Subgroups — C₁₉×#20837 #18026796

Order 4864.

1646 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1851	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1850	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1728	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	—	2	4	no	—
10	C₂²×M₁₆×C₁₉	—	2	8	no	—
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#423	—	2	8	no	—
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	8	yes	complemented
20	C₁₉×#407	—	2	4	no	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₄×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
26	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₄	1	2	yes	—
29	C₁₉×#336	C₂²	1	8	yes	complemented
30	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	4	no	—
32	C₂³×C₄×C₁₉	—	2	4	no	—
33	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	4	yes	—
38	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₁₉	—	2	32	no	—
43	C₂×M₁₆×C₁₉	—	2	4	no	—
44	C₂×M₁₆×C₁₉	—	2	4	no	—
45	C₂×M₁₆×C₁₉	—	2	4	no	—
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	—	2	8	no	—
51	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
52	C₂²×C₈×C₁₉	—	2	4	no	—
53	C₂²×C₈×C₁₉	—	2	8	no	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₁₉	—	2	4	no	—
62	C₂×C₄²×C₁₉	—	2	4	no	—
63	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
66	C₁₉×C₄⋊C₈	—	2	16	no	—
67	C₁₉×C₂²⋊C₈	—	2	4	no	—
68	C₁₉×C₂²⋊C₈	—	2	4	no	—
69	C₁₉×#95	C₂×C₄	1	2	yes	—
70	C₁₉×#95	C₂×C₄	1	4	yes	—
71	C₁₉×#95	C₂×C₄	1	2	yes	—
72	C₂⁴×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	4	2	no	—
75	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
76	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	8	no	—
83	C₂²×C₄×C₁₉	—	2	16	no	—
84	C₂²×C₄×C₁₉	—	2	8	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	8	no	—
91	C₂²×C₄×C₁₉	—	4	4	no	—
92	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₉	#41	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₁₉	—	2	16	no	—
110	M₁₆×C₁₉	—	2	16	no	—
111	M₁₆×C₁₉	—	4	4	no	—
112	M₁₆×C₁₉	—	4	4	no	—
113	C₂×C₈×C₁₉	—	2	16	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	2	4	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	4	no	—
119	C₂×C₈×C₁₉	—	2	4	no	—
120	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
121	C₂²⋊C₄×C₁₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₉	—	2	8	no	—
123	C₂²⋊C₄×C₁₉	M₁₆	1	8	yes	complemented
124	C₄²×C₁₉	—	2	4	no	—
125	C₄²×C₁₉	—	2	4	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	C₄²×C₁₉	—	2	4	no	—
128	#20837	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	8	no	—
137	C₂³×C₁₉	—	2	8	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	—	4	16	no	—
140	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
141	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
142	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
143	C₂³×C₁₉	C₄×D₄	1	4	yes	—
144	C₂³×C₁₉	C₂×M₁₆	1	4	yes	—
145	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	8	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	8	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	16	no	—
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
167	C₂×C₄×C₁₉	#120	1	4	yes	—
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
169	C₂×C₄×C₁₉	#123	1	4	yes	—
170	C₂×C₄×C₁₉	C₂×M₁₆	1	8	yes	complemented
171	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
175	C₈×C₁₉	—	2	8	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic
179	C₂×#423	C₂×C₁₉	1	2	yes	complemented
180	C₂×#407	C₂×C₁₉	1	1	yes	characteristic
181	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
182	#1851	C₂×C₁₉	1	4	yes	complemented
183	#1850	C₂×C₁₉	1	4	yes	complemented
184	#1728	C₂×C₁₉	1	2	yes	complemented
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	8	no	—
189	C₂²×C₁₉	—	2	8	no	—
190	C₂²×C₁₉	—	2	2	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	2	no	—
194	C₂²×C₁₉	—	4	16	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	#385	1	4	yes	—
197	C₂²×C₁₉	#423	1	4	yes	complemented
198	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
200	C₂²×C₁₉	C₂²×M₁₆	1	2	yes	—
201	C₂²×C₁₉	#568	1	2	yes	—
202	C₄×C₁₉	—	2	8	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	2	2	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	#385	1	4	yes	—
207	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
208	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
209	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
210	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
211	C₂²×M₁₆	—	2	4	no	—
212	C₂²×M₁₆	—	2	8	no	—
213	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
214	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
217	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
219	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
220	#423	—	2	8	no	—
221	C₂×C₄⋊C₈	C₂²×C₁₉	1	8	yes	complemented
222	#407	—	2	4	no	—
223	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
225	C₄×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
