Subgroups — C₁₉×#22889 #18028848

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3002	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2933	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1897	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#525	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₁₉×#452	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#452	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#451	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#450	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#449	C₄	1	1	yes	characteristic, complemented
30	C₁₉×#449	C₄	1	1	yes	characteristic, complemented
31	C₁₉×#448	C₄	1	1	yes	characteristic, complemented
32	C₁₉×#447	C₄	1	1	yes	characteristic, complemented
33	C₁₉×#443	—	2	4	no	—
34	C₁₉×#436	—	2	1	no	—
35	C₁₉×#435	—	2	1	no	—
36	C₁₉×#435	—	2	1	no	—
37	C₈×D₄×C₁₉	—	2	1	no	—
38	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#421	—	2	4	no	—
42	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
46	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#416	C₂²	1	1	yes	characteristic
49	C₁₉×#416	C₂²	1	1	yes	characteristic
50	C₁₉×#408	—	2	1	no	—
51	C₁₉×#408	—	2	1	no	—
52	C₁₉×#408	C₂²	1	1	yes	characteristic
53	C₁₉×#408	C₂²	1	1	yes	characteristic
54	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
55	C₁₉×#407	—	2	1	no	—
56	C₁₉×#407	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
58	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
63	C₁₉×#341	C₂²	1	1	yes	characteristic, complemented
64	C₁₉×#341	C₂²	1	1	yes	characteristic, complemented
65	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
66	C₁₉×#339	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
68	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
69	C₂×#41×C₁₉	—	2	1	no	—
70	C₂×#41×C₁₉	—	2	1	no	—
71	C₂×#41×C₁₉	—	2	2	no	—
72	C₂×#41×C₁₉	—	2	2	no	—
73	C₂×#41×C₁₉	—	4	1	no	—
74	C₂×#41×C₁₉	—	4	1	no	—
75	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂²×D₄×C₁₉	—	2	1	no	—
82	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	—	2	1	no	—
84	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#135	—	2	2	no	—
86	C₁₉×#135	—	2	2	no	—
87	C₁₉×#135	—	4	1	no	—
88	C₁₉×#135	—	4	1	no	—
89	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
95	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
96	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
97	C₁₉×#131	—	2	2	no	—
98	C₁₉×#131	—	2	2	no	—
99	C₁₉×#131	—	2	2	no	—
100	C₁₉×#131	—	4	1	no	—
101	C₁₉×#131	—	4	1	no	—
102	C₁₉×#131	—	4	1	no	—
103	C₂×M₁₆×C₁₉	—	2	1	no	—
104	C₂×M₁₆×C₁₉	—	2	1	no	—
105	C₂×M₁₆×C₁₉	—	2	1	no	—
106	C₂×M₁₆×C₁₉	—	2	1	no	—
107	C₂×M₁₆×C₁₉	—	2	2	no	—
108	C₂×M₁₆×C₁₉	—	4	1	no	—
109	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₉	—	2	1	no	—
114	C₂²×C₈×C₁₉	—	2	1	no	—
115	C₂²×C₈×C₁₉	—	2	1	no	—
116	C₂²×C₈×C₁₉	—	2	1	no	—
117	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
121	C₁₉×#123	—	2	1	no	—
122	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
123	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
124	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
125	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
126	C₁₉×#120	—	2	1	no	—
