Subgroups — C₁₉×#23108 #18029067

Order 4864.

994 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2366	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	—	2	1	no	—
20	C₂×C₄×D₄×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	C₁₉×#459	C₄	1	8	yes	complemented
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#390	—	2	1	no	—
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic
41	C₁₉×#390	C₂²	1	1	yes	characteristic
42	C₁₉×#390	C₂²	1	1	yes	characteristic
43	C₁₉×#388	—	2	1	no	—
44	C₁₉×#388	—	2	1	no	—
45	C₁₉×#386	—	2	1	no	—
46	C₁₉×#386	—	2	1	no	—
47	C₁₉×#382	C₂²	1	1	yes	characteristic
48	C₁₉×#381	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	2	1	no	—
61	C₂²×D₄×C₁₉	—	2	1	no	—
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×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×D₈×C₁₉	—	4	1	no	—
69	C₂×D₈×C₁₉	—	4	1	no	—
70	C₂×D₈×C₁₉	—	4	1	no	—
71	C₂×D₈×C₁₉	—	4	1	no	—
72	C₂×D₈×C₁₉	C₂×C₄	1	4	yes	complemented
73	C₂×D₈×C₁₉	C₂×C₄	1	4	yes	complemented
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×#127	—	2	2	no	—
79	C₁₉×#127	C₂×C₄	1	4	yes	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	4	1	no	—
84	C₄×D₄×C₁₉	—	4	1	no	—
85	C₄×D₄×C₁₉	—	4	4	no	—
86	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
87	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	—	2	1	no	—
106	C₂×C₄²×C₁₉	—	2	1	no	—
107	C₂×C₄²×C₁₉	—	2	1	no	—
108	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₁₉×#107	—	4	1	no	—
112	C₁₉×#106	—	4	1	no	—
113	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
114	C₁₉×#102	—	2	2	no	—
115	C₁₉×#102	—	2	2	no	—
116	C₁₉×#102	—	2	2	no	—
117	C₁₉×#102	—	2	2	no	—
118	C₁₉×#102	—	4	1	no	—
119	C₁₉×#102	—	4	1	no	—
120	C₁₉×#102	C₂×C₄	1	4	yes	complemented
121	C₁₉×#102	C₂×C₄	1	4	yes	complemented
122	C₁₉×#97	—	2	2	no	—
123	C₁₉×#97	—	4	1	no	—
124	C₄×C₈×C₁₉	—	4	1	no	—
125	C₁₉×#95	—	2	1	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	D₄	1	1	yes	characteristic
131	C₁₉×#95	D₄	1	1	yes	characteristic
132	C₂⁴×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	—	2	1	no	—
134	C₂⁴×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	4	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	2	no	—
154	C₂×D₄×C₁₉	—	8	1	no	—
155	C₂×D₄×C₁₉	—	8	1	no	—
156	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
157	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
158	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	4	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	—	4	2	no	—
166	C₂²×C₄×C₁₉	—	4	2	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	—	4	2	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	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	D₈×C₁₉	—	4	4	no	—
181	D₈×C₁₉	—	4	4	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	—	2	1	no	—
191	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
192	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
193	C₂×C₈×C₁₉	#41	1	2	yes	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
204	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
205	C₄⋊C₄×C₁₉	#41	1	2	yes	—
206	C₂²⋊C₄×C₁₉	—	2	4	no	—
207	C₂²⋊C₄×C₁₉	—	4	2	no	—
208	C₂²⋊C₄×C₁₉	—	4	2	no	—
209	C₂²⋊C₄×C₁₉	—	4	2	no	—
210	C₂²⋊C₄×C₁₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₉	—	4	2	no	—
212	C₂²⋊C₄×C₁₉	—	4	2	no	—
213	C₂²⋊C₄×C₁₉	—	8	1	no	—
214	C₂²⋊C₄×C₁₉	—	8	1	no	—
215	C₂²⋊C₄×C₁₉	—	8	1	no	—
216	C₂²⋊C₄×C₁₉	—	8	1	no	—
217	C₄²×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	—	2	1	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	4	2	no	—
222	C₄²×C₁₉	—	8	1	no	—
223	C₄²×C₁₉	—	8	1	no	—
224	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
