Subgroups — C₁₉×#21896 #18027855

Order 4864.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1893	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#542	—	2	4	no	—
19	C₁₉×#542	C₄	1	8	yes	complemented
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#126	—	2	1	no	—
22	C₂×C₁₉×#124	—	2	1	no	—
23	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#123	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₁₉×#424	—	2	4	no	—
32	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₁₉×#388	—	2	1	no	—
45	C₁₉×#388	—	2	1	no	—
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#387	—	2	1	no	—
48	C₁₉×#384	C₂²	1	1	yes	characteristic
49	C₁₉×#382	C₂²	1	1	yes	characteristic
50	C₁₉×#380	C₂²	1	1	yes	characteristic
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#340	C₂²	1	1	yes	characteristic
60	C₁₉×#340	C₂²	1	1	yes	characteristic
61	C₁₉×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	—	2	1	no	—
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	—	2	2	no	—
69	C₂×M₁₆×C₁₉	—	4	1	no	—
70	C₂×M₁₆×C₁₉	—	4	1	no	—
71	C₂²×C₈×C₁₉	—	2	2	no	—
72	C₂²×C₈×C₁₉	—	4	1	no	—
73	C₂²×C₈×C₁₉	—	4	1	no	—
74	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×C₄⋊Q₈	—	2	2	no	—
79	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
80	C₁₉×#126	—	2	8	no	—
81	C₁₉×#124	—	2	8	no	—
82	C₁₉×#124	—	2	2	no	—
83	C₁₉×#124	C₂×C₄	1	4	yes	—
84	C₁₉×#123	—	2	8	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	8	no	—
87	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#121	C₂×C₄	1	4	yes	—
90	C₄×Q₈×C₁₉	—	2	2	no	—
91	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
94	C₁₉×#117	C₂×C₄	1	4	yes	—
95	C₁₉×#117	D₄	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₉	—	2	1	no	—
119	C₂×C₄²×C₁₉	—	2	1	no	—
120	C₂×C₄²×C₁₉	—	2	1	no	—
121	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
123	C₁₉×C₄⋊C₈	—	2	2	no	—
124	C₁₉×C₄⋊C₈	—	2	2	no	—
125	C₁₉×C₄⋊C₈	—	2	2	no	—
126	C₁₉×C₄⋊C₈	—	2	2	no	—
127	C₁₉×#103	—	4	1	no	—
128	C₁₉×#103	—	4	1	no	—
129	C₁₉×#103	—	4	1	no	—
130	C₁₉×#103	—	4	1	no	—
131	C₁₉×#102	—	4	1	no	—
132	C₁₉×#102	—	4	1	no	—
133	C₁₉×#102	—	4	1	no	—
134	C₁₉×#102	—	4	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	C₁₉×#95	—	2	1	no	—
140	C₁₉×#95	—	2	1	no	—
141	C₂⁴×C₁₉	—	2	1	no	—
142	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₁₉	—	2	4	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	—	2	1	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	8	1	no	—
150	C₂×Q₈×C₁₉	—	8	1	no	—
151	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
152	C₂×D₄×C₁₉	—	2	4	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	—	2	1	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	8	1	no	—
159	C₂×D₄×C₁₉	—	8	1	no	—
160	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	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	4	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	—	8	1	no	—
174	C₂²×C₄×C₁₉	—	8	1	no	—
175	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
183	M₁₆×C₁₉	—	4	4	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	2	1	no	—
191	C₂×C₈×C₁₉	—	2	1	no	—
192	C₂×C₈×C₁₉	—	2	1	no	—
193	C₂×C₈×C₁₉	—	2	1	no	—
194	C₂×C₈×C₁₉	—	2	1	no	—
195	C₂×C₈×C₁₉	—	2	1	no	—
196	C₂×C₈×C₁₉	—	4	4	no	—
197	C₄⋊C₄×C₁₉	—	2	4	no	—
198	C₄⋊C₄×C₁₉	—	2	4	no	—
199	C₄⋊C₄×C₁₉	—	2	4	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	8	1	no	—
211	C₄⋊C₄×C₁₉	—	8	1	no	—
