Subgroups — C₁₉×#21190 #18027149

Order 4864.

2010 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#407	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1955	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1954	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₉	—	2	4	no	—
12	C₂×C₄×D₄×C₁₉	—	2	4	no	—
13	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#423	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₁₉×#407	—	2	16	no	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	16	yes	complemented
25	C₄×M₁₆×C₁₉	—	2	4	no	—
26	C₂×C₁₉×#97	C₂²	1	2	yes	complemented
27	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
28	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×D₄×C₁₉	—	2	8	no	—
30	C₂²×D₄×C₁₉	—	2	4	no	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₉	—	2	8	no	—
34	C₂³×C₄×C₁₉	—	2	4	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	8	no	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₁₉	—	2	4	no	—
44	C₂×M₁₆×C₁₉	—	2	4	no	—
45	C₂×M₁₆×C₁₉	—	2	8	no	—
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
48	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
50	C₄×D₄×C₁₉	—	2	8	no	—
51	C₄×D₄×C₁₉	—	2	8	no	—
52	C₄×D₄×C₁₉	—	2	4	no	—
53	C₄×D₄×C₁₉	—	2	4	no	—
54	C₄×D₄×C₁₉	—	2	4	no	—
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	D₄	1	4	yes	—
65	C₂×C₄²×C₁₉	D₄	1	4	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×C₄⋊C₈	—	2	4	no	—
69	C₁₉×C₄⋊C₈	—	2	4	no	—
70	C₁₉×C₂²⋊C₈	—	2	32	no	—
71	C₁₉×#97	—	2	4	no	—
72	C₄×C₈×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	8	no	—
75	C₂⁴×C₁₉	—	2	8	no	—
76	C₂⁴×C₁₉	—	4	4	no	—
77	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
78	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₉	—	2	32	no	—
80	C₂×D₄×C₁₉	—	2	8	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	4	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	M₁₆	1	8	yes	complemented
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	8	no	—
88	C₂²×C₄×C₁₉	—	2	8	no	—
89	C₂²×C₄×C₁₉	—	2	16	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	16	no	—
96	C₂²×C₄×C₁₉	—	4	8	no	—
97	C₂²×C₄×C₁₉	—	4	8	no	—
98	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₉	#41	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₉	—	2	16	no	—
112	M₁₆×C₁₉	—	4	8	no	—
113	C₂×C₈×C₁₉	—	2	4	no	—
114	C₂×C₈×C₁₉	—	2	4	no	—
115	C₂×C₈×C₁₉	—	2	8	no	—
116	C₂×C₈×C₁₉	—	2	4	no	—
117	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	complemented
118	C₄⋊C₄×C₁₉	—	2	4	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₉	—	2	8	no	—
122	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
123	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₁₉	C₂×D₄	1	2	yes	—
125	C₄²×C₁₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₉	C₂×D₄	1	2	yes	—
127	C₄²×C₁₉	C₂×D₄	1	2	yes	—
128	#21190	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	16	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	8	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	4	32	no	—
137	C₂³×C₁₉	—	4	8	no	—
138	C₂³×C₁₉	—	4	8	no	—
139	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₁₉	C₄×D₄	1	4	yes	—
141	C₂³×C₁₉	C₂×M₁₆	1	8	yes	—
142	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
143	D₄×C₁₉	—	2	16	no	—
144	D₄×C₁₉	—	2	16	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	8	no	—
151	C₂×C₄×C₁₉	—	4	4	no	—
152	C₂×C₄×C₁₉	—	4	8	no	—
153	C₂×C₄×C₁₉	—	4	8	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	16	no	—
157	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₁₉	#121	1	8	yes	—
164	C₂×C₄×C₁₉	#124	1	4	yes	—
165	C₂×C₄×C₁₉	#127	1	4	yes	—
166	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
167	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
171	C₈×C₁₉	—	2	8	no	—
172	C₈×C₁₉	—	4	4	no	—
173	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
174	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
175	C₂×#407	C₂×C₁₉	1	4	yes	complemented
176	C₂×C₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#1955	C₂×C₁₉	1	4	yes	complemented
178	#1954	C₂×C₁₉	1	4	yes	complemented
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	8	no	—
182	C₂²×C₁₉	—	2	8	no	—
183	C₂²×C₁₉	—	2	16	no	—
184	C₂²×C₁₉	—	4	32	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	8	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	#390	1	4	yes	—
189	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
191	C₂²×C₁₉	C₂²×M₁₆	1	2	yes	—
192	C₂²×C₁₉	#568	1	2	yes	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	4	4	no	—
197	C₄×C₁₉	#390	1	4	yes	—
198	C₄×C₁₉	#407	1	4	yes	complemented
199	C₄×C₁₉	C₂×#121	1	2	yes	—
200	C₄×C₁₉	C₂×#124	1	1	yes	characteristic
201	C₄×C₁₉	C₂×#127	1	1	yes	characteristic
202	C₂³×D₄	C₄×C₁₉	1	1	yes	characteristic
203	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
204	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
205	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
206	C₂×C₄×D₄	—	2	4	no	—
207	C₂×C₄×D₄	—	2	4	no	—
208	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
209	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
212	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
213	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
214	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
215	#423	—	2	4	no	—
216	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