127	C₄×D₄×C₁₉	—	2	1	no	—
128	C₄×D₄×C₁₉	—	2	1	no	—
129	C₁₉×#117	—	2	2	no	—
130	C₁₉×#117	—	4	1	no	—
131	C₁₉×#117	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
134	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
136	C₁₉×#108	—	2	2	no	—
137	C₁₉×#108	—	4	1	no	—
138	C₁₉×C₄⋊C₈	—	2	1	no	—
139	C₁₉×C₄⋊C₈	—	2	1	no	—
140	C₁₉×#104	—	2	2	no	—
141	C₁₉×#104	—	2	2	no	—
142	C₁₉×#104	—	2	2	no	—
143	C₁₉×#104	—	2	2	no	—
144	C₁₉×#104	—	4	1	no	—
145	C₁₉×#104	D₄	1	4	yes	complemented
146	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
147	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
148	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
149	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
150	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
151	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
152	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
153	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
154	C₁₉×C₂²⋊C₈	—	2	1	no	—
155	C₁₉×C₂²⋊C₈	—	2	1	no	—
156	C₁₉×C₂²⋊C₈	—	2	1	no	—
157	C₁₉×C₂²⋊C₈	—	2	1	no	—
158	C₁₉×C₂²⋊C₈	—	2	1	no	—
159	C₁₉×C₂²⋊C₈	—	2	1	no	—
160	C₁₉×C₂²⋊C₈	—	2	1	no	—
161	C₁₉×C₂²⋊C₈	—	2	1	no	—
162	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
163	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
164	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
165	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
166	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
167	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
168	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₁₉×#97	—	2	1	no	—
171	C₁₉×#97	—	4	1	no	—
172	C₄×C₈×C₁₉	—	2	1	no	—
173	C₄×C₈×C₁₉	—	2	2	no	—
174	C₂⁴×C₁₉	—	2	1	no	—
175	C₂⁴×C₁₉	#41	1	1	yes	characteristic
176	#41×C₁₉	—	2	1	no	—
177	#41×C₁₉	—	2	1	no	—
178	#41×C₁₉	—	2	2	no	—
179	#41×C₁₉	—	2	2	no	—
180	#41×C₁₉	—	2	1	no	—
181	#41×C₁₉	—	2	1	no	—
182	#41×C₁₉	—	2	1	no	—
183	#41×C₁₉	—	2	1	no	—
184	#41×C₁₉	—	2	1	no	—
185	#41×C₁₉	—	2	1	no	—
186	#41×C₁₉	—	2	1	no	—
187	#41×C₁₉	—	2	1	no	—
188	#41×C₁₉	—	4	2	no	—
189	#41×C₁₉	—	4	2	no	—
190	#41×C₁₉	—	4	1	no	—
191	#41×C₁₉	—	4	1	no	—
192	#41×C₁₉	—	4	2	no	—
193	#41×C₁₉	—	4	2	no	—
194	#41×C₁₉	C₂×D₄	1	2	yes	—
195	#41×C₁₉	#41	1	2	yes	—
196	C₂×Q₈×C₁₉	—	2	1	no	—
197	C₂×Q₈×C₁₉	—	2	2	no	—
198	C₂×Q₈×C₁₉	—	4	1	no	—
199	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
200	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
201	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
202	C₂×D₄×C₁₉	—	2	1	no	—
203	C₂×D₄×C₁₉	—	2	2	no	—
204	C₂×D₄×C₁₉	—	2	1	no	—
205	C₂×D₄×C₁₉	—	2	1	no	—
206	C₂×D₄×C₁₉	—	2	1	no	—
207	C₂×D₄×C₁₉	—	2	1	no	—
208	C₂×D₄×C₁₉	—	2	1	no	—
209	C₂×D₄×C₁₉	—	2	1	no	—
210	C₂×D₄×C₁₉	—	2	1	no	—
211	C₂×D₄×C₁₉	—	4	1	no	—
212	C₂×D₄×C₁₉	—	4	2	no	—
213	C₂×D₄×C₁₉	—	4	2	no	—
214	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
215	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
216	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₉	—	2	1	no	—
218	C₂²×C₄×C₁₉	—	2	1	no	—
219	C₂²×C₄×C₁₉	—	2	1	no	—
220	C₂²×C₄×C₁₉	—	2	1	no	—
221	C₂²×C₄×C₁₉	—	2	1	no	—
222	C₂²×C₄×C₁₉	—	2	1	no	—
223	C₂²×C₄×C₁₉	—	2	1	no	—
224	C₂²×C₄×C₁₉	—	2	1	no	—
225	C₂²×C₄×C₁₉	—	2	1	no	—
