Subgroups — C₂×C₁₉×#1742 #18026316

Order 4864.

2190 conjugacy classes of subgroups.

The subgroup lattice has 374 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	2	yes	maximal
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1742	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₉×#343	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₁₉	—	2	8	no	—
7	C₂²×M₁₆×C₁₉	—	2	2	no	—
8	C₂²×M₁₆×C₁₉	—	2	4	no	—
9	C₂²×M₁₆×C₁₉	C₄	1	16	yes	complemented
10	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
11	C₂²×M₁₆×C₁₉	C₂²	1	8	yes	—
12	C₂³×C₈×C₁₉	—	2	2	no	—
13	C₂×C₁₉×#117	—	2	2	no	—
14	C₂×C₁₉×#117	—	2	4	no	—
15	C₂×C₁₉×#117	—	2	2	no	—
16	C₂×C₁₉×#117	C₄	1	4	yes	—
17	C₂×C₁₉×#117	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₄	1	2	yes	—
21	C₁₉×#343	C₂²	1	16	yes	complemented
22	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
27	C₂³×C₄×C₁₉	D₄	1	4	yes	—
28	C₂³×C₄×C₁₉	D₄	1	2	yes	—
29	C₂³×C₄×C₁₉	D₄	1	4	yes	—
30	C₂³×C₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
34	C₂×M₁₆×C₁₉	—	2	16	no	—
35	C₂×M₁₆×C₁₉	—	2	32	no	—
36	C₂×M₁₆×C₁₉	—	2	8	no	—
37	C₂×M₁₆×C₁₉	—	2	16	no	—
38	C₂×M₁₆×C₁₉	—	2	4	no	—
39	C₂×M₁₆×C₁₉	—	2	8	no	—
40	C₂×M₁₆×C₁₉	C₂×C₄	1	16	yes	—
41	C₂×M₁₆×C₁₉	C₂×C₄	1	32	yes	complemented
42	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
43	C₂²×C₈×C₁₉	—	2	16	no	—
44	C₂²×C₈×C₁₉	—	2	4	no	—
45	C₂²×C₈×C₁₉	—	2	8	no	—
46	C₁₉×#117	—	2	8	no	—
47	C₁₉×#117	—	2	8	no	—
48	C₁₉×#117	—	2	8	no	—
49	C₁₉×#117	—	2	8	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₁₉	—	2	2	no	—
58	C₂×C₄²×C₁₉	—	2	4	no	—
59	C₂×C₄²×C₁₉	—	2	2	no	—
60	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
61	C₂⁴×C₁₉	—	4	4	no	—
62	C₂⁴×C₁₉	C₄²	1	4	yes	—
63	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
66	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₁₉	—	2	4	no	—
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	—	4	8	no	—
71	C₂²×C₄×C₁₉	C₄²	1	8	yes	—
72	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	16	yes	—
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	8	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
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	4	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₁₉	—	2	16	no	—
101	M₁₆×C₁₉	—	2	32	no	—
102	M₁₆×C₁₉	—	2	8	no	—
103	M₁₆×C₁₉	C₂²×C₄	1	16	yes	—
104	C₂×C₈×C₁₉	—	2	16	no	—
105	C₂×C₈×C₁₉	—	2	32	no	—
106	C₂×C₈×C₁₉	—	2	8	no	—
107	C₄⋊C₄×C₁₉	—	2	8	no	—
108	C₄⋊C₄×C₁₉	—	2	8	no	—
109	C₂²⋊C₄×C₁₉	—	2	16	no	—
110	C₄²×C₁₉	—	2	8	no	—
111	C₄²×C₁₉	—	2	8	no	—
112	C₂×#1742	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₉	—	2	4	no	—
114	C₂³×C₁₉	—	2	8	no	—
115	C₂³×C₁₉	—	4	8	no	—
116	C₂³×C₁₉	—	4	4	no	—
117	C₂³×C₁₉	—	4	8	no	—
118	C₂³×C₁₉	—	4	4	no	—
119	C₂³×C₁₉	#95	1	8	yes	—
120	C₂³×C₁₉	#95	1	8	yes	—
121	C₂³×C₁₉	C₂×C₄²	1	2	yes	—
122	C₂³×C₁₉	C₂×C₄²	1	4	yes	—
123	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
124	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
127	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
128	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	4	8	no	—
131	C₂×C₄×C₁₉	—	4	8	no	—
132	C₂×C₄×C₁₉	—	4	8	no	—
133	C₂×C₄×C₁₉	#95	1	8	yes	—
134	C₂×C₄×C₁₉	#95	1	16	yes	—
135	C₂×C₄×C₁₉	#95	1	16	yes	—
136	C₂×C₄×C₁₉	#95	1	4	yes	—
137	C₂×C₄×C₁₉	#95	1	4	yes	—
138	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
139	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
141	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
143	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
