Subgroups — C₁₉×#22301 #18028260

Order 4864.

654 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1940	C₂	1	2	yes	maximal
3	C₁₉×#1939	C₂	1	2	yes	maximal
4	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1939	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1917	C₂	1	2	yes	maximal
7	C₁₉×#1916	C₂	1	2	yes	maximal
8	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1770	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₉×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#389	C₄	1	1	yes	characteristic
24	C₁₉×#389	C₄	1	1	yes	characteristic
25	C₁₉×#387	C₄	1	2	yes	—
26	C₁₉×#387	C₄	1	2	yes	—
27	C₁₉×#382	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₄³×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#336	C₂²	1	1	yes	characteristic
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	2	yes	—
37	C₁₉×#336	C₂²	1	1	yes	characteristic
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₁₉×#336	C₂²	1	1	yes	characteristic
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×#125	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×C₄⋊C₈	—	2	2	no	—
66	C₁₉×C₄⋊C₈	—	2	2	no	—
67	C₁₉×C₄⋊C₈	—	4	2	no	—
68	C₁₉×C₄⋊C₈	—	4	2	no	—
69	C₁₉×C₄⋊C₈	—	4	2	no	—
70	C₁₉×C₄⋊C₈	—	4	2	no	—
71	C₁₉×#97	—	4	2	no	—
72	C₄×C₈×C₁₉	—	2	2	no	—
73	C₄×C₈×C₁₉	—	4	2	no	—
74	C₄×C₈×C₁₉	Q₈	1	4	yes	—
75	C₁₉×#95	C₂×C₄	1	2	yes	—
76	C₁₉×#95	C₂×C₄	1	2	yes	—
77	C₁₉×#95	C₂×C₄	1	2	yes	—
78	C₁₉×#95	C₂×C₄	1	2	yes	—
79	C₁₉×#95	C₂×C₄	1	2	yes	—
80	C₁₉×#95	C₂×C₄	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	2	1	no	—
95	C₂×C₈×C₁₉	—	2	1	no	—
96	C₂×C₈×C₁₉	—	2	1	no	—
97	C₂×C₈×C₁₉	—	2	1	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	1	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
109	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
110	C₄⋊C₄×C₁₉	—	2	4	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	—	2	4	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	M₁₆	1	4	yes	—
118	C₄²×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	2	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	2	2	no	—
124	C₄²×C₁₉	—	2	1	no	—
125	C₄²×C₁₉	—	2	1	no	—
126	C₄²×C₁₉	—	2	1	no	—
127	C₄²×C₁₉	—	2	1	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
131	C₄²×C₁₉	#41	1	2	yes	—
132	#22301	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
158	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
159	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
160	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₁₉	#131	1	2	yes	—
162	C₂×C₄×C₁₉	#131	1	2	yes	—
163	C₂×C₄×C₁₉	#131	1	2	yes	—
164	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
170	C₈×C₁₉	—	2	2	no	—
171	C₈×C₁₉	—	2	2	no	—
172	C₈×C₁₉	—	4	1	no	—
173	C₈×C₁₉	—	4	2	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₈×C₁₉	—	4	1	no	—
176	C₄×#125	C₂×C₁₉	1	1	yes	characteristic
177	#1940	C₂×C₁₉	1	2	yes	—
178	#1939	C₂×C₁₉	1	1	yes	characteristic
179	#1939	C₂×C₁₉	1	1	yes	characteristic
180	#1939	C₂×C₁₉	1	2	yes	—
181	#1917	C₂×C₁₉	1	2	yes	—
182	#1916	C₂×C₁₉	1	2	yes	—
183	#1842	C₂×C₁₉	1	1	yes	characteristic
184	#1770	C₂×C₁₉	1	1	yes	characteristic
185	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
186	#1744	C₂×C₁₉	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
188	C₂²×C₁₉	#520	1	1	yes	characteristic
189	C₂²×C₁₉	#520	1	1	yes	characteristic
190	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	4	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	#446	1	4	yes	—
204	C₄×C₁₉	#540	1	1	yes	characteristic
205	C₄×C₁₉	#541	1	1	yes	characteristic
206	C₄×C₁₉	#544	1	1	yes	characteristic
