Subgroups — C₁₉×#23012 #18028971

Order 4864.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2349	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1877	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#461	C₄	1	8	yes	complemented
25	C₁₉×#440	—	2	4	no	—
26	C₄×SD₁₆×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#391	C₂²	1	1	yes	characteristic
42	C₁₉×#391	C₂²	1	1	yes	characteristic
43	C₁₉×#389	—	2	1	no	—
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#389	C₂²	1	1	yes	characteristic
46	C₁₉×#387	—	2	1	no	—
47	C₁₉×#387	—	2	1	no	—
48	C₁₉×#385	—	2	1	no	—
49	C₁₉×#385	—	2	1	no	—
50	C₁₉×#382	C₂²	1	1	yes	characteristic
51	C₁₉×#380	—	2	1	no	—
52	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₁₉×#95	—	2	1	no	—
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×#336	C₂²	1	1	yes	characteristic
61	C₁₉×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂×SD₁₆×C₁₉	—	2	2	no	—
69	C₂×SD₁₆×C₁₉	—	2	2	no	—
70	C₂×SD₁₆×C₁₉	—	2	2	no	—
71	C₂×SD₁₆×C₁₉	—	2	2	no	—
72	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	—
73	C₂×SD₁₆×C₁₉	C₂×C₄	1	4	yes	—
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	complemented
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×Q₈×C₁₉	—	4	1	no	—
83	C₄×Q₈×C₁₉	—	4	1	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	—	2	2	no	—
87	C₄×D₄×C₁₉	—	4	1	no	—
88	C₄×D₄×C₁₉	—	4	1	no	—
89	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#107	—	2	2	no	—
113	C₁₉×#106	—	2	2	no	—
114	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
115	C₁₉×#103	—	2	2	no	—
116	C₁₉×#103	—	2	2	no	—
117	C₁₉×#103	—	4	1	no	—
118	C₁₉×#103	—	4	1	no	—
119	C₁₉×#103	C₂×C₄	1	4	yes	complemented
120	C₁₉×#103	C₂×C₄	1	4	yes	complemented
121	C₁₉×#102	—	2	2	no	—
122	C₁₉×#102	D₄	1	4	yes	—
123	C₁₉×#97	—	2	2	no	—
124	C₁₉×#97	—	2	2	no	—
125	C₄×C₈×C₁₉	—	2	2	no	—
126	C₁₉×#95	—	2	1	no	—
127	C₁₉×#95	—	2	1	no	—
128	C₁₉×#95	—	2	1	no	—
129	C₁₉×#95	—	2	1	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	D₄	1	1	yes	characteristic
136	C₁₉×#95	D₄	1	1	yes	characteristic
137	C₂⁴×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	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	C₂²×C₄	1	2	yes	—
149	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₉	#41	1	2	yes	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
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	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	2	no	—
166	C₂²×C₄×C₁₉	—	4	2	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	—	8	1	no	—
169	C₂²×C₄×C₁₉	—	8	1	no	—
170	C₂²×C₄×C₁₉	—	8	1	no	—
171	C₂²×C₄×C₁₉	—	8	1	no	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	SD₁₆×C₁₉	—	2	8	no	—
180	SD₁₆×C₁₉	—	2	8	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	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	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
192	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
193	C₄⋊C₄×C₁₉	—	2	4	no	—
194	C₄⋊C₄×C₁₉	—	2	4	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
205	C₄⋊C₄×C₁₉	—	4	2	no	—
206	C₄⋊C₄×C₁₉	—	4	2	no	—
207	C₄⋊C₄×C₁₉	—	8	1	no	—
208	C₄⋊C₄×C₁₉	—	8	1	no	—
209	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
211	C₂²⋊C₄×C₁₉	—	2	4	no	—
212	C₂²⋊C₄×C₁₉	—	4	2	no	—
213	C₂²⋊C₄×C₁₉	—	4	2	no	—
214	C₄²×C₁₉	—	2	1	no	—
215	C₄²×C₁₉	—	2	1	no	—
216	C₄²×C₁₉	—	2	1	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	4	2	no	—
219	C₄²×C₁₉	—	4	2	no	—
220	C₄²×C₁₉	—	4	2	no	—
221	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
222	C₄²×C₁₉	#41	1	2	yes	—
223	#23012	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₁₉	—	2	2	no	—
225	C₂³×C₁₉	—	2	2	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	4	1	no	—
228	C₂³×C₁₉	—	4	1	no	—
229	C₂³×C₁₉	—	4	1	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₉	—	2	2	no	—
233	Q₈×C₁₉	—	2	2	no	—
234	Q₈×C₁₉	—	2	2	no	—
235	Q₈×C₁₉	—	2	2	no	—
236	Q₈×C₁₉	—	4	1	no	—
237	Q₈×C₁₉	—	4	1	no	—
238	Q₈×C₁₉	—	4	1	no	—
239	Q₈×C₁₉	—	4	1	no	—
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	2	2	no	—
242	D₄×C₁₉	—	2	2	no	—
243	D₄×C₁₉	C₄×D₄	1	4	yes	—