226	C₂²×C₄×C₁₉	—	2	1	no	—
227	C₂²×C₄×C₁₉	—	2	1	no	—
228	C₂²×C₄×C₁₉	—	2	1	no	—
229	C₂²×C₄×C₁₉	—	4	2	no	—
230	C₂²×C₄×C₁₉	—	4	2	no	—
231	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
236	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	Q₁₆×C₁₉	—	2	2	no	—
238	Q₁₆×C₁₉	—	4	1	no	—
239	SD₁₆×C₁₉	—	2	2	no	—
240	SD₁₆×C₁₉	—	2	2	no	—
241	SD₁₆×C₁₉	—	4	1	no	—
242	SD₁₆×C₁₉	—	4	1	no	—
243	D₈×C₁₉	—	2	2	no	—
244	D₈×C₁₉	—	4	1	no	—
245	M₁₆×C₁₉	—	2	1	no	—
246	M₁₆×C₁₉	—	2	1	no	—
247	M₁₆×C₁₉	—	2	1	no	—
248	M₁₆×C₁₉	—	2	1	no	—
249	M₁₆×C₁₉	—	2	1	no	—
250	M₁₆×C₁₉	—	2	1	no	—
251	M₁₆×C₁₉	—	2	1	no	—
252	M₁₆×C₁₉	—	4	2	no	—
253	M₁₆×C₁₉	—	4	2	no	—
254	M₁₆×C₁₉	—	4	2	no	—
255	M₁₆×C₁₉	—	4	2	no	—
256	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
257	C₂×C₈×C₁₉	—	2	1	no	—
258	C₂×C₈×C₁₉	—	2	1	no	—
259	C₂×C₈×C₁₉	—	2	1	no	—
260	C₂×C₈×C₁₉	—	2	1	no	—
261	C₂×C₈×C₁₉	—	2	1	no	—
262	C₂×C₈×C₁₉	—	2	1	no	—
263	C₂×C₈×C₁₉	—	2	1	no	—
264	C₂×C₈×C₁₉	—	2	1	no	—
265	C₂×C₈×C₁₉	—	2	1	no	—
266	C₂×C₈×C₁₉	—	2	1	no	—
267	C₂×C₈×C₁₉	—	2	1	no	—
268	C₂×C₈×C₁₉	—	2	1	no	—
269	C₂×C₈×C₁₉	—	4	2	no	—
270	C₂×C₈×C₁₉	—	4	2	no	—
271	C₂×C₈×C₁₉	—	4	2	no	—
272	C₂×C₈×C₁₉	—	4	2	no	—
273	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
274	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
275	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
276	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
277	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
278	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
279	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
280	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
281	C₄⋊C₄×C₁₉	—	2	1	no	—
282	C₄⋊C₄×C₁₉	—	2	1	no	—
283	C₄⋊C₄×C₁₉	—	4	2	no	—
284	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
285	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
286	C₂²⋊C₄×C₁₉	—	2	1	no	—
287	C₂²⋊C₄×C₁₉	—	2	1	no	—
288	C₂²⋊C₄×C₁₉	—	2	1	no	—
289	C₂²⋊C₄×C₁₉	—	2	1	no	—
290	C₂²⋊C₄×C₁₉	—	2	1	no	—
291	C₂²⋊C₄×C₁₉	—	4	2	no	—
292	C₄²×C₁₉	—	2	1	no	—
293	C₄²×C₁₉	—	2	1	no	—
294	C₄²×C₁₉	—	2	1	no	—
295	C₄²×C₁₉	—	2	1	no	—
296	C₄²×C₁₉	C₂×D₄	1	2	yes	—
297	#22889	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂³×C₁₉	—	2	1	no	—
299	C₂³×C₁₉	—	2	1	no	—
300	C₂³×C₁₉	—	2	1	no	—
301	C₂³×C₁₉	—	2	1	no	—
302	C₂³×C₁₉	—	2	1	no	—
303	C₂³×C₁₉	—	4	1	no	—
304	C₂³×C₁₉	—	4	1	no	—
305	C₂³×C₁₉	—	4	2	no	—
306	C₂³×C₁₉	—	4	2	no	—
307	C₂³×C₁₉	—	8	1	no	—
308	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
309	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
310	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
311	Q₈×C₁₉	—	2	1	no	—
312	Q₈×C₁₉	—	2	1	no	—
313	Q₈×C₁₉	—	2	1	no	—
314	Q₈×C₁₉	—	2	1	no	—
315	Q₈×C₁₉	—	2	1	no	—
316	Q₈×C₁₉	—	4	2	no	—
317	Q₈×C₁₉	C₄×D₄	1	2	yes	—
318	D₄×C₁₉	—	2	2	no	—
319	D₄×C₁₉	—	2	2	no	—
320	D₄×C₁₉	—	2	1	no	—
321	D₄×C₁₉	—	2	1	no	—
322	D₄×C₁₉	—	2	1	no	—
323	D₄×C₁₉	—	2	1	no	—
324	D₄×C₁₉	—	2	1	no	—
325	D₄×C₁₉	—	4	2	no	—
326	D₄×C₁₉	—	4	2	no	—
327	D₄×C₁₉	—	4	2	no	—
328	D₄×C₁₉	—	4	2	no	—
329	D₄×C₁₉	—	4	1	no	—
330	D₄×C₁₉	—	4	1	no	—
331	D₄×C₁₉	—	4	1	no	—
332	D₄×C₁₉	—	4	1	no	—
333	D₄×C₁₉	—	8	1	no	—
334	D₄×C₁₉	C₄×D₄	1	2	yes	—
335	C₂×C₄×C₁₉	—	2	1	no	—
336	C₂×C₄×C₁₉	—	2	1	no	—