207	C₄×C₁₉	#544	1	1	yes	characteristic
208	C₂×#125	C₄×C₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
215	C₂×#97	C₂²×C₁₉	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
219	#389	C₄×C₁₉	1	1	yes	characteristic
220	#389	C₄×C₁₉	1	1	yes	characteristic
221	#387	C₄×C₁₉	1	2	yes	—
222	#387	C₄×C₁₉	1	2	yes	—
223	#382	C₄×C₁₉	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
225	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
228	C₄³	C₂²×C₁₉	1	1	yes	characteristic
229	#336	C₂²×C₁₉	1	1	yes	characteristic
230	#336	C₂²×C₁₉	1	2	yes	—
231	#336	C₂²×C₁₉	1	2	yes	—
232	#336	C₂²×C₁₉	1	2	yes	—
233	#336	C₂²×C₁₉	1	1	yes	characteristic
234	#336	C₂²×C₁₉	1	2	yes	—
235	#336	C₂²×C₁₉	1	1	yes	characteristic
236	#336	C₂²×C₁₉	1	1	yes	characteristic
237	C₂×C₁₉	#2330	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#446	1	1	yes	characteristic
239	C₂×C₁₉	#2960	1	1	yes	characteristic
240	C₂×C₁₉	#2990	1	1	yes	characteristic
241	C₂×C₁₉	#2991	1	1	yes	characteristic
242	C₂×C₁₉	#2994	1	1	yes	characteristic
243	C₂×C₁₉	#2994	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
250	#125	—	2	4	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	4	2	no	—
271	C₄⋊C₈	—	4	2	no	—
272	C₄⋊C₈	—	4	2	no	—
273	C₄⋊C₈	—	4	2	no	—
274	#97	—	4	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	4	2	no	—
277	C₄×C₈	Q₈×C₁₉	1	4	yes	—
278	#95	C₂×C₄×C₁₉	1	2	yes	—
279	#95	C₂×C₄×C₁₉	1	2	yes	—
280	#95	C₂×C₄×C₁₉	1	2	yes	—
281	#95	C₂×C₄×C₁₉	1	2	yes	—
282	#95	C₂×C₄×C₁₉	1	2	yes	—
283	#95	C₂×C₄×C₁₉	1	2	yes	—
284	C₁₉	#22301	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
313	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	M₁₆×C₁₉	1	4	yes	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
335	C₄²	#41×C₁₉	1	2	yes	—
336	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
361	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
362	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
363	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
364	C₂×C₄	C₁₉×#131	1	2	yes	—
365	C₂×C₄	C₁₉×#131	1	2	yes	—
366	C₂×C₄	C₁₉×#131	1	2	yes	—
367	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
369	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
372	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
373	C₈	—	2	2	no	—
374	C₈	—	2	2	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
380	C₂²	C₁₉×#520	1	1	yes	characteristic
381	C₂²	C₁₉×#520	1	1	yes	characteristic
382	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
383	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
384	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
385	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	C₁₉×#446	1	4	yes	—
396	C₄	C₁₉×#540	1	1	yes	characteristic
397	C₄	C₁₉×#541	1	1	yes	characteristic
398	C₄	C₁₉×#544	1	1	yes	characteristic
399	C₄	C₁₉×#544	1	1	yes	characteristic
400	C₂	C₁₉×#2330	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#446	1	1	yes	characteristic
402	C₂	C₁₉×#2960	1	1	yes	characteristic
403	C₂	C₁₉×#2990	1	1	yes	characteristic
404	C₂	C₁₉×#2991	1	1	yes	characteristic
405	C₂	C₁₉×#2994	1	1	yes	characteristic
406	C₂	C₁₉×#2994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle, prime radical	C₂³×C₁₉	C₂³×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
132. #22301	C₁₉	direct (N × H)
284. C₁₉	#22301	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×#125	2
C₁₉×#1940	2
C₁₉×#1939	2
C₁₉×#1917	2
C₁₉×#1916	2
C₁₉×#1842	2
C₁₉×#1770	2
C₈×C₄⋊C₄×C₁₉	2
C₁₉×#1744	2
#22301	19

Subgroups — C19×#22301 #18028260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22301 #18028260