212	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
213	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
214	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
215	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
216	C₂²⋊C₄×C₁₉	—	2	4	no	—
217	C₂²⋊C₄×C₁₉	—	2	4	no	—
218	C₂²⋊C₄×C₁₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₉	—	2	4	no	—
220	C₂²⋊C₄×C₁₉	—	2	4	no	—
221	C₂²⋊C₄×C₁₉	—	8	1	no	—
222	C₂²⋊C₄×C₁₉	—	8	1	no	—
223	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
224	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
225	C₄²×C₁₉	—	2	4	no	—
226	C₄²×C₁₉	—	8	1	no	—
227	C₄²×C₁₉	—	8	1	no	—
228	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
229	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
230	C₄²×C₁₉	C₂×D₄	1	2	yes	—
231	C₄²×C₁₉	C₂×D₄	1	2	yes	—
232	#21896	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	—	2	1	no	—
239	C₂³×C₁₉	—	2	2	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	4	1	no	—
244	C₂³×C₁₉	—	4	1	no	—
245	C₂³×C₁₉	—	4	1	no	—
246	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₁₉	—	2	2	no	—
249	Q₈×C₁₉	—	2	2	no	—
250	Q₈×C₁₉	—	4	1	no	—
251	Q₈×C₁₉	—	4	1	no	—
252	Q₈×C₁₉	—	8	4	no	—
253	D₄×C₁₉	—	2	2	no	—
254	D₄×C₁₉	—	2	2	no	—
255	D₄×C₁₉	—	4	1	no	—
256	D₄×C₁₉	—	4	1	no	—
257	D₄×C₁₉	—	8	4	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	1	no	—
261	C₂×C₄×C₁₉	—	2	1	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	1	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	2	2	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	1	no	—
293	C₂×C₄×C₁₉	—	8	4	no	—
294	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
304	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
305	C₈×C₁₉	—	4	1	no	—
306	C₈×C₁₉	—	4	1	no	—
307	C₈×C₁₉	—	4	1	no	—
308	C₈×C₁₉	—	4	1	no	—
309	C₂×#542	C₂×C₁₉	1	1	yes	characteristic
310	C₂×#424	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2314	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1988	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1987	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1983	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1983	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1895	C₂×C₁₉	1	1	yes	characteristic
317	#1894	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1893	C₂×C₁₉	1	1	yes	characteristic
319	#1892	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#1805	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1804	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
323	#1802	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂²×C₁₉	—	2	2	no	—
325	C₂²×C₁₉	—	2	2	no	—
326	C₂²×C₁₉	—	2	2	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	2	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	4	2	no	—
334	C₂²×C₁₉	—	8	1	no	—
335	C₂²×C₁₉	—	8	1	no	—
336	C₂²×C₁₉	—	8	1	no	—
337	C₂²×C₁₉	—	8	1	no	—
338	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²×C₁₉	#537	1	1	yes	characteristic
340	C₂²×C₁₉	#537	1	1	yes	characteristic
341	C₂²×C₁₉	#576	1	1	yes	characteristic
342	C₂²×C₁₉	#577	1	1	yes	characteristic
343	C₂²×C₁₉	#577	1	1	yes	characteristic
344	C₂²×C₁₉	#578	1	1	yes	characteristic
345	C₄×C₁₉	—	2	2	no	—
346	C₄×C₁₉	—	2	2	no	—
347	C₄×C₁₉	—	2	2	no	—
348	C₄×C₁₉	—	2	2	no	—
349	C₄×C₁₉	—	2	2	no	—
350	C₄×C₁₉	—	4	2	no	—
351	C₄×C₁₉	—	4	2	no	—
352	C₄×C₁₉	—	4	2	no	—
353	C₄×C₁₉	—	8	1	no	—
354	C₄×C₁₉	—	8	1	no	—
355	C₄×C₁₉	—	8	1	no	—