244	C₂×C₄×C₁₉	—	2	1	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	1	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	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	4	1	no	—
267	C₂×C₄×C₁₉	—	4	1	no	—
268	C₂×C₄×C₁₉	—	4	1	no	—
269	C₂×C₄×C₁₉	—	4	1	no	—
270	C₂×C₄×C₁₉	—	4	1	no	—
271	C₂×C₄×C₁₉	—	4	1	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	1	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	—	8	4	no	—
281	C₂×C₄×C₁₉	—	8	4	no	—
282	C₂×C₄×C₁₉	—	8	4	no	—
283	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
284	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
285	C₂×C₄×C₁₉	#137	1	2	yes	—
286	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
292	C₈×C₁₉	—	2	2	no	—
293	C₈×C₁₉	—	2	2	no	—
294	C₈×C₁₉	—	2	2	no	—
295	C₈×C₁₉	—	4	1	no	—
296	C₂×#461	C₂×C₁₉	1	1	yes	characteristic
297	C₂×#440	C₂×C₁₉	1	1	yes	characteristic
298	C₂×C₄×SD₁₆	C₂×C₁₉	1	1	yes	characteristic
299	#2365	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#2349	C₂×C₁₉	1	1	yes	characteristic
301	#1960	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#1949	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
305	#1877	C₂×C₁₉	1	1	yes	characteristic
306	#1877	C₂×C₁₉	1	1	yes	characteristic
307	#1865	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1771	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1762	C₂×C₁₉	1	1	yes	characteristic
311	C₂²×C₁₉	—	2	4	no	—
312	C₂²×C₁₉	—	4	2	no	—
313	C₂²×C₁₉	—	4	2	no	—
314	C₂²×C₁₉	—	4	2	no	—
315	C₂²×C₁₉	—	4	2	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
319	C₂²×C₁₉	D₄²	1	1	yes	characteristic
320	C₂²×C₁₉	#548	1	1	yes	characteristic
321	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
322	C₂²×C₁₉	#575	1	1	yes	characteristic
323	C₂²×C₁₉	#577	1	1	yes	characteristic
324	C₂²×C₁₉	#577	1	1	yes	characteristic
325	C₄×C₁₉	—	2	2	no	—
326	C₄×C₁₉	—	2	2	no	—
327	C₄×C₁₉	—	2	2	no	—
328	C₄×C₁₉	—	4	2	no	—
329	C₄×C₁₉	—	4	2	no	—
330	C₄×C₁₉	—	4	2	no	—
331	C₄×C₁₉	—	4	1	no	—
332	C₄×C₁₉	—	4	1	no	—
333	C₄×C₁₉	—	4	1	no	—
334	C₄×C₁₉	—	4	2	no	—
335	C₄×C₁₉	—	8	1	no	—
336	C₄×C₁₉	—	8	1	no	—
337	C₄×C₁₉	—	8	1	no	—
338	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₁₉	#520	1	1	yes	characteristic
340	C₄×C₁₉	#547	1	1	yes	characteristic
341	C₄×C₁₉	#553	1	1	yes	characteristic
342	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
343	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
345	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
350	#461	C₄×C₁₉	1	8	yes	complemented
351	#440	—	2	4	no	—
352	C₄×SD₁₆	—	2	4	no	—
353	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
354	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
362	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
363	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
367	#391	C₂²×C₁₉	1	1	yes	characteristic
368	#391	C₂²×C₁₉	1	1	yes	characteristic
369	#389	—	2	1	no	—
370	#389	C₂²×C₁₉	1	1	yes	characteristic
371	#389	C₂²×C₁₉	1	1	yes	characteristic
372	#387	—	2	1	no	—
373	#387	—	2	1	no	—
374	#385	—	2	1	no	—
375	#385	—	2	1	no	—
376	#382	C₂²×C₁₉	1	1	yes	characteristic
377	#380	—	2	1	no	—
378	C₄×C₄⋊C₄	—	2	1	no	—
379	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#95	—	2	1	no	—
382	#340	C₂²×C₁₉	1	1	yes	characteristic
383	#340	C₂²×C₁₉	1	1	yes	characteristic
384	#340	C₂²×C₁₉	1	1	yes	characteristic
385	#340	C₂²×C₁₉	1	1	yes	characteristic
386	#336	C₂²×C₁₉	1	1	yes	characteristic
387	#336	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₁₉	—	4	4	no	—
389	C₂×C₁₉	#2361	1	1	yes	characteristic
390	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
391	C₂×C₁₉	#2949	1	1	yes	characteristic
392	C₂×C₁₉	#3266	1	1	yes	characteristic
393	C₂×C₁₉	#3267	1	1	yes	characteristic
394	C₂×C₁₉	#3372	1	1	yes	characteristic
395	C₂×C₁₉	#3376	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
397	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
399	C₂³×C₄	—	2	1	no	—
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂×SD₁₆	—	2	2	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×SD₁₆	—	2	2	no	—
406	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	—
407	C₂×SD₁₆	C₂×C₄×C₁₉	1	4	yes	—
408	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	4	1	no	—