225	C₄²×C₁₉	#41	1	2	yes	—
226	#23108	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂³×C₁₉	—	2	2	no	—
228	C₂³×C₁₉	—	2	2	no	—
229	C₂³×C₁₉	—	2	2	no	—
230	C₂³×C₁₉	—	4	1	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	—	4	1	no	—
234	C₂³×C₁₉	—	4	1	no	—
235	C₂³×C₁₉	—	4	1	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	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	—	4	1	no	—
247	C₂³×C₁₉	—	4	1	no	—
248	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	2	no	—
252	D₄×C₁₉	—	2	2	no	—
253	D₄×C₁₉	—	2	2	no	—
254	D₄×C₁₉	—	2	2	no	—
255	D₄×C₁₉	—	4	8	no	—
256	D₄×C₁₉	—	4	1	no	—
257	D₄×C₁₉	—	4	1	no	—
258	D₄×C₁₉	—	4	1	no	—
259	D₄×C₁₉	—	4	1	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	8	4	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	1	no	—
269	C₂×C₄×C₁₉	—	2	2	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	1	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	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	—	8	4	no	—
295	C₂×C₄×C₁₉	—	8	4	no	—
296	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
297	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
298	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
299	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
305	C₈×C₁₉	—	2	2	no	—
306	C₈×C₁₉	—	2	2	no	—
307	C₈×C₁₉	—	2	2	no	—
308	C₈×C₁₉	—	4	1	no	—
309	C₂×#459	C₂×C₁₉	1	1	yes	characteristic
310	#2366	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2357	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1972	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1970	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1961	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1949	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1926	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1925	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
319	#1879	C₂×C₁₉	1	1	yes	characteristic, complemented
320	#1771	C₂×C₁₉	1	1	yes	characteristic, complemented
321	#1762	C₂×C₁₉	1	1	yes	characteristic, complemented
322	#1762	C₂×C₁₉	1	1	yes	characteristic, complemented
323	C₄×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂²×C₁₉	—	4	2	no	—
325	C₂²×C₁₉	—	4	2	no	—
326	C₂²×C₁₉	—	4	2	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	2	no	—
329	C₂²×C₁₉	—	4	2	no	—
330	C₂²×C₁₉	—	4	2	no	—
331	C₂²×C₁₉	—	4	2	no	—
332	C₂²×C₁₉	—	4	2	no	—
333	C₂²×C₁₉	—	8	1	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	—	8	1	no	—
339	C₂²×C₁₉	—	8	1	no	—
340	C₂²×C₁₉	—	8	1	no	—
341	C₂²×C₁₉	—	8	1	no	—
342	C₂²×C₁₉	—	8	1	no	—
343	C₂²×C₁₉	—	8	1	no	—
344	C₂²×C₁₉	—	8	1	no	—
345	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
346	C₂²×C₁₉	#546	1	1	yes	characteristic
347	C₂²×C₁₉	#550	1	1	yes	characteristic
348	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂²×C₁₉	#575	1	1	yes	characteristic
350	C₂²×C₁₉	#576	1	1	yes	characteristic
351	C₂²×C₁₉	#576	1	1	yes	characteristic
352	C₄×C₁₉	—	2	2	no	—
353	C₄×C₁₉	—	2	2	no	—
354	C₄×C₁₉	—	2	2	no	—
355	C₄×C₁₉	—	4	2	no	—
356	C₄×C₁₉	—	4	1	no	—
357	C₄×C₁₉	—	4	1	no	—
358	C₄×C₁₉	—	4	1	no	—
359	C₄×C₁₉	—	4	2	no	—
360	C₄×C₁₉	—	8	1	no	—
361	C₄×C₁₉	—	8	1	no	—
362	C₄×C₁₉	—	8	1	no	—
363	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
364	C₄×C₁₉	#518	1	1	yes	characteristic
365	C₄×C₁₉	#553	1	1	yes	characteristic
366	C₄×C₁₉	#555	1	1	yes	characteristic
367	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
368	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
370	C₂×C₄×D₄	—	2	1	no	—
371	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
374	#459	C₄×C₁₉	1	8	yes	complemented
375	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