356	C₄×C₁₉	—	8	1	no	—
357	C₄×C₁₉	#520	1	1	yes	characteristic
358	C₄×C₁₉	#520	1	1	yes	characteristic
359	C₄×C₁₉	#535	1	1	yes	characteristic
360	C₄×C₁₉	#536	1	1	yes	characteristic
361	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
362	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
363	#542	—	2	4	no	—
364	#542	C₄×C₁₉	1	8	yes	complemented
365	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#126	—	2	1	no	—
367	C₂×#124	—	2	1	no	—
368	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#123	—	2	1	no	—
370	C₂×C₂²⋊Q₈	—	2	1	no	—
371	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
376	#424	—	2	4	no	—
377	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#384	C₂²×C₁₉	1	1	yes	characteristic
394	#382	C₂²×C₁₉	1	1	yes	characteristic
395	#380	C₂²×C₁₉	1	1	yes	characteristic
396	#380	C₂²×C₁₉	1	1	yes	characteristic
397	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
399	#340	C₂²×C₁₉	1	1	yes	characteristic
400	#340	C₂²×C₁₉	1	1	yes	characteristic
401	#340	C₂²×C₁₉	1	1	yes	characteristic
402	#340	C₂²×C₁₉	1	1	yes	characteristic
403	#340	C₂²×C₁₉	1	1	yes	characteristic
404	#340	C₂²×C₁₉	1	1	yes	characteristic
405	#340	C₂²×C₁₉	1	1	yes	characteristic
406	#340	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₁₉	—	4	2	no	—
408	C₂×C₁₉	—	8	2	no	—
409	C₂×C₁₉	#2311	1	1	yes	characteristic
410	C₂×C₁₉	#2897	1	1	yes	characteristic
411	C₂×C₁₉	#2898	1	1	yes	characteristic
412	C₂×C₁₉	#3257	1	1	yes	characteristic
413	C₂×C₁₉	#3258	1	1	yes	characteristic
414	C₂×C₁₉	#3262	1	1	yes	characteristic
415	C₂×C₁₉	#3263	1	1	yes	characteristic
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
418	C₂²×D₄	—	2	1	no	—
419	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
420	C₂³×C₄	—	2	1	no	—
421	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	4	1	no	—
424	C₂×M₁₆	—	4	1	no	—
425	C₂²×C₈	—	2	2	no	—
426	C₂²×C₈	—	4	1	no	—
427	C₂²×C₈	—	4	1	no	—
428	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
432	C₄⋊Q₈	—	2	2	no	—
433	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
434	#126	—	2	8	no	—
435	#124	—	2	8	no	—
436	#124	—	2	2	no	—
437	#124	C₂×C₄×C₁₉	1	4	yes	—
438	#123	—	2	8	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	8	no	—
441	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
442	#121	—	2	2	no	—
443	#121	C₂×C₄×C₁₉	1	4	yes	—
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
448	#117	C₂×C₄×C₁₉	1	4	yes	—
449	#117	D₄×C₁₉	1	4	yes	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄²	—	2	1	no	—
473	C₂×C₄²	—	2	1	no	—
474	C₂×C₄²	—	2	1	no	—
475	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
477	C₄⋊C₈	—	2	2	no	—
478	C₄⋊C₈	—	2	2	no	—
479	C₄⋊C₈	—	2	2	no	—
480	C₄⋊C₈	—	2	2	no	—
481	#103	—	4	1	no	—
482	#103	—	4	1	no	—
483	#103	—	4	1	no	—
484	#103	—	4	1	no	—
485	#102	—	4	1	no	—
486	#102	—	4	1	no	—
487	#102	—	4	1	no	—
488	#102	—	4	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	C₁₉	#21896	1	1	yes	characteristic, direct product factor, Sylow
496	C₂⁴	—	2	1	no	—
497	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	8	1	no	—
505	C₂×Q₈	—	8	1	no	—
506	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	8	1	no	—
514	C₂×D₄	—	8	1	no	—
515	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	8	1	no	—
529	C₂²×C₄	—	8	1	no	—
530	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
531	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