417	C₄×Q₈	—	4	1	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	4	1	no	—
422	C₄×D₄	—	4	1	no	—
423	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
446	#107	—	2	2	no	—
447	#106	—	2	2	no	—
448	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	4	1	no	—
452	#103	—	4	1	no	—
453	#103	C₂×C₄×C₁₉	1	4	yes	complemented
454	#103	C₂×C₄×C₁₉	1	4	yes	complemented
455	#102	—	2	2	no	—
456	#102	D₄×C₁₉	1	4	yes	—
457	#97	—	2	2	no	—
458	#97	—	2	2	no	—
459	C₄×C₈	—	2	2	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	D₄×C₁₉	1	1	yes	characteristic
470	#95	D₄×C₁₉	1	1	yes	characteristic
471	C₁₉	#23012	1	1	yes	characteristic, direct product factor, Sylow
472	C₂⁴	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
484	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
489	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
490	C₂×D₄	#41×C₁₉	1	2	yes	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	—	8	1	no	—
505	C₂²×C₄	—	8	1	no	—
506	C₂²×C₄	—	8	1	no	—
507	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
514	SD₁₆	—	2	8	no	—
515	SD₁₆	—	2	8	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
526	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
527	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
545	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	4	2	no	—
554	C₄²	—	4	2	no	—
555	C₄²	—	4	2	no	—
556	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
557	C₄²	#41×C₁₉	1	2	yes	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	C₄×D₄×C₁₉	1	4	yes	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	8	4	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	—	8	4	no	—
617	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
618	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
619	C₂×C₄	C₁₉×#137	1	2	yes	—
620	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
624	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
626	C₈	—	2	2	no	—
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	4	1	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
638	C₂²	D₄²×C₁₉	1	1	yes	characteristic
639	C₂²	C₁₉×#548	1	1	yes	characteristic
640	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
641	C₂²	C₁₉×#575	1	1	yes	characteristic
642	C₂²	C₁₉×#577	1	1	yes	characteristic
643	C₂²	C₁₉×#577	1	1	yes	characteristic
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
658	C₄	C₁₉×#520	1	1	yes	characteristic
659	C₄	C₁₉×#547	1	1	yes	characteristic
660	C₄	C₁₉×#553	1	1	yes	characteristic
661	C₂	—	4	4	no	—
662	C₂	C₁₉×#2361	1	1	yes	characteristic
663	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
664	C₂	C₁₉×#2949	1	1	yes	characteristic
665	C₂	C₁₉×#3266	1	1	yes	characteristic
666	C₂	C₁₉×#3267	1	1	yes	characteristic
667	C₂	C₁₉×#3372	1	1	yes	characteristic
668	C₂	C₁₉×#3376	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	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#2365	C₂	semidirect
6. C₁₉×#1960	C₂	semidirect
7. C₁₉×#1949	C₂	semidirect
8. C₁₉×#1935	C₂	semidirect
9. C₁₉×#1933	C₂	semidirect
12. C₁₉×#1865	C₂	semidirect
13. C₁₉×#1863	C₂	semidirect
14. C₁₉×#1771	C₂	semidirect
24. C₁₉×#461	C₄	semidirect
79. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
114. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
119. C₁₉×#103	C₂×C₄	semidirect
120. C₁₉×#103	C₂×C₄	semidirect
223. #23012	C₁₉	direct (N × H)
299. #2365	C₂×C₁₉	semidirect
301. #1960	C₂×C₁₉	semidirect
302. #1949	C₂×C₁₉	semidirect
303. #1935	C₂×C₁₉	semidirect
304. #1933	C₂×C₁₉	semidirect
307. #1865	C₂×C₁₉	semidirect
308. #1863	C₂×C₁₉	semidirect
309. #1771	C₂×C₁₉	semidirect
350. #461	C₄×C₁₉	semidirect
413. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
448. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
453. #103	C₂×C₄×C₁₉	semidirect
454. #103	C₂×C₄×C₁₉	semidirect
471. C₁₉	#23012	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×#461	2
C₂×C₁₉×#440	2
C₂×C₄×SD₁₆×C₁₉	2
C₁₉×#2365	2
C₁₉×#2349	2
C₁₉×#1960	2
C₁₉×#1949	2
C₁₉×#1935	2
C₁₉×#1933	2
C₁₉×#1877	2
C₁₉×#1865	2
C₁₉×#1863	2
C₁₉×#1771	2
C₁₉×#1762	2
#23012	19

Subgroups — C19×#23012 #18028971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23012 #18028971