Subgroups — C₁₉×#23166 #18029125

Order 4864.

750 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#501	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2370	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2365	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1943	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1941	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
19	C₁₉×#501	C₄	1	8	yes	complemented
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	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×#97	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#391	—	2	1	no	—
31	C₁₉×#389	—	2	1	no	—
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#389	C₂²	1	1	yes	characteristic
34	C₁₉×#389	C₂²	1	1	yes	characteristic
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#387	—	2	1	no	—
37	C₁₉×#387	—	2	1	no	—
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#387	—	2	1	no	—
40	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
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×Q₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×C₄⋊Q₈	—	2	2	no	—
66	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	C₂×C₄	1	4	yes	—
69	C₄×Q₈×C₁₉	—	4	4	no	—
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	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×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	C₂×C₄	1	4	yes	—
97	C₁₉×#107	C₂×C₄	1	4	yes	—
98	C₁₉×#107	Q₈	1	4	yes	complemented
99	C₁₉×#106	—	2	2	no	—
100	C₁₉×#106	C₂×C₄	1	4	yes	—
101	C₁₉×#106	C₂×C₄	1	4	yes	—
102	C₁₉×C₄⋊C₈	—	2	2	no	—
103	C₁₉×#97	—	2	2	no	—
104	C₁₉×#97	C₂×C₄	1	4	yes	—
105	C₄×C₈×C₁₉	—	2	2	no	—
106	C₁₉×#95	—	2	1	no	—
107	C₁₉×#95	—	2	1	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	D₄	1	1	yes	characteristic
117	C₁₉×#95	D₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₉	—	2	4	no	—
119	C₂×Q₈×C₁₉	—	4	2	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
147	C₂×C₈×C₁₉	#41	1	2	yes	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	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	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	8	1	no	—
167	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
173	C₄²×C₁₉	—	2	1	no	—
174	C₄²×C₁₉	—	2	1	no	—
175	C₄²×C₁₉	—	2	1	no	—
176	C₄²×C₁₉	—	2	1	no	—
177	C₄²×C₁₉	—	4	2	no	—
178	C₄²×C₁₉	—	4	2	no	—
179	C₄²×C₁₉	—	4	2	no	—
180	C₄²×C₁₉	—	4	2	no	—
181	C₄²×C₁₉	—	8	1	no	—
182	C₄²×C₁₉	—	8	1	no	—
183	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
184	C₄²×C₁₉	#41	1	2	yes	—
185	#23166	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₉	—	4	8	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	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	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₁₉	—	2	2	no	—
237	C₈×C₁₉	—	4	1	no	—
238	C₈×C₁₉	—	4	1	no	—
239	C₈×C₁₉	C₄×Q₈	1	4	yes	complemented
240	C₂×#501	C₂×C₁₉	1	1	yes	characteristic
241	#2370	C₂×C₁₉	1	1	yes	characteristic
242	#2365	C₂×C₁₉	1	1	yes	characteristic
243	#1989	C₂×C₁₉	1	1	yes	characteristic
244	#1987	C₂×C₁₉	1	1	yes	characteristic
245	#1943	C₂×C₁₉	1	1	yes	characteristic
246	#1941	C₂×C₁₉	1	1	yes	characteristic
247	#1921	C₂×C₁₉	1	1	yes	characteristic
248	#1920	C₂×C₁₉	1	1	yes	characteristic
249	#1920	C₂×C₁₉	1	1	yes	characteristic
250	#1918	C₂×C₁₉	1	1	yes	characteristic
251	#1776	C₂×C₁₉	1	1	yes	characteristic
252	#1776	C₂×C₁₉	1	1	yes	characteristic
253	C₄×#107	C₂×C₁₉	1	1	yes	characteristic
254	#1771	C₂×C₁₉	1	1	yes	characteristic
255	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂²×C₁₉	#547	1	1	yes	characteristic
257	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂²×C₁₉	#575	1	1	yes	characteristic
260	C₂²×C₁₉	#577	1	1	yes	characteristic
261	C₂²×C₁₉	#578	1	1	yes	characteristic
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	2	2	no	—
265	C₄×C₁₉	—	4	1	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	4	1	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	1	no	—
276	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
277	C₄×C₁₉	#519	1	1	yes	characteristic
278	C₄×C₁₉	#556	1	1	yes	characteristic
279	C₄×C₁₉	#557	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×C₄×Q₈	—	2	1	no	—
283	#501	C₄×C₁₉	1	8	yes	complemented
284	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
294	#391	—	2	1	no	—
295	#389	—	2	1	no	—
296	#389	C₂²×C₁₉	1	1	yes	characteristic
297	#389	C₂²×C₁₉	1	1	yes	characteristic
298	#389	C₂²×C₁₉	1	1	yes	characteristic
299	#389	C₂²×C₁₉	1	1	yes	characteristic
300	#387	—	2	1	no	—
301	#387	—	2	1	no	—
302	#387	—	2	1	no	—
