Subgroups — C₁₉×#22062 #18028021

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 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	C₁₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1938	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×#1929	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×#1871	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1789	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×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#525	C₂²	1	1	yes	characteristic
23	C₁₉×#452	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#452	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#451	C₄	1	1	yes	characteristic, complemented
26	C₁₉×#450	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#449	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#449	C₄	1	1	yes	characteristic, complemented
29	C₁₉×#448	C₄	1	1	yes	characteristic, complemented
30	C₁₉×#447	C₄	1	1	yes	characteristic, complemented
31	C₁₉×#436	—	2	1	no	—
32	C₁₉×#436	—	2	1	no	—
33	C₁₉×#435	—	2	1	no	—
34	C₁₉×#435	—	2	1	no	—
35	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#416	C₂²	1	1	yes	characteristic
45	C₁₉×#416	C₂²	1	1	yes	characteristic
46	C₁₉×#408	—	2	1	no	—
47	C₁₉×#408	—	2	1	no	—
48	C₁₉×#408	C₂²	1	1	yes	characteristic
49	C₁₉×#408	C₂²	1	1	yes	characteristic
50	C₁₉×#408	C₂²	1	1	yes	characteristic
51	C₁₉×#408	C₂²	1	1	yes	characteristic
52	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#407	—	2	1	no	—
54	C₁₉×#407	—	2	1	no	—
55	C₁₉×#407	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
61	C₁₉×#341	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#341	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	—	4	1	no	—
70	C₂×#41×C₁₉	—	4	1	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	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₁₉	—	2	1	no	—
80	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	—	2	1	no	—
82	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₁₉×#135	—	4	1	no	—
84	C₁₉×#135	—	4	1	no	—
85	C₁₉×#135	—	4	1	no	—
86	C₁₉×#135	—	4	1	no	—
87	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
88	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₂×SD₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×SD₁₆×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×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
95	C₁₉×#131	—	4	1	no	—
96	C₁₉×#131	—	4	1	no	—
97	C₂×M₁₆×C₁₉	—	2	1	no	—
98	C₂×M₁₆×C₁₉	—	2	1	no	—
99	C₂×M₁₆×C₁₉	—	4	1	no	—
100	C₂×M₁₆×C₁₉	—	4	1	no	—
101	C₂×M₁₆×C₁₉	—	4	1	no	—
102	C₂×M₁₆×C₁₉	—	4	1	no	—
103	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
104	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
105	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
106	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
107	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₉	—	2	1	no	—
112	C₂²×C₈×C₁₉	—	2	1	no	—
113	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#123	—	2	1	no	—
118	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
119	C₁₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
120	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
121	C₁₉×#121	C₂×C₄	1	1	yes	characteristic
122	C₁₉×#120	—	2	1	no	—
123	C₄×D₄×C₁₉	—	2	1	no	—
124	C₄×D₄×C₁₉	—	2	1	no	—
125	C₁₉×#117	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
129	C₁₉×#108	—	4	1	no	—
