Subgroups — C₁₉×#23065 #18029024

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#478	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2357	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#478	C₄	1	8	yes	complemented
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#390	C₂²	1	1	yes	characteristic
32	C₁₉×#390	C₂²	1	1	yes	characteristic
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#388	—	2	1	no	—
37	C₁₉×#388	—	2	1	no	—
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₁₉×#382	C₂²	1	1	yes	characteristic
41	C₁₉×#381	—	2	1	no	—
42	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	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×#336	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	C₂×C₄	1	4	yes	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×#107	—	2	2	no	—
97	C₁₉×#107	C₂×C₄	1	4	yes	—
98	C₁₉×#106	—	2	2	no	—
99	C₁₉×#106	C₂×C₄	1	4	yes	—
100	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×#102	C₂×C₄	1	4	yes	—
104	C₁₉×#102	C₂×C₄	1	4	yes	—
105	C₄×C₈×C₁₉	—	2	2	no	—
106	C₄×C₈×C₁₉	—	2	2	no	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	D₄	1	1	yes	characteristic
118	C₁₉×#95	D₄	1	1	yes	characteristic
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	8	1	no	—
135	C₂²×C₄×C₁₉	—	8	1	no	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₉	#41	1	2	yes	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	—	8	1	no	—
171	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
173	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
174	C₄⋊C₄×C₁₉	#41	1	2	yes	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	4	2	no	—
177	C₂²⋊C₄×C₁₉	—	4	2	no	—
178	C₂²⋊C₄×C₁₉	—	8	1	no	—
179	C₂²⋊C₄×C₁₉	—	8	1	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	2	1	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	4	2	no	—
185	C₄²×C₁₉	—	8	1	no	—
186	C₄²×C₁₉	—	8	1	no	—
187	C₄²×C₁₉	—	8	1	no	—
188	C₄²×C₁₉	—	8	1	no	—
189	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
190	C₄²×C₁₉	#41	1	2	yes	—
191	#23065	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	—	4	1	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	D₄×C₁₉	—	2	2	no	—
201	D₄×C₁₉	—	2	2	no	—
202	D₄×C₁₉	—	4	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	8	4	no	—
240	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₁₉	#135	1	2	yes	—
243	C₂×C₄×C₁₉	#135	1	2	yes	—
244	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
250	C₈×C₁₉	—	2	2	no	—
251	C₈×C₁₉	—	2	2	no	—
252	C₈×C₁₉	—	2	2	no	—
253	C₈×C₁₉	—	4	1	no	—
254	C₂×#478	C₂×C₁₉	1	1	yes	characteristic
255	#2370	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2357	C₂×C₁₉	1	1	yes	characteristic
257	#1991	C₂×C₁₉	1	1	yes	characteristic, complemented
258	#1949	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#1934	C₂×C₁₉	1	1	yes	characteristic
260	#1934	C₂×C₁₉	1	1	yes	characteristic
261	#1926	C₂×C₁₉	1	1	yes	characteristic
262	#1925	C₂×C₁₉	1	1	yes	characteristic
263	#1921	C₂×C₁₉	1	1	yes	characteristic, complemented
264	#1919	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₄×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
266	C₄×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
268	C₄×#102	C₂×C₁₉	1	1	yes	characteristic
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	8	1	no	—
273	C₂²×C₁₉	—	8	1	no	—
274	C₂²×C₁₉	—	8	1	no	—
275	C₂²×C₁₉	—	8	1	no	—
276	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂²×C₁₉	#547	1	1	yes	characteristic
278	C₂²×C₁₉	#548	1	1	yes	characteristic
279	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
280	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
281	C₂²×C₁₉	#576	1	1	yes	characteristic
282	C₂²×C₁₉	#577	1	1	yes	characteristic
283	C₄×C₁₉	—	2	2	no	—
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	2	2	no	—
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	2	no	—
293	C₄×C₁₉	—	8	1	no	—
294	C₄×C₁₉	—	8	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
297	C₄×C₁₉	#519	1	1	yes	characteristic
298	C₄×C₁₉	#552	1	1	yes	characteristic
299	C₄×C₁₉	#556	1	1	yes	characteristic
300	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
302	#478	C₄×C₁₉	1	8	yes	complemented
303	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
315	#390	C₂²×C₁₉	1	1	yes	characteristic
316	#390	C₂²×C₁₉	1	1	yes	characteristic
317	#389	—	2	1	no	—
318	#389	C₂²×C₁₉	1	1	yes	characteristic
319	#389	C₂²×C₁₉	1	1	yes	characteristic
320	#388	—	2	1	no	—
321	#388	—	2	1	no	—
322	#387	—	2	1	no	—
323	#387	—	2	1	no	—