227	C₄×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
228	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
230	C₂×#95	C₄×C₁₉	1	2	yes	—
231	#336	C₂²×C₁₉	1	8	yes	complemented
232	C₂×C₁₉	—	2	4	no	—
233	C₂×C₁₉	—	2	4	no	—
234	C₂×C₁₉	—	4	2	no	—
235	C₂×C₁₉	C₂×#385	1	1	yes	characteristic
236	C₂×C₁₉	C₂×#423	1	1	yes	characteristic
237	C₂×C₁₉	#2905	1	1	yes	characteristic
238	C₂×C₁₉	D₄×M₁₆	1	4	yes	—
239	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	—	2	4	no	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
243	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
244	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
245	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₁₉	1	4	yes	—
247	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
248	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×M₁₆	—	2	32	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	2	8	no	—
260	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	—	2	8	no	—
263	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
264	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
266	C₂×C₂²⋊C₄	—	2	8	no	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
270	C₂×C₄²	—	2	4	no	—
271	C₂×C₄²	—	2	4	no	—
272	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
274	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
275	C₄⋊C₈	—	2	16	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	C₂²⋊C₈	—	2	4	no	—
278	#95	C₂×C₄×C₁₉	1	2	yes	—
279	#95	C₂×C₄×C₁₉	1	4	yes	—
280	#95	C₂×C₄×C₁₉	1	2	yes	—
281	C₁₉	#20837	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	4	2	no	—
285	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
286	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
287	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
288	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	16	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
303	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
304	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
314	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
316	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
317	C₂²×C₄	#41×C₁₉	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
319	M₁₆	—	2	16	no	—
320	M₁₆	—	2	16	no	—
321	M₁₆	—	4	4	no	—
322	M₁₆	—	4	4	no	—
323	C₂×C₈	—	2	16	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	M₁₆×C₁₉	1	8	yes	complemented
334	C₄²	—	2	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	4	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	16	no	—
349	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
350	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
351	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
352	C₂³	C₄×D₄×C₁₉	1	4	yes	—
353	C₂³	C₂×M₁₆×C₁₉	1	4	yes	—
354	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
373	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
374	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
375	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
376	C₂×C₄	C₁₉×#120	1	4	yes	—
377	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
378	C₂×C₄	C₁₉×#123	1	4	yes	—
379	C₂×C₄	C₂×M₁₆×C₁₉	1	8	yes	complemented
380	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
384	C₈	—	2	8	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	4	16	no	—
397	C₂²	—	4	4	no	—
398	C₂²	C₁₉×#385	1	4	yes	—
399	C₂²	C₁₉×#423	1	4	yes	complemented
400	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
402	C₂²	C₂²×M₁₆×C₁₉	1	2	yes	—
403	C₂²	C₁₉×#568	1	2	yes	—
404	C₄	—	2	8	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	4	no	—
408	C₄	C₁₉×#385	1	4	yes	—
409	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
410	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
411	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
412	C₂	—	2	4	no	—
413	C₂	—	2	4	no	—
414	C₂	—	4	2	no	—
415	C₂	C₂×C₁₉×#385	1	1	yes	characteristic
416	C₂	C₂×C₁₉×#423	1	1	yes	characteristic
417	C₂	C₁₉×#2905	1	1	yes	characteristic
418	C₂	D₄×M₁₆×C₁₉	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂⁵×C₁₉	C₂×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
2. C₂×C₁₉×#423	C₂	semidirect
5. C₁₉×#1851	C₂	semidirect
6. C₁₉×#1850	C₂	semidirect
7. C₁₉×#1728	C₂	semidirect
19. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
29. C₁₉×#336	C₂²	semidirect
123. C₂²⋊C₄×C₁₉	M₁₆	semidirect
128. #20837	C₁₉	direct (N × H)
170. C₂×C₄×C₁₉	C₂×M₁₆	semidirect
179. C₂×#423	C₂×C₁₉	semidirect
182. #1851	C₂×C₁₉	semidirect
183. #1850	C₂×C₁₉	semidirect
184. #1728	C₂×C₁₉	semidirect
197. C₂²×C₁₉	#423	semidirect
221. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
231. #336	C₂²×C₁₉	semidirect
281. C₁₉	#20837	direct (N × H)
333. C₂²⋊C₄	M₁₆×C₁₉	semidirect
379. C₂×C₄	C₂×M₁₆×C₁₉	semidirect
399. C₂²	C₁₉×#423	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂×C₁₉×#423	2
C₂×C₁₉×#407	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1851	2
C₁₉×#1850	2
C₁₉×#1728	2
#20837	19

Subgroups — C19×#20837 #18026796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20837 #18026796