380	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
381	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
382	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
386	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
387	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
389	#390	—	2	1	no	—
390	#390	C₂²×C₁₉	1	1	yes	characteristic
391	#390	C₂²×C₁₉	1	1	yes	characteristic
392	#390	C₂²×C₁₉	1	1	yes	characteristic
393	#390	C₂²×C₁₉	1	1	yes	characteristic
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#386	—	2	1	no	—
397	#386	—	2	1	no	—
398	#382	C₂²×C₁₉	1	1	yes	characteristic
399	#381	—	2	1	no	—
400	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
401	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
404	C₄×C₂²⋊C₄	—	2	1	no	—
405	#340	C₂²×C₁₉	1	1	yes	characteristic
406	#340	C₂²×C₁₉	1	1	yes	characteristic
407	#340	C₂²×C₁₉	1	1	yes	characteristic
408	#340	C₂²×C₁₉	1	1	yes	characteristic
409	#336	C₂²×C₁₉	1	1	yes	characteristic
410	#336	C₂²×C₁₉	1	1	yes	characteristic
411	C₂×C₁₉	—	8	2	no	—
412	C₂×C₁₉	—	8	2	no	—
413	C₂×C₁₉	—	8	2	no	—
414	C₂×C₁₉	#2363	1	1	yes	characteristic
415	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
416	C₂×C₁₉	#2948	1	1	yes	characteristic
417	C₂×C₁₉	#3309	1	1	yes	characteristic
418	C₂×C₁₉	#3318	1	1	yes	characteristic
419	C₂×C₁₉	#3399	1	1	yes	characteristic
420	C₂×C₁₉	#3403	1	1	yes	characteristic
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
424	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	—	2	1	no	—
429	C₂×D₈	—	4	1	no	—
430	C₂×D₈	—	4	1	no	—
431	C₂×D₈	—	4	1	no	—
432	C₂×D₈	—	4	1	no	—
433	C₂×D₈	C₂×C₄×C₁₉	1	4	yes	complemented
434	C₂×D₈	C₂×C₄×C₁₉	1	4	yes	complemented
435	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
439	#127	—	2	2	no	—
440	#127	C₂×C₄×C₁₉	1	4	yes	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	4	1	no	—
445	C₄×D₄	—	4	1	no	—
446	C₄×D₄	—	4	4	no	—
447	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
448	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
472	#107	—	4	1	no	—
473	#106	—	4	1	no	—
474	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	complemented
475	#102	—	2	2	no	—
476	#102	—	2	2	no	—
477	#102	—	2	2	no	—
478	#102	—	2	2	no	—
479	#102	—	4	1	no	—
480	#102	—	4	1	no	—
481	#102	C₂×C₄×C₁₉	1	4	yes	complemented
482	#102	C₂×C₄×C₁₉	1	4	yes	complemented
483	#97	—	2	2	no	—
484	#97	—	4	1	no	—
485	C₄×C₈	—	4	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	D₄×C₁₉	1	1	yes	characteristic
492	#95	D₄×C₁₉	1	1	yes	characteristic
493	C₁₉	#23108	1	1	yes	characteristic, direct product factor, Sylow
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	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	—	2	1	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	8	1	no	—
517	C₂×D₄	—	8	1	no	—
518	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
519	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
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	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
542	D₈	—	4	4	no	—
543	D₈	—	4	4	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	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
554	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
555	C₂×C₈	#41×C₁₉	1	2	yes	—
556	C₄⋊C₄	—	2	2	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	—	4	1	no	—
566	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
567	C₄⋊C₄	#41×C₁₉	1	2	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	8	1	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₂²⋊C₄	—	8	1	no	—
578	C₂²⋊C₄	—	8	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	4	2	no	—
584	C₄²	—	8	1	no	—
585	C₄²	—	8	1	no	—