130	C₁₉×#108	—	4	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#104	—	4	1	no	—
134	C₁₉×#104	—	4	1	no	—
135	C₁₉×#104	—	4	1	no	—
136	C₁₉×#104	—	4	1	no	—
137	C₁₉×#104	—	4	1	no	—
138	C₁₉×#104	—	4	1	no	—
139	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
140	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
141	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
142	C₁₉×#103	C₂×C₄	1	1	yes	characteristic
143	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
144	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
145	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
146	C₁₉×#102	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
152	C₁₉×C₂²⋊C₈	—	2	1	no	—
153	C₁₉×C₂²⋊C₈	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
160	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
161	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
162	C₁₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
163	C₁₉×#97	—	2	1	no	—
164	C₁₉×#97	—	4	1	no	—
165	C₄×C₈×C₁₉	—	2	1	no	—
166	C₄×C₈×C₁₉	—	4	1	no	—
167	C₁₉×#95	—	2	1	no	—
168	C₂⁴×C₁₉	—	2	1	no	—
169	C₂⁴×C₁₉	#41	1	1	yes	characteristic
170	#41×C₁₉	—	2	1	no	—
171	#41×C₁₉	—	2	1	no	—
172	#41×C₁₉	—	2	1	no	—
173	#41×C₁₉	—	2	1	no	—
174	#41×C₁₉	—	2	1	no	—
175	#41×C₁₉	—	2	1	no	—
176	#41×C₁₉	—	2	1	no	—
177	#41×C₁₉	—	2	1	no	—
178	#41×C₁₉	—	2	1	no	—
179	#41×C₁₉	—	2	1	no	—
180	#41×C₁₉	—	2	1	no	—
181	#41×C₁₉	—	2	1	no	—
182	#41×C₁₉	—	4	1	no	—
183	#41×C₁₉	—	4	1	no	—
184	#41×C₁₉	—	4	1	no	—
185	#41×C₁₉	—	4	1	no	—
186	#41×C₁₉	—	4	2	no	—
187	#41×C₁₉	—	4	2	no	—
188	#41×C₁₉	—	4	2	no	—
189	#41×C₁₉	—	4	2	no	—
190	C₂×Q₈×C₁₉	—	2	1	no	—
191	C₂×Q₈×C₁₉	—	4	1	no	—
192	C₂×Q₈×C₁₉	—	4	1	no	—
193	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
194	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
195	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
196	C₂×D₄×C₁₉	—	2	1	no	—
197	C₂×D₄×C₁₉	—	2	1	no	—
198	C₂×D₄×C₁₉	—	2	1	no	—
199	C₂×D₄×C₁₉	—	2	1	no	—
200	C₂×D₄×C₁₉	—	2	1	no	—
201	C₂×D₄×C₁₉	—	2	1	no	—
202	C₂×D₄×C₁₉	—	2	1	no	—
203	C₂×D₄×C₁₉	—	2	1	no	—
204	C₂×D₄×C₁₉	—	4	1	no	—
205	C₂×D₄×C₁₉	—	4	1	no	—
206	C₂×D₄×C₁₉	—	4	2	no	—
207	C₂×D₄×C₁₉	—	4	2	no	—
208	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
209	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
210	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	—	2	1	no	—
212	C₂²×C₄×C₁₉	—	2	1	no	—
213	C₂²×C₄×C₁₉	—	2	1	no	—
214	C₂²×C₄×C₁₉	—	2	1	no	—
215	C₂²×C₄×C₁₉	—	2	1	no	—
216	C₂²×C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
224	C₂²×C₄×C₁₉	—	4	2	no	—
225	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
230	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₁₉	—	4	1	no	—
232	Q₁₆×C₁₉	—	4	1	no	—
233	SD₁₆×C₁₉	—	4	1	no	—
234	SD₁₆×C₁₉	—	4	1	no	—
235	SD₁₆×C₁₉	—	4	1	no	—
236	SD₁₆×C₁₉	—	4	1	no	—
237	D₈×C₁₉	—	4	1	no	—
238	D₈×C₁₉	—	4	1	no	—
239	M₁₆×C₁₉	—	2	1	no	—
240	M₁₆×C₁₉	—	2	1	no	—
241	M₁₆×C₁₉	—	2	1	no	—
242	M₁₆×C₁₉	—	2	1	no	—
243	M₁₆×C₁₉	—	2	1	no	—
244	M₁₆×C₁₉	—	2	1	no	—
245	M₁₆×C₁₉	—	2	1	no	—
246	M₁₆×C₁₉	—	2	1	no	—
247	M₁₆×C₁₉	—	4	1	no	—
248	M₁₆×C₁₉	—	4	1	no	—
249	M₁₆×C₁₉	—	4	1	no	—
250	M₁₆×C₁₉	—	4	1	no	—
251	M₁₆×C₁₉	—	4	2	no	—
252	M₁₆×C₁₉	—	4	2	no	—
253	C₂×C₈×C₁₉	—	2	1	no	—
254	C₂×C₈×C₁₉	—	2	1	no	—
255	C₂×C₈×C₁₉	—	2	1	no	—
256	C₂×C₈×C₁₉	—	2	1	no	—
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	—	4	2	no	—
266	C₂×C₈×C₁₉	—	4	2	no	—