303	#387	—	2	1	no	—
304	C₄×C₄⋊C₄	—	2	1	no	—
305	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
307	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	#340	C₂²×C₁₉	1	1	yes	characteristic
313	#340	C₂²×C₁₉	1	1	yes	characteristic
314	#340	C₂²×C₁₉	1	1	yes	characteristic
315	#340	C₂²×C₁₉	1	1	yes	characteristic
316	#340	C₂²×C₁₉	1	1	yes	characteristic
317	#340	C₂²×C₁₉	1	1	yes	characteristic
318	#340	C₂²×C₁₉	1	1	yes	characteristic
319	#340	C₂²×C₁₉	1	1	yes	characteristic
320	#340	C₂²×C₁₉	1	1	yes	characteristic
321	#340	C₂²×C₁₉	1	1	yes	characteristic
322	#336	C₂²×C₁₉	1	1	yes	characteristic
323	#336	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₁₉	#2365	1	1	yes	characteristic
325	C₂×C₁₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₂×C₁₉	#2947	1	1	yes	characteristic
327	C₂×C₁₉	#3343	1	1	yes	characteristic
328	C₂×C₁₉	#3350	1	1	yes	characteristic
329	C₂×C₁₉	#3384	1	1	yes	characteristic
330	C₂×C₁₉	#3390	1	1	yes	characteristic
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
338	#125	—	2	2	no	—
339	#125	C₂×C₄×C₁₉	1	4	yes	—
340	C₄×Q₈	—	4	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	#107	C₂×C₄×C₁₉	1	4	yes	—
368	#107	C₂×C₄×C₁₉	1	4	yes	—
369	#107	Q₈×C₁₉	1	4	yes	complemented
370	#106	—	2	2	no	—
371	#106	C₂×C₄×C₁₉	1	4	yes	—
372	#106	C₂×C₄×C₁₉	1	4	yes	—
373	C₄⋊C₈	—	2	2	no	—
374	#97	—	2	2	no	—
375	#97	C₂×C₄×C₁₉	1	4	yes	—
376	C₄×C₈	—	2	2	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	D₄×C₁₉	1	1	yes	characteristic
388	#95	D₄×C₁₉	1	1	yes	characteristic
389	C₁₉	#23166	1	1	yes	characteristic, direct product factor, Sylow
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
417	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
418	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
419	C₂×C₈	#41×C₁₉	1	2	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	4	1	no	—
435	C₄⋊C₄	—	4	2	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	4	2	no	—
438	C₄⋊C₄	—	8	1	no	—
439	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
440	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
441	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
442	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
443	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
444	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	4	2	no	—
450	C₄²	—	4	2	no	—
451	C₄²	—	4	2	no	—
452	C₄²	—	4	2	no	—
453	C₄²	—	8	1	no	—
454	C₄²	—	8	1	no	—
455	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
456	C₄²	#41×C₁₉	1	2	yes	—
457	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	Q₈	—	4	8	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
499	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
500	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
501	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
505	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
506	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
507	C₈	—	2	2	no	—
508	C₈	—	4	1	no	—
509	C₈	—	4	1	no	—
510	C₈	C₄×Q₈×C₁₉	1	4	yes	complemented
511	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
512	C₂²	C₁₉×#547	1	1	yes	characteristic
513	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
514	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₂²	C₁₉×#575	1	1	yes	characteristic
516	C₂²	C₁₉×#577	1	1	yes	characteristic
517	C₂²	C₁₉×#578	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	8	1	no	—
531	C₄	—	8	1	no	—
532	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
533	C₄	C₁₉×#519	1	1	yes	characteristic
534	C₄	C₁₉×#556	1	1	yes	characteristic
535	C₄	C₁₉×#557	1	1	yes	characteristic
536	C₂	C₁₉×#2365	1	1	yes	characteristic
537	C₂	C₄×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂	C₁₉×#2947	1	1	yes	characteristic
539	C₂	C₁₉×#3343	1	1	yes	characteristic
540	C₂	C₁₉×#3350	1	1	yes	characteristic
541	C₂	C₁₉×#3384	1	1	yes	characteristic
542	C₂	C₁₉×#3390	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
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
19. C₁₉×#501	C₄	semidirect
98. C₁₉×#107	Q₈	semidirect
185. #23166	C₁₉	direct (N × H)
239. C₈×C₁₉	C₄×Q₈	semidirect
283. #501	C₄×C₁₉	semidirect
369. #107	Q₈×C₁₉	semidirect
389. C₁₉	#23166	direct (N × H)
510. C₈	C₄×Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#501	2
C₁₉×#2370	2
C₁₉×#2365	2
C₁₉×#1989	2
C₁₉×#1987	2
C₁₉×#1943	2
C₁₉×#1941	2
C₁₉×#1921	2
C₁₉×#1920	2
C₁₉×#1918	2
C₁₉×#1776	2
C₄×C₁₉×#107	2
C₁₉×#1771	2
#23166	19

Subgroups — C19×#23166 #18029125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23166 #18029125