324	#382	C₂²×C₁₉	1	1	yes	characteristic
325	#381	—	2	1	no	—
326	C₄×C₄⋊C₄	—	2	1	no	—
327	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
329	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
333	C₄×C₂²⋊C₄	—	2	1	no	—
334	#340	C₂²×C₁₉	1	1	yes	characteristic
335	#340	C₂²×C₁₉	1	1	yes	characteristic
336	#340	C₂²×C₁₉	1	1	yes	characteristic
337	#340	C₂²×C₁₉	1	1	yes	characteristic
338	#340	C₂²×C₁₉	1	1	yes	characteristic
339	#340	C₂²×C₁₉	1	1	yes	characteristic
340	#340	C₂²×C₁₉	1	1	yes	characteristic
341	#340	C₂²×C₁₉	1	1	yes	characteristic
342	#336	C₂²×C₁₉	1	1	yes	characteristic
343	#336	C₂²×C₁₉	1	1	yes	characteristic
344	C₂×C₁₉	—	8	2	no	—
345	C₂×C₁₉	#2362	1	1	yes	characteristic
346	C₂×C₁₉	C₄×#135	1	1	yes	characteristic
347	C₂×C₁₉	#2946	1	1	yes	characteristic
348	C₂×C₁₉	#3337	1	1	yes	characteristic
349	C₂×C₁₉	#3339	1	1	yes	characteristic
350	C₂×C₁₉	#3361	1	1	yes	characteristic
351	C₂×C₁₉	#3365	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
358	#125	—	2	2	no	—
359	#125	C₂×C₄×C₁₉	1	4	yes	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
388	#107	—	2	2	no	—
389	#107	C₂×C₄×C₁₉	1	4	yes	—
390	#106	—	2	2	no	—
391	#106	C₂×C₄×C₁₉	1	4	yes	—
392	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	C₂×C₄×C₁₉	1	4	yes	—
396	#102	C₂×C₄×C₁₉	1	4	yes	—
397	C₄×C₈	—	2	2	no	—
398	C₄×C₈	—	2	2	no	—
399	C₄×C₈	—	2	2	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	D₄×C₁₉	1	1	yes	characteristic
410	#95	D₄×C₁₉	1	1	yes	characteristic
411	C₁₉	#23065	1	1	yes	characteristic, direct product factor, Sylow
412	C₂⁴	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	8	1	no	—
428	C₂²×C₄	—	8	1	no	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
446	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
447	C₂×C₈	#41×C₁₉	1	2	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	8	1	no	—
464	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
465	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
466	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
467	C₄⋊C₄	#41×C₁₉	1	2	yes	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₂²⋊C₄	—	8	1	no	—
472	C₂²⋊C₄	—	8	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	4	2	no	—
478	C₄²	—	8	1	no	—
479	C₄²	—	8	1	no	—
480	C₄²	—	8	1	no	—
481	C₄²	—	8	1	no	—
482	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
483	C₄²	#41×C₁₉	1	2	yes	—
484	C₂³	—	2	2	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
533	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
534	C₂×C₄	C₁₉×#135	1	2	yes	—
535	C₂×C₄	C₁₉×#135	1	2	yes	—
536	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
540	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	4	1	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
554	C₂²	C₁₉×#547	1	1	yes	characteristic
555	C₂²	C₁₉×#548	1	1	yes	characteristic
556	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
557	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
558	C₂²	C₁₉×#576	1	1	yes	characteristic
559	C₂²	C₁₉×#577	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
574	C₄	C₁₉×#519	1	1	yes	characteristic
575	C₄	C₁₉×#552	1	1	yes	characteristic
576	C₄	C₁₉×#556	1	1	yes	characteristic
577	C₂	—	8	2	no	—
578	C₂	C₁₉×#2362	1	1	yes	characteristic
579	C₂	C₄×C₁₉×#135	1	1	yes	characteristic
580	C₂	C₁₉×#2946	1	1	yes	characteristic
581	C₂	C₁₉×#3337	1	1	yes	characteristic
582	C₂	C₁₉×#3339	1	1	yes	characteristic
583	C₂	C₁₉×#3361	1	1	yes	characteristic
584	C₂	C₁₉×#3365	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
2. C₁₉×#2370	C₂	semidirect
4. C₁₉×#1991	C₂	semidirect
5. C₁₉×#1949	C₂	semidirect
10. C₁₉×#1921	C₂	semidirect
11. C₁₉×#1919	C₂	semidirect
12. C₄×C₁₉×#107	C₂	semidirect
13. C₄×C₁₉×#106	C₂	semidirect
14. C₈×C₄⋊C₄×C₁₉	C₂	semidirect
18. C₁₉×#478	C₄	semidirect
191. #23065	C₁₉	direct (N × H)
255. #2370	C₂×C₁₉	semidirect
257. #1991	C₂×C₁₉	semidirect
258. #1949	C₂×C₁₉	semidirect
263. #1921	C₂×C₁₉	semidirect
264. #1919	C₂×C₁₉	semidirect
265. C₄×#107	C₂×C₁₉	semidirect
266. C₄×#106	C₂×C₁₉	semidirect
267. C₈×C₄⋊C₄	C₂×C₁₉	semidirect
302. #478	C₄×C₁₉	semidirect
411. C₁₉	#23065	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×#478	2
C₁₉×#2370	2
C₁₉×#2357	2
C₁₉×#1991	2
C₁₉×#1949	2
C₁₉×#1934	2
C₁₉×#1926	2
C₁₉×#1925	2
C₁₉×#1921	2
C₁₉×#1919	2
C₄×C₁₉×#107	2
C₄×C₁₉×#106	2
C₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×#102	2
#23065	19

Subgroups — C19×#23065 #18029024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23065 #18029024