267	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
268	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
269	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
270	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
271	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
272	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
273	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
274	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
275	C₄⋊C₄×C₁₉	—	2	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
278	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
279	C₂²⋊C₄×C₁₉	—	2	1	no	—
280	C₂²⋊C₄×C₁₉	—	2	1	no	—
281	C₂²⋊C₄×C₁₉	—	2	1	no	—
282	C₂²⋊C₄×C₁₉	—	2	1	no	—
283	C₂²⋊C₄×C₁₉	—	2	1	no	—
284	C₂²⋊C₄×C₁₉	—	4	2	no	—
285	C₄²×C₁₉	—	2	1	no	—
286	C₄²×C₁₉	—	2	1	no	—
287	C₄²×C₁₉	—	2	1	no	—
288	C₄²×C₁₉	—	2	1	no	—
289	C₄²×C₁₉	—	2	1	no	—
290	#22062	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂³×C₁₉	—	2	1	no	—
292	C₂³×C₁₉	—	2	1	no	—
293	C₂³×C₁₉	—	2	1	no	—
294	C₂³×C₁₉	—	2	1	no	—
295	C₂³×C₁₉	—	2	1	no	—
296	C₂³×C₁₉	—	4	1	no	—
297	C₂³×C₁₉	—	4	1	no	—
298	C₂³×C₁₉	—	4	2	no	—
299	C₂³×C₁₉	—	8	1	no	—
300	C₂³×C₁₉	—	8	1	no	—
301	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
302	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
303	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
304	Q₈×C₁₉	—	2	1	no	—
305	Q₈×C₁₉	—	2	1	no	—
306	Q₈×C₁₉	—	2	1	no	—
307	Q₈×C₁₉	—	2	1	no	—
308	Q₈×C₁₉	—	2	1	no	—
309	Q₈×C₁₉	—	2	1	no	—
310	Q₈×C₁₉	—	4	2	no	—
311	D₄×C₁₉	—	2	1	no	—
312	D₄×C₁₉	—	2	1	no	—
313	D₄×C₁₉	—	2	1	no	—
314	D₄×C₁₉	—	2	1	no	—
315	D₄×C₁₉	—	2	1	no	—
316	D₄×C₁₉	—	2	1	no	—
317	D₄×C₁₉	—	4	2	no	—
318	D₄×C₁₉	—	4	2	no	—
319	D₄×C₁₉	—	4	2	no	—
320	D₄×C₁₉	—	4	1	no	—
321	D₄×C₁₉	—	4	1	no	—
322	D₄×C₁₉	—	4	1	no	—
323	D₄×C₁₉	—	4	1	no	—
324	D₄×C₁₉	—	4	1	no	—
325	D₄×C₁₉	—	4	1	no	—
326	D₄×C₁₉	—	8	1	no	—
327	D₄×C₁₉	—	8	1	no	—
328	C₂×C₄×C₁₉	—	2	1	no	—
329	C₂×C₄×C₁₉	—	2	1	no	—
330	C₂×C₄×C₁₉	—	2	1	no	—
331	C₂×C₄×C₁₉	—	2	1	no	—
332	C₂×C₄×C₁₉	—	2	1	no	—
333	C₂×C₄×C₁₉	—	2	1	no	—
334	C₂×C₄×C₁₉	—	2	1	no	—
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	2	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	1	no	—
344	C₂×C₄×C₁₉	—	4	2	no	—
345	C₂×C₄×C₁₉	—	4	2	no	—
346	C₂×C₄×C₁₉	—	4	1	no	—
347	C₂×C₄×C₁₉	—	4	2	no	—
348	C₂×C₄×C₁₉	—	4	1	no	—
349	C₂×C₄×C₁₉	—	4	1	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	1	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
361	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
366	C₈×C₁₉	—	2	1	no	—
367	C₈×C₁₉	—	2	1	no	—
368	C₈×C₁₉	—	2	1	no	—
369	C₈×C₁₉	—	2	1	no	—
370	C₈×C₁₉	—	2	1	no	—
371	C₈×C₁₉	—	2	1	no	—
372	C₈×C₁₉	—	2	1	no	—
373	C₈×C₁₉	—	2	1	no	—
374	C₈×C₁₉	—	4	1	no	—
375	C₈×C₁₉	—	4	1	no	—
376	C₈×C₁₉	—	4	1	no	—
377	C₈×C₁₉	—	4	1	no	—
378	#3002	C₂×C₁₉	1	1	yes	characteristic
379	#2930	C₂×C₁₉	1	1	yes	characteristic, complemented
380	#2879	C₂×C₁₉	1	1	yes	characteristic, complemented
381	#1975	C₂×C₁₉	1	1	yes	characteristic, complemented
382	#1974	C₂×C₁₉	1	1	yes	characteristic, complemented
383	#1938	C₂×C₁₉	1	1	yes	characteristic, complemented
384	#1937	C₂×C₁₉	1	1	yes	characteristic, complemented
385	#1929	C₂×C₁₉	1	1	yes	characteristic, complemented
386	#1929	C₂×C₁₉	1	1	yes	characteristic, complemented
387	#1876	C₂×C₁₉	1	1	yes	characteristic, complemented
388	#1876	C₂×C₁₉	1	1	yes	characteristic, complemented