337	C₂×C₄×C₁₉	—	2	1	no	—
338	C₂×C₄×C₁₉	—	2	1	no	—
339	C₂×C₄×C₁₉	—	2	1	no	—
340	C₂×C₄×C₁₉	—	2	1	no	—
341	C₂×C₄×C₁₉	—	2	1	no	—
342	C₂×C₄×C₁₉	—	2	1	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	1	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	1	no	—
347	C₂×C₄×C₁₉	—	2	1	no	—
348	C₂×C₄×C₁₉	—	2	1	no	—
349	C₂×C₄×C₁₉	—	2	1	no	—
350	C₂×C₄×C₁₉	—	2	1	no	—
351	C₂×C₄×C₁₉	—	2	1	no	—
352	C₂×C₄×C₁₉	—	2	2	no	—
353	C₂×C₄×C₁₉	—	4	2	no	—
354	C₂×C₄×C₁₉	—	4	2	no	—
355	C₂×C₄×C₁₉	—	4	2	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	—	4	1	no	—
359	C₂×C₄×C₁₉	—	4	1	no	—
360	C₂×C₄×C₁₉	—	4	1	no	—
361	C₂×C₄×C₁₉	—	4	1	no	—
362	C₂×C₄×C₁₉	—	4	1	no	—
363	C₂×C₄×C₁₉	—	4	1	no	—
364	C₂×C₄×C₁₉	—	4	1	no	—
365	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
373	C₈×C₁₉	—	2	1	no	—
374	C₈×C₁₉	—	2	1	no	—
375	C₈×C₁₉	—	2	1	no	—
376	C₈×C₁₉	—	2	1	no	—
377	C₈×C₁₉	—	2	1	no	—
378	C₈×C₁₉	—	2	1	no	—
379	C₈×C₁₉	—	2	2	no	—
380	C₈×C₁₉	—	2	1	no	—
381	C₈×C₁₉	—	2	1	no	—
382	C₈×C₁₉	—	4	1	no	—
383	C₈×C₁₉	—	4	1	no	—
384	C₈×C₁₉	—	4	1	no	—
385	#3002	C₂×C₁₉	1	1	yes	characteristic
386	C₂×#443	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#2933	C₂×C₁₉	1	1	yes	characteristic, complemented
388	C₂×#421	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#2880	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#1975	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#1937	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#1929	C₂×C₁₉	1	1	yes	characteristic, complemented
393	#1897	C₂×C₁₉	1	1	yes	characteristic, complemented
394	#1876	C₂×C₁₉	1	1	yes	characteristic, complemented
395	#1876	C₂×C₁₉	1	1	yes	characteristic, complemented
396	#1866	C₂×C₁₉	1	1	yes	characteristic, complemented
397	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
398	#1765	C₂×C₁₉	1	1	yes	characteristic, complemented
399	#1750	C₂×C₁₉	1	1	yes	characteristic, complemented
400	C₂²×C₁₉	—	2	1	no	—
401	C₂²×C₁₉	—	2	1	no	—
402	C₂²×C₁₉	—	2	1	no	—
403	C₂²×C₁₉	—	2	1	no	—
404	C₂²×C₁₉	—	2	2	no	—
405	C₂²×C₁₉	—	2	1	no	—
406	C₂²×C₁₉	—	2	1	no	—
407	C₂²×C₁₉	—	2	1	no	—
408	C₂²×C₁₉	—	2	1	no	—
409	C₂²×C₁₉	—	4	1	no	—
410	C₂²×C₁₉	—	4	1	no	—
411	C₂²×C₁₉	—	4	1	no	—
412	C₂²×C₁₉	—	4	1	no	—
413	C₂²×C₁₉	—	4	1	no	—
414	C₂²×C₁₉	—	4	1	no	—
415	C₂²×C₁₉	—	4	1	no	—
416	C₂²×C₁₉	—	4	1	no	—
417	C₂²×C₁₉	—	8	1	no	—
418	C₂²×C₁₉	—	8	1	no	—
419	C₂²×C₁₉	—	8	4	no	—
420	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×C₁₉	#546	1	1	yes	characteristic
422	C₂²×C₁₉	#551	1	1	yes	characteristic
423	C₄×C₁₉	—	2	1	no	—
424	C₄×C₁₉	—	2	1	no	—
425	C₄×C₁₉	—	2	2	no	—
426	C₄×C₁₉	—	4	2	no	—
427	C₄×C₁₉	—	4	1	no	—
428	C₄×C₁₉	—	4	1	no	—
429	C₄×C₁₉	—	4	1	no	—
430	C₄×C₁₉	—	4	1	no	—
431	C₄×C₁₉	—	8	1	no	—
432	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
433	C₄×C₁₉	#518	1	1	yes	characteristic
434	C₄×C₁₉	D₄²	1	1	yes	characteristic
435	C₄×C₁₉	#546	1	1	yes	characteristic
436	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
438	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
439	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
441	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
442	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
443	#525	C₂²×C₁₉	1	1	yes	characteristic