586	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
587	C₄²	#41×C₁₉	1	2	yes	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	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	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	4	8	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	8	4	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	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	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	8	4	no	—
655	C₂×C₄	—	8	4	no	—
656	C₂×C₄	—	8	4	no	—
657	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
658	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
659	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
660	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
661	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
664	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
666	C₈	—	2	2	no	—
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	4	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	—	8	1	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
692	C₂²	C₁₉×#546	1	1	yes	characteristic
693	C₂²	C₁₉×#550	1	1	yes	characteristic
694	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
695	C₂²	C₁₉×#575	1	1	yes	characteristic
696	C₂²	C₁₉×#576	1	1	yes	characteristic
697	C₂²	C₁₉×#576	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	2	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
710	C₄	C₁₉×#518	1	1	yes	characteristic
711	C₄	C₁₉×#553	1	1	yes	characteristic
712	C₄	C₁₉×#555	1	1	yes	characteristic
713	C₂	—	8	2	no	—
714	C₂	—	8	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₁₉×#2363	1	1	yes	characteristic
717	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
718	C₂	C₁₉×#2948	1	1	yes	characteristic
719	C₂	C₁₉×#3309	1	1	yes	characteristic
720	C₂	C₁₉×#3318	1	1	yes	characteristic
721	C₂	C₁₉×#3399	1	1	yes	characteristic
722	C₂	C₁₉×#3403	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×#459	C₂
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×#2366	C₂	semidirect
3. C₁₉×#2357	C₂	semidirect
4. C₁₉×#1972	C₂	semidirect
5. C₁₉×#1970	C₂	semidirect
6. C₁₉×#1961	C₂	semidirect
7. C₁₉×#1949	C₂	semidirect
8. C₁₉×#1926	C₂	semidirect
9. C₁₉×#1925	C₂	semidirect
10. C₁₉×#1879	C₂	semidirect
11. C₁₉×#1879	C₂	semidirect
12. C₁₉×#1771	C₂	semidirect
13. C₁₉×#1762	C₂	semidirect
14. C₁₉×#1762	C₂	semidirect
15. C₄×C₁₉×#102	C₂	semidirect
23. C₁₉×#459	C₄	semidirect
72. C₂×D₈×C₁₉	C₂×C₄	semidirect
73. C₂×D₈×C₁₉	C₂×C₄	semidirect
86. C₄×D₄×C₁₉	C₂×C₄	semidirect
113. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
120. C₁₉×#102	C₂×C₄	semidirect
121. C₁₉×#102	C₂×C₄	semidirect
226. #23108	C₁₉	direct (N × H)
310. #2366	C₂×C₁₉	semidirect
311. #2357	C₂×C₁₉	semidirect
312. #1972	C₂×C₁₉	semidirect
313. #1970	C₂×C₁₉	semidirect
314. #1961	C₂×C₁₉	semidirect
315. #1949	C₂×C₁₉	semidirect
316. #1926	C₂×C₁₉	semidirect
317. #1925	C₂×C₁₉	semidirect
318. #1879	C₂×C₁₉	semidirect
319. #1879	C₂×C₁₉	semidirect
320. #1771	C₂×C₁₉	semidirect
321. #1762	C₂×C₁₉	semidirect
322. #1762	C₂×C₁₉	semidirect
323. C₄×#102	C₂×C₁₉	semidirect
374. #459	C₄×C₁₉	semidirect
433. C₂×D₈	C₂×C₄×C₁₉	semidirect
434. C₂×D₈	C₂×C₄×C₁₉	semidirect
447. C₄×D₄	C₂×C₄×C₁₉	semidirect
474. C₄⋊C₈	C₂×C₄×C₁₉	semidirect
481. #102	C₂×C₄×C₁₉	semidirect
482. #102	C₂×C₄×C₁₉	semidirect
493. C₁₉	#23108	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×#459	2
C₁₉×#2366	2
C₁₉×#2357	2
C₁₉×#1972	2
C₁₉×#1970	2
C₁₉×#1961	2
C₁₉×#1949	2
C₁₉×#1926	2
C₁₉×#1925	2
C₁₉×#1879	2
C₁₉×#1771	2
C₁₉×#1762	2
C₄×C₁₉×#102	2
#23108	19

Subgroups — C19×#23108 #18029067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23108 #18029067