389	#1871	C₂×C₁₉	1	1	yes	characteristic, complemented
390	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
391	#1789	C₂×C₁₉	1	1	yes	characteristic, complemented
392	#1753	C₂×C₁₉	1	1	yes	characteristic, complemented
393	C₂²×C₁₉	—	2	1	no	—
394	C₂²×C₁₉	—	2	1	no	—
395	C₂²×C₁₉	—	2	1	no	—
396	C₂²×C₁₉	—	2	1	no	—
397	C₂²×C₁₉	—	2	1	no	—
398	C₂²×C₁₉	—	2	1	no	—
399	C₂²×C₁₉	—	2	1	no	—
400	C₂²×C₁₉	—	2	1	no	—
401	C₂²×C₁₉	—	4	1	no	—
402	C₂²×C₁₉	—	4	1	no	—
403	C₂²×C₁₉	—	4	1	no	—
404	C₂²×C₁₉	—	4	1	no	—
405	C₂²×C₁₉	—	4	1	no	—
406	C₂²×C₁₉	—	4	1	no	—
407	C₂²×C₁₉	—	4	1	no	—
408	C₂²×C₁₉	—	4	1	no	—
409	C₂²×C₁₉	—	4	1	no	—
410	C₂²×C₁₉	—	8	1	no	—
411	C₂²×C₁₉	—	8	1	no	—
412	C₂²×C₁₉	—	8	4	no	—
413	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂²×C₁₉	#538	1	1	yes	characteristic
415	C₂²×C₁₉	#538	1	1	yes	characteristic
416	C₄×C₁₉	—	2	1	no	—
417	C₄×C₁₉	—	2	1	no	—
418	C₄×C₁₉	—	4	2	no	—
419	C₄×C₁₉	—	4	1	no	—
420	C₄×C₁₉	—	4	1	no	—
421	C₄×C₁₉	—	4	1	no	—
422	C₄×C₁₉	—	4	1	no	—
423	C₄×C₁₉	—	4	1	no	—
424	C₄×C₁₉	—	8	1	no	—
425	C₄×C₁₉	#518	1	1	yes	characteristic
426	C₄×C₁₉	#518	1	1	yes	characteristic
427	C₄×C₁₉	#534	1	1	yes	characteristic
428	C₄×C₁₉	#535	1	1	yes	characteristic
429	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
431	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
432	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
433	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
434	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
435	#525	C₂²×C₁₉	1	1	yes	characteristic
436	#452	C₄×C₁₉	1	1	yes	characteristic, complemented
437	#452	C₄×C₁₉	1	1	yes	characteristic, complemented
438	#451	C₄×C₁₉	1	1	yes	characteristic, complemented
439	#450	C₄×C₁₉	1	1	yes	characteristic, complemented
440	#449	C₄×C₁₉	1	1	yes	characteristic, complemented
441	#449	C₄×C₁₉	1	1	yes	characteristic, complemented
442	#448	C₄×C₁₉	1	1	yes	characteristic, complemented
443	#447	C₄×C₁₉	1	1	yes	characteristic, complemented
444	#436	—	2	1	no	—
445	#436	—	2	1	no	—
446	#435	—	2	1	no	—
447	#435	—	2	1	no	—
448	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
449	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic, complemented
450	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
454	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
455	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic, complemented
457	#416	C₂²×C₁₉	1	1	yes	characteristic
458	#416	C₂²×C₁₉	1	1	yes	characteristic
459	#408	—	2	1	no	—
460	#408	—	2	1	no	—
461	#408	C₂²×C₁₉	1	1	yes	characteristic
462	#408	C₂²×C₁₉	1	1	yes	characteristic
463	#408	C₂²×C₁₉	1	1	yes	characteristic
464	#408	C₂²×C₁₉	1	1	yes	characteristic
465	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
466	#407	—	2	1	no	—
467	#407	—	2	1	no	—
468	#407	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
470	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
471	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
472	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
473	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
474	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
475	#341	C₂²×C₁₉	1	1	yes	characteristic, complemented
476	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
477	#339	C₂²×C₁₉	1	1	yes	characteristic, complemented
478	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
479	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
