	no	—
567	#41	—	4	2	no	—
568	#41	—	4	2	no	—
569	#41	—	4	1	no	—
570	#41	—	4	1	no	—
571	#41	—	4	2	no	—
572	#41	—	4	2	no	—
573	#41	#41×C₁₉	1	2	yes	—
574	#41	#41×C₁₉	1	2	yes	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	4	1	no	—
578	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
579	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
590	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
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	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
607	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
610	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
612	M₁₆	—	2	1	no	—
613	M₁₆	—	2	1	no	—
614	M₁₆	—	2	1	no	—
615	M₁₆	—	2	1	no	—
616	M₁₆	—	2	1	no	—
617	M₁₆	—	2	1	no	—
618	M₁₆	—	2	1	no	—
619	M₁₆	—	2	1	no	—
620	M₁₆	—	4	1	no	—
621	M₁₆	—	4	1	no	—
622	M₁₆	—	4	1	no	—
623	M₁₆	—	4	1	no	—
624	M₁₆	—	4	2	no	—
625	M₁₆	—	4	2	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	4	2	no	—
639	C₂×C₈	—	4	2	no	—
640	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
641	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
642	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
643	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
644	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
645	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
647	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
651	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
652	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
653	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	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	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	8	1	no	—
676	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
677	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
678	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
679	Q₈	—	2	1	no	—
680	Q₈	—	2	1	no	—
681	Q₈	—	2	1	no	—
682	Q₈	—	4	2	no	—
683	Q₈	C₁₉×#117	1	2	yes	—
684	D₄	—	2	2	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	1	no	—
687	D₄	—	2	1	no	—
688	D₄	—	2	1	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	C₁₉×#117	1	2	yes	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	2	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	—	8	1	no	—
726	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
727	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
728	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
730	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
732	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	1	no	—
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	1	no	—
741	C₈	—	2	1	no	—
742	C₈	—	4	1	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	4	no	—
763	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
764	C₂²	C₁₉×#551	1	1	yes	characteristic
765	C₂²	C₁₉×#551	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	8	1	no	—
776	C₄	C₂×C₁₉×#117	1	1	yes	characteristic
777	C₄	C₁₉×#518	1	1	yes	characteristic
778	C₄	C₁₉×#546	1	1	yes	characteristic
779	C₄	C₁₉×#546	1	1	yes	characteristic
780	C₂	—	2	1	no	—
781	C₂	—	2	1	no	—
782	C₂	—	4	1	no	—
783	C₂	—	4	1	no	—
784	C₂	—	4	2	no	—
785	C₂	—	8	1	no	—
786	C₂	C₁₉×#2342	1	1	yes	characteristic
787	C₂	C₁₉×#2955	1	1	yes	characteristic
788	C₂	C₁₉×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2924	C₂	semidirect
4. C₁₉×#1938	C₂	semidirect
5. C₁₉×#1937	C₂	semidirect
6. C₁₉×#1929	C₂	semidirect
7. C₁₉×#1929	C₂	semidirect
8. C₁₉×#1866	C₂	semidirect
9. C₁₉×#1866	C₂	semidirect
10. C₁₉×#1826	C₂	semidirect
11. C₁₉×#1811	C₂	semidirect
13. C₁₉×#1765	C₂	semidirect
14. C₁₉×#1764	C₂	semidirect
15. C₁₉×#1753	C₂	semidirect
25. C₂×C₁₉×#108	C₂²	semidirect
26. C₂×C₁₉×#108	C₂²	semidirect
27. C₁₉×#424	C₂²	semidirect
28. C₁₉×#424	C₂²	semidirect
33. C₁₉×#419	C₄	semidirect
34. C₁₉×#419	C₄	semidirect
35. C₁₉×#418	C₄	semidirect
36. C₁₉×#418	C₄	semidirect
37. C₁₉×#417	C₄	semidirect
38. C₁₉×#417	C₄	semidirect
39. C₁₉×#417	C₄	semidirect
40. C₁₉×#417	C₄	semidirect
54. C₁₉×#405	C₂²	semidirect
55. C₁₉×#405	C₂²	semidirect
56. C₂×C₁₉×#97	C₂²	semidirect
57. C₂×C₄×C₈×C₁₉	C₂²	semidirect
59. C₁₉×#341	C₂²	semidirect
60. C₁₉×#341	C₂²	semidirect
61. C₁₉×#339	C₂²	semidirect
62. C₁₉×#339	C₂²	semidirect
63. C₁₉×#339	C₂²	semidirect
64. C₁₉×#339	C₂²	semidirect
65. C₁₉×#336	C₂²	semidirect
66. C₁₉×#336	C₂²	semidirect
272. #22588	C₁₉	direct (N × H)
352. #2924	C₂×C₁₉	semidirect
355. #1938	C₂×C₁₉	semidirect
356. #1937	C₂×C₁₉	semidirect
357. #1929	C₂×C₁₉	semidirect
358. #1929	C₂×C₁₉	semidirect
359. #1866	C₂×C₁₉	semidirect
360. #1866	C₂×C₁₉	semidirect
361. #1826	C₂×C₁₉	semidirect
362. #1811	C₂×C₁₉	semidirect
364. #1765	C₂×C₁₉	semidirect
365. #1764	C₂×C₁₉	semidirect
366. #1753	C₂×C₁₉	semidirect
410. C₂×#108	C₂²×C₁₉	semidirect
411. C₂×#108	C₂²×C₁₉	semidirect
412. #424	C₂²×C₁₉	semidirect
413. #424	C₂²×C₁₉	semidirect
418. #419	C₄×C₁₉	semidirect
419. #419	C₄×C₁₉	semidirect
420. #418	C₄×C₁₉	semidirect
421. #418	C₄×C₁₉	semidirect
422. #417	C₄×C₁₉	semidirect
423. #417	C₄×C₁₉	semidirect
424. #417	C₄×C₁₉	semidirect
425. #417	C₄×C₁₉	semidirect
439. #405	C₂²×C₁₉	semidirect
440. #405	C₂²×C₁₉	semidirect
441. C₂×#97	C₂²×C₁₉	semidirect
442. C₂×C₄×C₈	C₂²×C₁₉	semidirect
444. #341	C₂²×C₁₉	semidirect
445. #341	C₂²×C₁₉	semidirect
446. #339	C₂²×C₁₉	semidirect
447. #339	C₂²×C₁₉	semidirect
448. #339	C₂²×C₁₉	semidirect
449. #339	C₂²×C₁₉	semidirect
450. #336	C₂²×C₁₉	semidirect
451. #336	C₂²×C₁₉	semidirect
556. C₁₉	#22588	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×#2924	2
C₁₉×#2896	2
C₁₉×#2880	2
C₁₉×#1938	2
C₁₉×#1937	2
C₁₉×#1929	2
C₁₉×#1866	2
C₁₉×#1826	2
C₁₉×#1811	2
C₁₉×#1789	2
C₁₉×#1765	2
C₁₉×#1764	2
C₁₉×#1753	2
#22588	19

Subgroups — C19×#22588 #18028547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22588 #18028547