444	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
445	#452	C₄×C₁₉	1	1	yes	characteristic, complemented
446	#452	C₄×C₁₉	1	1	yes	characteristic, complemented
447	#451	C₄×C₁₉	1	1	yes	characteristic, complemented
448	#450	C₄×C₁₉	1	1	yes	characteristic, complemented
449	#449	C₄×C₁₉	1	1	yes	characteristic, complemented
450	#449	C₄×C₁₉	1	1	yes	characteristic, complemented
451	#448	C₄×C₁₉	1	1	yes	characteristic, complemented
452	#447	C₄×C₁₉	1	1	yes	characteristic, complemented
453	#443	—	2	4	no	—
454	#436	—	2	1	no	—
455	#435	—	2	1	no	—
456	#435	—	2	1	no	—
457	C₈×D₄	—	2	1	no	—
458	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
459	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
460	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#421	—	2	4	no	—
462	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
463	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
464	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
465	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
466	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
467	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
468	#416	C₂²×C₁₉	1	1	yes	characteristic
469	#416	C₂²×C₁₉	1	1	yes	characteristic
470	#408	—	2	1	no	—
471	#408	—	2	1	no	—
472	#408	C₂²×C₁₉	1	1	yes	characteristic
473	#408	C₂²×C₁₉	1	1	yes	characteristic
474	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
475	#407	—	2	1	no	—
476	#407	C₂²×C₁₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₈	—	2	1	no	—
478	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
480	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
481	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
482	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
483	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
484	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
485	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
486	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
487	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	C₂×C₁₉	—	2	1	no	—
490	C₂×C₁₉	—	2	1	no	—
491	C₂×C₁₉	—	4	1	no	—
492	C₂×C₁₉	—	4	1	no	—
493	C₂×C₁₉	—	4	2	no	—
494	C₂×C₁₉	—	8	1	no	—
495	C₂×C₁₉	—	8	1	no	—
496	C₂×C₁₉	#2358	1	1	yes	characteristic
497	C₂×C₁₉	#2955	1	1	yes	characteristic
498	C₂×C₁₉	#2957	1	1	yes	characteristic
499	C₂×#41	—	2	1	no	—
500	C₂×#41	—	2	1	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
506	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
507	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
508	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
509	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
510	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
515	#135	—	2	2	no	—
516	#135	—	2	2	no	—
517	#135	—	4	1	no	—
518	#135	—	4	1	no	—
519	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
520	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
521	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
522	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
523	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
524	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
525	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