480	C₂×C₁₉	—	2	1	no	—
481	C₂×C₁₉	—	2	1	no	—
482	C₂×C₁₉	—	4	1	no	—
483	C₂×C₁₉	—	4	1	no	—
484	C₂×C₁₉	—	8	1	no	—
485	C₂×C₁₉	—	8	1	no	—
486	C₂×C₁₉	—	8	1	no	—
487	C₂×C₁₉	#2321	1	1	yes	characteristic
488	C₂×C₁₉	#2956	1	1	yes	characteristic
489	C₂×C₁₉	#2957	1	1	yes	characteristic
490	C₂×#41	—	2	1	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	4	1	no	—
493	C₂×#41	—	4	1	no	—
494	C₂×#41	—	4	1	no	—
495	C₂×#41	—	4	1	no	—
496	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
497	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
498	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
499	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
500	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
501	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
506	#135	—	4	1	no	—
507	#135	—	4	1	no	—
508	#135	—	4	1	no	—
509	#135	—	4	1	no	—
510	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
511	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
512	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
513	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
514	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
515	C₂×SD₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
516	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
517	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
518	#131	—	4	1	no	—
519	#131	—	4	1	no	—
520	C₂×M₁₆	—	2	1	no	—
521	C₂×M₁₆	—	2	1	no	—
522	C₂×M₁₆	—	4	1	no	—
523	C₂×M₁₆	—	4	1	no	—
524	C₂×M₁₆	—	4	1	no	—
525	C₂×M₁₆	—	4	1	no	—
526	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
527	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
528	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
529	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
530	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
531	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
532	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
533	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
534	C₂²×C₈	—	2	1	no	—
535	C₂²×C₈	—	2	1	no	—
536	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
537	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
540	#123	—	2	1	no	—
541	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
542	C₂²⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
543	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
544	#121	C₂×C₄×C₁₉	1	1	yes	characteristic
545	#120	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	#117	C₂³×C₁₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
552	#108	—	4	1	no	—
553	#108	—	4	1	no	—
554	C₄⋊C₈	—	2	1	no	—
555	C₄⋊C₈	—	2	1	no	—
556	#104	—	4	1	no	—
557	#104	—	4	1	no	—
558	#104	—	4	1	no	—
559	#104	—	4	1	no	—
560	#104	—	4	1	no	—
561	#104	—	4	1	no	—
562	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
563	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
564	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
565	#103	C₂×C₄×C₁₉	1	1	yes	characteristic
566	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
567	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
568	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
569	#102	C₂×C₄×C₁₉	1	1	yes	characteristic
570	C₂²⋊C₈	—	2	1	no	—
571	C₂²⋊C₈	—	2	1	no	—
572	C₂²⋊C₈	—	2	1	no	—
573	C₂²⋊C₈	—	2	1	no	—
574	C₂²⋊C₈	—	2	1	no	—
575	C₂²⋊C₈	—	2	1	no	—
576	C₂²⋊C₈	—	2	1	no	—