538	M₁₆	—	4	4	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	4	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	8	1	no	—
566	C₄⋊C₄	—	8	1	no	—
567	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
568	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₂²⋊C₄	—	8	1	no	—
578	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
579	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
580	C₄²	—	2	4	no	—
581	C₄²	—	8	1	no	—
582	C₄²	—	8	1	no	—
583	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
584	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
585	C₄²	C₂×D₄×C₁₉	1	2	yes	—
586	C₄²	C₂×D₄×C₁₉	1	2	yes	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
601	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
602	Q₈	—	2	2	no	—
603	Q₈	—	2	2	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	8	4	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	2	no	—
609	D₄	—	4	1	no	—
610	D₄	—	4	1	no	—
611	D₄	—	8	4	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	8	4	no	—
648	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
649	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
650	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
651	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
652	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
655	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₈	—	4	1	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
678	C₂²	C₁₉×#537	1	1	yes	characteristic
679	C₂²	C₁₉×#537	1	1	yes	characteristic
680	C₂²	C₁₉×#576	1	1	yes	characteristic
681	C₂²	C₁₉×#577	1	1	yes	characteristic
682	C₂²	C₁₉×#577	1	1	yes	characteristic
683	C₂²	C₁₉×#578	1	1	yes	characteristic
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₁₉×#520	1	1	yes	characteristic
697	C₄	C₁₉×#520	1	1	yes	characteristic
698	C₄	C₁₉×#535	1	1	yes	characteristic
699	C₄	C₁₉×#536	1	1	yes	characteristic
700	C₂	—	4	2	no	—
701	C₂	—	8	2	no	—
702	C₂	C₁₉×#2311	1	1	yes	characteristic
703	C₂	C₁₉×#2897	1	1	yes	characteristic
704	C₂	C₁₉×#2898	1	1	yes	characteristic
705	C₂	C₁₉×#3257	1	1	yes	characteristic
706	C₂	C₁₉×#3258	1	1	yes	characteristic
707	C₂	C₁₉×#3262	1	1	yes	characteristic
708	C₂	C₁₉×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#424	C₂	semidirect
3. C₁₉×#2314	C₂	semidirect
4. C₁₉×#1988	C₂	semidirect
5. C₁₉×#1987	C₂	semidirect
6. C₁₉×#1983	C₂	semidirect
7. C₁₉×#1983	C₂	semidirect
9. C₁₉×#1894	C₂	semidirect
11. C₁₉×#1892	C₂	semidirect
12. C₁₉×#1805	C₂	semidirect
13. C₁₉×#1804	C₂	semidirect
14. C₁₉×#1803	C₂	semidirect
15. C₁₉×#1802	C₂	semidirect
19. C₁₉×#542	C₄	semidirect
232. #21896	C₁₉	direct (N × H)
310. C₂×#424	C₂×C₁₉	semidirect
311. #2314	C₂×C₁₉	semidirect
312. #1988	C₂×C₁₉	semidirect
313. #1987	C₂×C₁₉	semidirect
314. #1983	C₂×C₁₉	semidirect
315. #1983	C₂×C₁₉	semidirect
317. #1894	C₂×C₁₉	semidirect
319. #1892	C₂×C₁₉	semidirect
320. #1805	C₂×C₁₉	semidirect
321. #1804	C₂×C₁₉	semidirect
322. #1803	C₂×C₁₉	semidirect
323. #1802	C₂×C₁₉	semidirect
364. #542	C₄×C₁₉	semidirect
495. C₁₉	#21896	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#542	2
C₂×C₁₉×#424	2
C₁₉×#2314	2
C₁₉×#1988	2
C₁₉×#1987	2
C₁₉×#1983	2
C₁₉×#1895	2
C₁₉×#1894	2
C₁₉×#1893	2
C₁₉×#1892	2
C₁₉×#1805	2
C₁₉×#1804	2
C₁₉×#1803	2
C₁₉×#1802	2
#21896	19

Subgroups — C19×#21896 #18027855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21896 #18027855