144	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
148	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
152	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
157	C₈×C₁₉	—	2	16	no	—
158	C₂³×M₁₆	C₂×C₁₉	1	2	yes	—
159	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
160	#1742	C₂×C₁₉	1	8	yes	direct product factor
161	C₂×#343	C₂×C₁₉	1	4	yes	complemented
162	C₂²×C₁₉	—	2	2	no	—
163	C₂²×C₁₉	—	2	2	no	—
164	C₂²×C₁₉	—	2	8	no	—
165	C₂²×C₁₉	—	2	16	no	—
166	C₂²×C₁₉	—	2	4	no	—
167	C₂²×C₁₉	—	2	4	no	—
168	C₂²×C₁₉	—	4	8	no	—
169	C₂²×C₁₉	—	4	4	no	—
170	C₂²×C₁₉	—	4	4	no	—
171	C₂²×C₁₉	C₂×#95	1	8	yes	—
172	C₂²×C₁₉	C₂×#95	1	2	yes	—
173	C₂²×C₁₉	C₂×#95	1	2	yes	—
174	C₂²×C₁₉	#413	1	4	yes	—
175	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
176	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₄×C₁₉	—	4	8	no	—
179	C₄×C₁₉	C₂×#95	1	4	yes	—
180	C₄×C₁₉	C₂×#95	1	4	yes	—
181	C₄×C₁₉	C₂×#95	1	4	yes	—
182	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
183	C₄×C₁₉	C₂²×C₄⋊C₄	1	2	yes	—
184	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
185	C₂²×M₁₆	—	2	8	no	—
186	C₂²×M₁₆	—	2	2	no	—
187	C₂²×M₁₆	—	2	4	no	—
188	C₂²×M₁₆	C₄×C₁₉	1	16	yes	complemented
189	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
190	C₂²×M₁₆	C₂²×C₁₉	1	8	yes	—
191	C₂³×C₈	—	2	2	no	—
192	C₂×#117	—	2	2	no	—
193	C₂×#117	—	2	2	no	—
194	C₂×#117	—	2	4	no	—
195	C₂×#117	C₄×C₁₉	1	4	yes	—
196	C₂×#117	C₂²×C₁₉	1	4	yes	—
197	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
198	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
199	C₂²×C₄²	C₄×C₁₉	1	2	yes	—
200	#343	C₂²×C₁₉	1	16	yes	complemented
201	C₂×C₁₉	—	2	1	no	—
202	C₂×C₁₉	—	2	2	no	—
203	C₂×C₁₉	—	2	8	no	—
204	C₂×C₁₉	—	2	1	no	—
205	C₂×C₁₉	#1742	1	4	yes	direct product factor
206	C₂×C₁₉	C₂²×#95	1	1	yes	characteristic
207	C₂×C₁₉	C₂×#413	1	2	yes	—
208	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
209	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
210	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
211	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
212	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
213	C₂³×C₄	D₄×C₁₉	1	4	yes	—
214	C₂³×C₄	D₄×C₁₉	1	2	yes	—
215	C₂³×C₄	D₄×C₁₉	1	2	yes	—
216	C₂³×C₄	D₄×C₁₉	1	4	yes	—
217	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
218	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
220	C₂×M₁₆	—	2	16	no	—
221	C₂×M₁₆	—	2	32	no	—
222	C₂×M₁₆	—	2	8	no	—
223	C₂×M₁₆	—	2	16	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	2	8	no	—
226	C₂×M₁₆	C₂×C₄×C₁₉	1	16	yes	—
227	C₂×M₁₆	C₂×C₄×C₁₉	1	32	yes	complemented
228	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
229	C₂²×C₈	—	2	16	no	—
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	—	2	8	no	—
232	#117	—	2	8	no	—
233	#117	—	2	8	no	—
234	#117	—	2	8	no	—
235	#117	—	2	8	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
247	C₁₉	C₂×#1742	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	—	4	4	no	—
249	C₂⁴	C₄²×C₁₉	1	4	yes	—
250	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
251	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
252	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
253	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
254	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	8	no	—
258	C₂²×C₄	C₄²×C₁₉	1	4	yes	—
259	C₂²×C₄	C₄²×C₁₉	1	8	yes	—
260	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
261	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