577	C₂²⋊C₈	—	2	1	no	—
578	C₂²⋊C₈	—	2	1	no	—
579	C₂²⋊C₈	—	2	1	no	—
580	C₂²⋊C₈	—	2	1	no	—
581	C₂²⋊C₈	—	2	1	no	—
582	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
583	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
584	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
585	C₂²⋊C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
586	#97	—	2	1	no	—
587	#97	—	4	1	no	—
588	C₄×C₈	—	2	1	no	—
589	C₄×C₈	—	4	1	no	—
590	#95	—	2	1	no	—
591	C₁₉	#22062	1	1	yes	characteristic, direct product factor, Sylow
592	C₂⁴	—	2	1	no	—
593	C₂⁴	#41×C₁₉	1	1	yes	characteristic
594	#41	—	2	1	no	—
595	#41	—	2	1	no	—
596	#41	—	2	1	no	—
597	#41	—	2	1	no	—
598	#41	—	2	1	no	—
599	#41	—	2	1	no	—
600	#41	—	2	1	no	—
601	#41	—	2	1	no	—
602	#41	—	2	1	no	—
603	#41	—	2	1	no	—
604	#41	—	2	1	no	—
605	#41	—	2	1	no	—
606	#41	—	4	1	no	—
607	#41	—	4	1	no	—
608	#41	—	4	1	no	—
609	#41	—	4	1	no	—
610	#41	—	4	2	no	—
611	#41	—	4	2	no	—
612	#41	—	4	2	no	—
613	#41	—	4	2	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	—	4	1	no	—
617	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
618	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
619	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
633	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
634	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
650	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
653	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
655	Q₁₆	—	4	1	no	—
656	Q₁₆	—	4	1	no	—
657	SD₁₆	—	4	1	no	—
658	SD₁₆	—	4	1	no	—
659	SD₁₆	—	4	1	no	—
660	SD₁₆	—	4	1	no	—
661	D₈	—	4	1	no	—
662	D₈	—	4	1	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	—	2	1	no	—
671	M₁₆	—	4	1	no	—
672	M₁₆	—	4	1	no	—
673	M₁₆	—	4	1	no	—
674	M₁₆	—	4	1	no	—
675	M₁₆	—	4	2	no	—
676	M₁₆	—	4	2	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	4	2	no	—
690	C₂×C₈	—	4	2	no	—
691	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
692	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
693	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
694	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
695	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
696	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
697	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
698	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
702	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	2	no	—
722	C₂³	—	8	1	no	—
723	C₂³	—	8	1	no	—
724	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
725	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
726	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	2	1	no	—
733	Q₈	—	4	2	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	2	1	no	—
737	D₄	—	2	1	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	1	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	8	1	no	—
750	D₄	—	8	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
782	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
783	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
785	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
786	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
787	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
789	C₈	—	2	1	no	—
790	C₈	—	2	1	no	—
791	C₈	—	2	1	no	—
792	C₈	—	2	1	no	—
793	C₈	—	2	1	no	—
794	C₈	—	2	1	no	—
795	C₈	—	2	1	no	—
796	C₈	—	2	1	no	—
797	C₈	—	4	1	no	—
798	C₈	—	4	1	no	—
