Subgroups — C₁₉×#22981 #18028940

Order 4864.

774 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2369	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1993	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1949	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1944	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1941	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1865	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#475	C₄	1	8	yes	complemented
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#391	—	2	1	no	—
34	C₁₉×#391	—	2	1	no	—
35	C₁₉×#389	—	2	1	no	—
36	C₁₉×#389	—	2	1	no	—
37	C₁₉×#389	—	2	1	no	—
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#382	—	2	1	no	—
43	C₁₉×#382	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
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×C₄⋊C₄×C₁₉	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×Q₈×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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	—	2	2	no	—
67	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	4	1	no	—
72	C₄×Q₈×C₁₉	—	4	1	no	—
73	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
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	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	D₄	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×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	—	2	1	no	—
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	—	2	1	no	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₁₉×#107	—	4	1	no	—
101	C₁₉×#106	—	4	1	no	—
102	C₁₉×#106	C₂×C₄	1	4	yes	—
103	C₁₉×#106	C₂×C₄	1	4	yes	—
104	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
105	C₁₉×#103	—	2	2	no	—
106	C₁₉×#103	C₂×C₄	1	4	yes	—
107	C₁₉×#103	C₂×C₄	1	4	yes	—
108	C₁₉×#103	Q₈	1	4	yes	complemented
109	C₁₉×#97	—	2	2	no	—
110	C₁₉×#97	—	4	1	no	—
111	C₄×C₈×C₁₉	—	4	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	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₁₉×#95	D₄	1	1	yes	characteristic
122	C₁₉×#95	D₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	8	1	no	—
128	C₂×Q₈×C₁₉	—	8	1	no	—
129	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
130	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
131	C₂×Q₈×C₁₉	#41	1	2	yes	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
159	C₄⋊C₄×C₁₉	—	2	4	no	—
160	C₄⋊C₄×C₁₉	—	2	4	no	—
161	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	4	1	no	—
173	C₄⋊C₄×C₁₉	—	4	2	no	—
174	C₄⋊C₄×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	4	2	no	—
176	C₄⋊C₄×C₁₉	—	4	2	no	—
177	C₄⋊C₄×C₁₉	—	8	1	no	—
178	C₄⋊C₄×C₁₉	—	8	1	no	—
179	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
180	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
181	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
182	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
183	C₄²×C₁₉	—	2	4	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	4	2	no	—
189	C₄²×C₁₉	—	4	2	no	—
190	C₄²×C₁₉	—	4	2	no	—
191	C₄²×C₁₉	—	8	1	no	—
192	C₄²×C₁₉	—	8	1	no	—
193	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
194	C₄²×C₁₉	#41	1	2	yes	—
195	#22981	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₉	—	2	2	no	—
198	Q₈×C₁₉	—	2	2	no	—
199	Q₈×C₁₉	—	2	2	no	—
200	Q₈×C₁₉	—	8	4	no	—
201	Q₈×C₁₉	C₄×Q₈	1	4	yes	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	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	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₁₉	#137	1	2	yes	—
244	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×Q₈	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	H(5,𝔽₂)	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×#475	C₂×C₁₉	1	1	yes	characteristic
255	#2369	C₂×C₁₉	1	1	yes	characteristic
256	#2351	C₂×C₁₉	1	1	yes	characteristic
257	#1993	C₂×C₁₉	1	1	yes	characteristic
258	#1949	C₂×C₁₉	1	1	yes	characteristic
259	#1944	C₂×C₁₉	1	1	yes	characteristic
260	#1941	C₂×C₁₉	1	1	yes	characteristic
261	#1920	C₂×C₁₉	1	1	yes	characteristic
262	#1919	C₂×C₁₉	1	1	yes	characteristic
263	#1865	C₂×C₁₉	1	1	yes	characteristic
264	#1863	C₂×C₁₉	1	1	yes	characteristic
265	#1771	C₂×C₁₉	1	1	yes	characteristic
266	#1763	C₂×C₁₉	1	1	yes	characteristic
267	#1763	C₂×C₁₉	1	1	yes	characteristic
268	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
269	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₁₉	#546	1	1	yes	characteristic
271	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
272	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
273	C₂²×C₁₉	#575	1	1	yes	characteristic
274	C₂²×C₁₉	#577	1	1	yes	characteristic
275	C₂²×C₁₉	#577	1	1	yes	characteristic
276	C₄×C₁₉	—	2	4	no	—
277	C₄×C₁₉	—	2	2	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	2	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
291	C₄×C₁₉	#520	1	1	yes	characteristic
292	C₄×C₁₉	#552	1	1	yes	characteristic
293	C₄×C₁₉	#554	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
298	#475	C₄×C₁₉	1	8	yes	complemented
299	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
307	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
311	#391	—	2	1	no	—
312	#391	—	2	1	no	—
313	#389	—	2	1	no	—
314	#389	—	2	1	no	—
315	#389	—	2	1	no	—
316	#389	C₂²×C₁₉	1	1	yes	characteristic