217	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
218	#407	—	2	16	no	—
219	C₂×C₂²⋊C₈	C₂²×C₁₉	1	16	yes	complemented
220	C₄×M₁₆	—	2	4	no	—
221	C₂×#97	C₂²×C₁₉	1	2	yes	complemented
222	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	complemented
223	C₂×C₁₉	—	2	4	no	—
224	C₂×C₁₉	—	4	8	no	—
225	C₂×C₁₉	C₂×#390	1	1	yes	characteristic
226	C₂×C₁₉	C₂×#407	1	1	yes	characteristic
227	C₂×C₁₉	#2879	1	1	yes	characteristic
228	C₂×C₁₉	D₄×M₁₆	1	4	yes	—
229	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
230	C₂²×D₄	—	2	8	no	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
233	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
234	C₂³×C₄	—	2	4	no	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	8	no	—
237	C₂³×C₄	—	2	8	no	—
238	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
239	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
240	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
243	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	8	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
249	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
250	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
251	C₄×D₄	—	2	8	no	—
252	C₄×D₄	—	2	8	no	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	8	no	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
263	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₁₉	1	4	yes	—
266	C₂×C₄²	D₄×C₁₉	1	4	yes	—
267	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
269	C₄⋊C₈	—	2	4	no	—
270	C₄⋊C₈	—	2	4	no	—
271	C₂²⋊C₈	—	2	32	no	—
272	#97	—	2	4	no	—
273	C₄×C₈	—	2	4	no	—
274	C₁₉	#21190	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	8	no	—
278	C₂⁴	—	4	4	no	—
279	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
280	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
281	C₂×D₄	—	2	32	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	M₁₆×C₁₉	1	8	yes	complemented
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	16	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	16	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
311	C₂²×C₄	#41×C₁₉	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
313	M₁₆	—	2	16	no	—
314	M₁₆	—	4	8	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	8	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	complemented
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
325	C₄²	C₂²⋊C₄×C₁₉	1	4	yes	—
326	C₄²	C₂×D₄×C₁₉	1	2	yes	—
327	C₄²	C₂×D₄×C₁₉	1	2	yes	—
328	C₄²	C₂×D₄×C₁₉	1	2	yes	—
329	C₄²	C₂×D₄×C₁₉	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	16	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	4	32	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	8	no	—
340	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
341	C₂³	C₄×D₄×C₁₉	1	4	yes	—
342	C₂³	C₂×M₁₆×C₁₉	1	8	yes	—
343	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
344	D₄	—	2	16	no	—
345	D₄	—	2	16	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	16	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
364	C₂×C₄	C₁₉×#121	1	8	yes	—
365	C₂×C₄	C₁₉×#124	1	4	yes	—
366	C₂×C₄	C₁₉×#127	1	4	yes	—
367	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	16	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	4	32	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	C₁₉×#390	1	4	yes	—
384	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
385	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
386	C₂²	C₂²×M₁₆×C₁₉	1	2	yes	—
387	C₂²	C₁₉×#568	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	C₁₉×#390	1	4	yes	—
393	C₄	C₁₉×#407	1	4	yes	complemented
394	C₄	C₂×C₁₉×#121	1	2	yes	—
395	C₄	C₂×C₁₉×#124	1	1	yes	characteristic
396	C₄	C₂×C₁₉×#127	1	1	yes	characteristic
397	C₂	—	2	4	no	—
398	C₂	—	4	8	no	—
399	C₂	C₂×C₁₉×#390	1	1	yes	characteristic
400	C₂	C₂×C₁₉×#407	1	1	yes	characteristic
401	C₂	C₁₉×#2879	1	1	yes	characteristic
402	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	C₂³×D₄×C₁₉	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
3. C₂×C₁₉×#407	C₂	semidirect
4. C₂×C₄×M₁₆×C₁₉	C₂	semidirect
5. C₁₉×#1955	C₂	semidirect
6. C₁₉×#1954	C₂	semidirect
21. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
22. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
24. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
26. C₂×C₁₉×#97	C₂²	semidirect
27. C₂×C₄×C₈×C₁₉	C₂²	semidirect
47. C₂×M₁₆×C₁₉	D₄	semidirect
84. C₂×D₄×C₁₉	M₁₆	semidirect
117. C₂×C₈×C₁₉	C₂×D₄	semidirect
128. #21190	C₁₉	direct (N × H)
174. C₂×#423	C₂×C₁₉	semidirect
175. C₂×#407	C₂×C₁₉	semidirect
176. C₂×C₄×M₁₆	C₂×C₁₉	semidirect
177. #1955	C₂×C₁₉	semidirect
178. #1954	C₂×C₁₉	semidirect
198. C₄×C₁₉	#407	semidirect
216. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
217. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
219. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
221. C₂×#97	C₂²×C₁₉	semidirect
222. C₂×C₄×C₈	C₂²×C₁₉	semidirect
248. C₂×M₁₆	D₄×C₁₉	semidirect
274. C₁₉	#21190	direct (N × H)
286. C₂×D₄	M₁₆×C₁₉	semidirect
319. C₂×C₈	C₂×D₄×C₁₉	semidirect
393. C₄	C₁₉×#407	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₉	2
C₂×C₁₉×#423	2
C₂×C₁₉×#407	2
C₂×C₄×M₁₆×C₁₉	2
C₁₉×#1955	2
C₁₉×#1954	2
#21190	19

Subgroups — C19×#21190 #18027149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21190 #18027149