799	C₈	—	4	1	no	—
800	C₈	—	4	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	4	no	—
821	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
822	C₂²	C₁₉×#538	1	1	yes	characteristic
823	C₂²	C₁₉×#538	1	1	yes	characteristic
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	8	1	no	—
833	C₄	C₁₉×#518	1	1	yes	characteristic
834	C₄	C₁₉×#518	1	1	yes	characteristic
835	C₄	C₁₉×#534	1	1	yes	characteristic
836	C₄	C₁₉×#535	1	1	yes	characteristic
837	C₂	—	2	1	no	—
838	C₂	—	2	1	no	—
839	C₂	—	4	1	no	—
840	C₂	—	4	1	no	—
841	C₂	—	8	1	no	—
842	C₂	—	8	1	no	—
843	C₂	—	8	1	no	—
844	C₂	C₁₉×#2321	1	1	yes	characteristic
845	C₂	C₁₉×#2956	1	1	yes	characteristic
846	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 ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2930	C₂	semidirect
3. C₁₉×#2879	C₂	semidirect
4. C₁₉×#1975	C₂	semidirect
5. C₁₉×#1974	C₂	semidirect
6. C₁₉×#1938	C₂	semidirect
7. C₁₉×#1937	C₂	semidirect
8. C₁₉×#1929	C₂	semidirect
9. C₁₉×#1929	C₂	semidirect
10. C₁₉×#1876	C₂	semidirect
11. C₁₉×#1876	C₂	semidirect
12. C₁₉×#1871	C₂	semidirect
13. C₁₉×#1855	C₂	semidirect
14. C₁₉×#1789	C₂	semidirect
15. C₁₉×#1753	C₂	semidirect
19. C₂×C₁₉×#131	C₂²	semidirect
23. C₁₉×#452	C₄	semidirect
24. C₁₉×#452	C₄	semidirect
25. C₁₉×#451	C₄	semidirect
26. C₁₉×#450	C₄	semidirect
27. C₁₉×#449	C₄	semidirect
28. C₁₉×#449	C₄	semidirect
29. C₁₉×#448	C₄	semidirect
30. C₁₉×#447	C₄	semidirect
35. C₂×C₁₉×#108	C₂²	semidirect
36. C₂×C₁₉×#108	C₂²	semidirect
37. C₁₉×#424	C₂²	semidirect
42. C₂×C₁₉×#104	C₂²	semidirect
43. C₂×C₁₉×#104	C₂²	semidirect
52. C₁₉×#408	C₂²	semidirect
57. C₁₉×#405	C₂²	semidirect
58. C₂×C₁₉×#97	C₂²	semidirect
59. C₂×C₄×C₈×C₁₉	C₂²	semidirect
61. C₁₉×#341	C₂²	semidirect
62. C₁₉×#341	C₂²	semidirect
63. C₁₉×#339	C₂²	semidirect
64. C₁₉×#339	C₂²	semidirect
65. C₁₉×#336	C₂²	semidirect
66. C₁₉×#336	C₂²	semidirect
290. #22062	C₁₉	direct (N × H)
379. #2930	C₂×C₁₉	semidirect
380. #2879	C₂×C₁₉	semidirect
381. #1975	C₂×C₁₉	semidirect
382. #1974	C₂×C₁₉	semidirect
383. #1938	C₂×C₁₉	semidirect
384. #1937	C₂×C₁₉	semidirect
385. #1929	C₂×C₁₉	semidirect
386. #1929	C₂×C₁₉	semidirect
387. #1876	C₂×C₁₉	semidirect
388. #1876	C₂×C₁₉	semidirect
389. #1871	C₂×C₁₉	semidirect
390. #1855	C₂×C₁₉	semidirect
391. #1789	C₂×C₁₉	semidirect
392. #1753	C₂×C₁₉	semidirect
432. C₂×#131	C₂²×C₁₉	semidirect
436. #452	C₄×C₁₉	semidirect
437. #452	C₄×C₁₉	semidirect
438. #451	C₄×C₁₉	semidirect
439. #450	C₄×C₁₉	semidirect
440. #449	C₄×C₁₉	semidirect
441. #449	C₄×C₁₉	semidirect
442. #448	C₄×C₁₉	semidirect
443. #447	C₄×C₁₉	semidirect
448. C₂×#108	C₂²×C₁₉	semidirect
449. C₂×#108	C₂²×C₁₉	semidirect
450. #424	C₂²×C₁₉	semidirect
455. C₂×#104	C₂²×C₁₉	semidirect
456. C₂×#104	C₂²×C₁₉	semidirect
465. #408	C₂²×C₁₉	semidirect
470. #405	C₂²×C₁₉	semidirect
471. C₂×#97	C₂²×C₁₉	semidirect
472. C₂×C₄×C₈	C₂²×C₁₉	semidirect
474. #341	C₂²×C₁₉	semidirect
475. #341	C₂²×C₁₉	semidirect
476. #339	C₂²×C₁₉	semidirect
477. #339	C₂²×C₁₉	semidirect
478. #336	C₂²×C₁₉	semidirect
479. #336	C₂²×C₁₉	semidirect
591. C₁₉	#22062	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
C₁₉×#2930	2
C₁₉×#2879	2
C₁₉×#1975	2
C₁₉×#1974	2
C₁₉×#1938	2
C₁₉×#1937	2
C₁₉×#1929	2
C₁₉×#1876	2
C₁₉×#1871	2
C₁₉×#1855	2
C₁₉×#1789	2
C₁₉×#1753	2
#22062	19

Subgroups — C19×#22062 #18028021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22062 #18028021