317	#389	C₂²×C₁₉	1	1	yes	characteristic
318	#389	C₂²×C₁₉	1	1	yes	characteristic
319	#389	C₂²×C₁₉	1	1	yes	characteristic
320	#382	—	2	1	no	—
321	#382	C₂²×C₁₉	1	1	yes	characteristic
322	C₄×C₄⋊C₄	—	2	1	no	—
323	C₄×C₄⋊C₄	—	2	1	no	—
324	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
325	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
328	#340	C₂²×C₁₉	1	1	yes	characteristic
329	#340	C₂²×C₁₉	1	1	yes	characteristic
330	#340	C₂²×C₁₉	1	1	yes	characteristic
331	#340	C₂²×C₁₉	1	1	yes	characteristic
332	#340	C₂²×C₁₉	1	1	yes	characteristic
333	#340	C₂²×C₁₉	1	1	yes	characteristic
334	#340	C₂²×C₁₉	1	1	yes	characteristic
335	#340	C₂²×C₁₉	1	1	yes	characteristic
336	#336	C₂²×C₁₉	1	1	yes	characteristic
337	#336	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₁₉	#2360	1	1	yes	characteristic
339	C₂×C₁₉	C₄×#137	1	1	yes	characteristic
340	C₂×C₁₉	#2949	1	1	yes	characteristic
341	C₂×C₁₉	#3316	1	1	yes	characteristic
342	C₂×C₁₉	#3321	1	1	yes	characteristic
343	C₂×C₁₉	#3387	1	1	yes	characteristic
344	C₂×C₁₉	#3388	1	1	yes	characteristic
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	—	4	1	no	—
357	C₄×Q₈	—	4	1	no	—
358	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
367	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
385	#107	—	4	1	no	—
386	#106	—	4	1	no	—
387	#106	C₂×C₄×C₁₉	1	4	yes	—
388	#106	C₂×C₄×C₁₉	1	4	yes	—
389	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
390	#103	—	2	2	no	—
391	#103	C₂×C₄×C₁₉	1	4	yes	—
392	#103	C₂×C₄×C₁₉	1	4	yes	—
393	#103	Q₈×C₁₉	1	4	yes	complemented
394	#97	—	2	2	no	—
395	#97	—	4	1	no	—
396	C₄×C₈	—	4	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	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	D₄×C₁₉	1	1	yes	characteristic
407	#95	D₄×C₁₉	1	1	yes	characteristic
408	C₁₉	#22981	1	1	yes	characteristic, direct product factor, Sylow
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	8	1	no	—
414	C₂×Q₈	—	8	1	no	—
415	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
416	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
417	C₂×Q₈	#41×C₁₉	1	2	yes	—
418	C₂²×C₄	—	2	1	no	—
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	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
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	C₂⁴×C₁₉	1	1	yes	characteristic
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
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	C₂²×C₄×C₁₉	1	2	yes	—
443	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
444	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	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	—	4	1	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	8	1	no	—
464	C₄⋊C₄	—	8	1	no	—
465	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
466	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
467	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
468	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
469	C₄²	—	2	4	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	4	2	no	—
475	C₄²	—	4	2	no	—
476	C₄²	—	4	2	no	—
477	C₄²	—	8	1	no	—
478	C₄²	—	8	1	no	—
479	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
480	C₄²	#41×C₁₉	1	2	yes	—
481	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
482	Q₈	—	2	2	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	8	4	no	—
486	Q₈	C₄×Q₈×C₁₉	1	4	yes	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	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	C₄×D₄×C₁₉	1	2	yes	—
527	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
528	C₂×C₄	C₁₉×#137	1	2	yes	—
529	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
530	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
531	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
532	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
533	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
535	C₈	—	2	2	no	—
536	C₈	—	2	2	no	—
537	C₈	—	2	2	no	—
538	C₈	—	4	1	no	—
539	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
540	C₂²	C₁₉×#546	1	1	yes	characteristic
541	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
542	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
543	C₂²	C₁₉×#575	1	1	yes	characteristic
544	C₂²	C₁₉×#577	1	1	yes	characteristic
545	C₂²	C₁₉×#577	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
561	C₄	C₁₉×#520	1	1	yes	characteristic
562	C₄	C₁₉×#552	1	1	yes	characteristic
563	C₄	C₁₉×#554	1	1	yes	characteristic
564	C₂	C₁₉×#2360	1	1	yes	characteristic
565	C₂	C₄×C₁₉×#137	1	1	yes	characteristic
566	C₂	C₁₉×#2949	1	1	yes	characteristic
567	C₂	C₁₉×#3316	1	1	yes	characteristic
568	C₂	C₁₉×#3321	1	1	yes	characteristic
569	C₂	C₁₉×#3387	1	1	yes	characteristic
570	C₂	C₁₉×#3388	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
20. C₁₉×#475	C₄	semidirect
108. C₁₉×#103	Q₈	semidirect
195. #22981	C₁₉	direct (N × H)
298. #475	C₄×C₁₉	semidirect
393. #103	Q₈×C₁₉	semidirect
408. C₁₉	#22981	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×#475	2
C₁₉×#2369	2
C₁₉×#2351	2
C₁₉×#1993	2
C₁₉×#1949	2
C₁₉×#1944	2
C₁₉×#1941	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1865	2
C₁₉×#1863	2
C₁₉×#1771	2
C₁₉×#1763	2
C₄×C₁₉×#103	2
#22981	19

Subgroups — C19×#22981 #18028940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22981 #18028940