526	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
527	#131	—	2	2	no	—
528	#131	—	2	2	no	—
529	#131	—	2	2	no	—
530	#131	—	4	1	no	—
531	#131	—	4	1	no	—
532	#131	—	4	1	no	—
533	C₂×M₁₆	—	2	1	no	—
534	C₂×M₁₆	—	2	1	no	—
535	C₂×M₁₆	—	2	1	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	2	no	—
538	C₂×M₁₆	—	4	1	no	—
539	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
540	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
541	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
542	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
543	C₂²×C₈	—	2	1	no	—
544	C₂²×C₈	—	2	1	no	—
545	C₂²×C₈	—	2	1	no	—
546	C₂²×C₈	—	2	1	no	—
547	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
548	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
551	#123	—	2	1	no	—
552	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
553	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
554	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
555	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
556	#120	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	#117	—	2	2	no	—
560	#117	—	4	1	no	—
561	#117	C₂³×C₁₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
566	#108	—	2	2	no	—
567	#108	—	4	1	no	—
568	C₄⋊C₈	—	2	1	no	—
569	C₄⋊C₈	—	2	1	no	—
570	#104	—	2	2	no	—
571	#104	—	2	2	no	—
572	#104	—	2	2	no	—
573	#104	—	2	2	no	—
574	#104	—	4	1	no	—
575	#104	D₄×C₁₉	1	4	yes	complemented
576	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
577	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
578	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
579	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
580	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
581	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
582	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
583	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
584	C₂²⋊C₈	—	2	1	no	—
585	C₂²⋊C₈	—	2	1	no	—
586	C₂²⋊C₈	—	2	1	no	—
587	C₂²⋊C₈	—	2	1	no	—
588	C₂²⋊C₈	—	2	1	no	—
589	C₂²⋊C₈	—	2	1	no	—
590	C₂²⋊C₈	—	2	1	no	—
591	C₂²⋊C₈	—	2	1	no	—
592	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
593	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
594	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
595	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
596	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
597	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
598	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
599	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
600	#97	—	2	1	no	—
601	#97	—	4	1	no	—
602	C₄×C₈	—	2	1	no	—
603	C₄×C₈	—	2	2	no	—
604	C₁₉	#22889	1	1	yes	characteristic, direct product factor, Sylow
605	C₂⁴	—	2	1	no	—
606	C₂⁴	#41×C₁₉	1	1	yes	characteristic
607	#41	—	2	1	no	—
608	#41	—	2	1	no	—
609	#41	—	2	2	no	—
610	#41	—	2	2	no	—
611	#41	—	2	1	no	—
612	#41	—	2	1	no	—
613	#41	—	2	1	no	—
614	#41	—	2	1	no	—
615	#41	—	2	1	no	—
616	#41	—	2	1	no	—
617	#41	—	2	1	no	—
618	#41	—	2	1	no	—
619	#41	—	4	2	no	—
620	#41	—	4	2	no	—
621	#41	—	4	1	no	—
622	#41	—	4	1	no	—
623	#41	—	4	2	no	—
624	#41	—	4	2	no	—
625	#41	C₂×D₄×C₁₉	1	2	yes	—
626	#41	#41×C₁₉	1	2	yes	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	4	1	no	—
630	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
631	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
632	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	4	1	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
646	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
647	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
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	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
663	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
666	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
668	Q₁₆	—	2	2	no	—
669	Q₁₆	—	4	1	no	—
670	SD₁₆	—	2	2	no	—
671	SD₁₆	—	2	2	no	—
672	SD₁₆	—	4	1	no	—
673	SD₁₆	—	4	1	no	—
674	D₈	—	2	2	no	—
675	D₈	—	4	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	2	1	no	—
678	M₁₆	—	2	1	no	—
679	M₁₆	—	2	1	no	—
680	M₁₆	—	2	1	no	—
681	M₁₆	—	2	1	no	—
682	M₁₆	—	2	1	no	—
683	M₁₆	—	4	2	no	—
684	M₁₆	—	4	2	no	—
685	M₁₆	—	4	2	no	—
686	M₁₆	—	4	2	no	—
687	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	—	4	2	no	—
702	C₂×C₈	—	4	2	no	—
703	C₂×C₈	—	4	2	no	—
704	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
705	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
706	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
707	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
708	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
709	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
710	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
711	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
716	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	C₂×D₄×C₁₉	1	2	yes	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	8	1	no	—
738	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
739	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
740	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	2	1	no	—
744	Q₈	—	2	1	no	—
745	Q₈	—	2	1	no	—
746	Q₈	—	4	2	no	—
747	Q₈	C₄×D₄×C₁₉	1	2	yes	—
748	D₄	—	2	2	no	—
749	D₄	—	2	2	no	—
750	D₄	—	2	1	no	—
751	D₄	—	2	1	no	—
752	D₄	—	2	1	no	—
753	D₄	—	2	1	no	—
754	D₄	—	2	1	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	2	no	—
757	D₄	—	4	2	no	—
758	D₄	—	4	2	no	—
759	D₄	—	4	1	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	1	no	—
763	D₄	—	8	1	no	—
764	D₄	C₄×D₄×C₁₉	1	2	yes	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
796	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
797	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
800	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
801	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	1	no	—
806	C₈	—	2	1	no	—
807	C₈	—	2	1	no	—
808	C₈	—	2	1	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	1	no	—
811	C₈	—	2	1	no	—
812	C₈	—	4	1	no	—
813	C₈	—	4	1	no	—
814	C₈	—	4	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	8	1	no	—
833	C₂²	—	8	1	no	—
834	C₂²	—	8	4	no	—
835	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
836	C₂²	C₁₉×#546	1	1	yes	characteristic
837	C₂²	C₁₉×#551	1	1	yes	characteristic
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	8	1	no	—
847	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
848	C₄	C₁₉×#518	1	1	yes	characteristic
849	C₄	D₄²×C₁₉	1	1	yes	characteristic
850	C₄	C₁₉×#546	1	1	yes	characteristic
851	C₂	—	2	1	no	—
852	C₂	—	2	1	no	—
853	C₂	—	4	1	no	—
854	C₂	—	4	1	no	—
855	C₂	—	4	2	no	—
856	C₂	—	8	1	no	—
857	C₂	—	8	1	no	—
858	C₂	C₁₉×#2358	1	1	yes	characteristic
859	C₂	C₁₉×#2955	1	1	yes	characteristic
860	C₂	C₁₉×#2957	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	C₁₉×#3002	C₂
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
2. C₂×C₁₉×#443	C₂	semidirect
3. C₁₉×#2933	C₂	semidirect
4. C₂×C₁₉×#421	C₂	semidirect
5. C₁₉×#2880	C₂	semidirect
6. C₁₉×#1975	C₂	semidirect
7. C₁₉×#1937	C₂	semidirect
8. C₁₉×#1929	C₂	semidirect
9. C₁₉×#1897	C₂	semidirect
10. C₁₉×#1876	C₂	semidirect
11. C₁₉×#1876	C₂	semidirect
12. C₁₉×#1866	C₂	semidirect
13. C₁₉×#1855	C₂	semidirect
14. C₁₉×#1765	C₂	semidirect
15. C₁₉×#1750	C₂	semidirect
21. C₂×C₁₉×#131	C₂²	semidirect
25. C₁₉×#452	C₄	semidirect
26. C₁₉×#452	C₄	semidirect
27. C₁₉×#451	C₄	semidirect
28. C₁₉×#450	C₄	semidirect
29. C₁₉×#449	C₄	semidirect
30. C₁₉×#449	C₄	semidirect
31. C₁₉×#448	C₄	semidirect
32. C₁₉×#447	C₄	semidirect
38. C₂×C₁₉×#108	C₂²	semidirect
39. C₂×C₁₉×#108	C₂²	semidirect
40. C₁₉×#424	C₂²	semidirect
46. C₂×C₁₉×#104	C₂²	semidirect
47. C₂×C₁₉×#104	C₂²	semidirect
54. C₁₉×#408	C₂²	semidirect
60. C₁₉×#405	C₂²	semidirect
61. C₂×C₁₉×#97	C₂²	semidirect
62. C₂×C₄×C₈×C₁₉	C₂²	semidirect
63. C₁₉×#341	C₂²	semidirect
64. C₁₉×#341	C₂²	semidirect
65. C₁₉×#339	C₂²	semidirect
66. C₁₉×#339	C₂²	semidirect
67. C₁₉×#336	C₂²	semidirect
68. C₁₉×#336	C₂²	semidirect
145. C₁₉×#104	D₄	semidirect
297. #22889	C₁₉	direct (N × H)
386. C₂×#443	C₂×C₁₉	semidirect
387. #2933	C₂×C₁₉	semidirect
388. C₂×#421	C₂×C₁₉	semidirect
389. #2880	C₂×C₁₉	semidirect
390. #1975	C₂×C₁₉	semidirect
391. #1937	C₂×C₁₉	semidirect
392. #1929	C₂×C₁₉	semidirect
393. #1897	C₂×C₁₉	semidirect
394. #1876	C₂×C₁₉	semidirect
395. #1876	C₂×C₁₉	semidirect
396. #1866	C₂×C₁₉	semidirect
397. #1855	C₂×C₁₉	semidirect
398. #1765	C₂×C₁₉	semidirect
399. #1750	C₂×C₁₉	semidirect
441. C₂×#131	C₂²×C₁₉	semidirect
445. #452	C₄×C₁₉	semidirect
446. #452	C₄×C₁₉	semidirect
447. #451	C₄×C₁₉	semidirect
448. #450	C₄×C₁₉	semidirect
449. #449	C₄×C₁₉	semidirect
450. #449	C₄×C₁₉	semidirect
451. #448	C₄×C₁₉	semidirect
452. #447	C₄×C₁₉	semidirect
458. C₂×#108	C₂²×C₁₉	semidirect
459. C₂×#108	C₂²×C₁₉	semidirect
460. #424	C₂²×C₁₉	semidirect
466. C₂×#104	C₂²×C₁₉	semidirect
467. C₂×#104	C₂²×C₁₉	semidirect
474. #408	C₂²×C₁₉	semidirect
480. #405	C₂²×C₁₉	semidirect
481. C₂×#97	C₂²×C₁₉	semidirect
482. C₂×C₄×C₈	C₂²×C₁₉	semidirect
483. #341	C₂²×C₁₉	semidirect
484. #341	C₂²×C₁₉	semidirect
485. #339	C₂²×C₁₉	semidirect
486. #339	C₂²×C₁₉	semidirect
487. #336	C₂²×C₁₉	semidirect
488. #336	C₂²×C₁₉	semidirect
575. #104	D₄×C₁₉	semidirect
604. C₁₉	#22889	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×#3002	2
C₂×C₁₉×#443	2
C₁₉×#2933	2
C₂×C₁₉×#421	2
C₁₉×#2880	2
C₁₉×#1975	2
C₁₉×#1937	2
C₁₉×#1929	2
C₁₉×#1897	2
C₁₉×#1876	2
C₁₉×#1866	2
C₁₉×#1855	2
C₁₉×#1765	2
C₁₉×#1750	2
#22889	19

Subgroups — C19×#22889 #18028848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22889 #18028848