262	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	—
263	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
264	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
266	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
267	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
269	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
270	C₂²×C₄	C₄⋊C₄×C₁₉	1	16	yes	—
271	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
272	C₂²×C₄	C₄⋊C₄×C₁₉	1	8	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
278	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
283	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
284	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
285	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
287	M₁₆	—	2	16	no	—
288	M₁₆	—	2	32	no	—
289	M₁₆	—	2	8	no	—
290	M₁₆	C₂²×C₄×C₁₉	1	16	yes	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	—	2	32	no	—
293	C₂×C₈	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	4	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	4	no	—
305	C₂³	C₁₉×#95	1	8	yes	—
306	C₂³	C₁₉×#95	1	8	yes	—
307	C₂³	C₂×C₄²×C₁₉	1	2	yes	—
308	C₂³	C₂×C₄²×C₁₉	1	4	yes	—
309	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
310	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
311	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
312	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
313	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
314	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	C₁₉×#95	1	16	yes	—
320	C₂×C₄	C₁₉×#95	1	8	yes	—
321	C₂×C₄	C₁₉×#95	1	16	yes	—
322	C₂×C₄	C₁₉×#95	1	4	yes	—
323	C₂×C₄	C₁₉×#95	1	4	yes	—
324	C₂×C₄	C₂×C₄²×C₁₉	1	4	yes	—
325	C₂×C₄	C₂×C₄²×C₁₉	1	2	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
329	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
333	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
334	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
335	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
336	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
337	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
338	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
339	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
340	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
342	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
343	C₈	—	2	16	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	16	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	8	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	8	no	—
353	C₂²	C₂×C₁₉×#95	1	8	yes	—
354	C₂²	C₂×C₁₉×#95	1	2	yes	—
355	C₂²	C₂×C₁₉×#95	1	2	yes	—
356	C₂²	C₁₉×#413	1	4	yes	—
357	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
358	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
359	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
360	C₄	—	4	8	no	—
361	C₄	C₂×C₁₉×#95	1	4	yes	—
362	C₄	C₂×C₁₉×#95	1	4	yes	—
363	C₄	C₂×C₁₉×#95	1	4	yes	—
364	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
365	C₄	C₂²×C₄⋊C₄×C₁₉	1	2	yes	—
366	C₂	—	2	2	no	—
367	C₂	—	2	8	no	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	C₁₉×#1742	1	4	yes	direct product factor
371	C₂	C₂²×C₁₉×#95	1	1	yes	characteristic
372	C₂	C₂×C₁₉×#413	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1742	C₂	direct (N × H)
4. C₂×C₁₉×#343	C₂	semidirect
9. C₂²×M₁₆×C₁₉	C₄	semidirect
21. C₁₉×#343	C₂²	semidirect
41. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
112. C₂×#1742	C₁₉	direct (N × H)
160. #1742	C₂×C₁₉	direct (N × H)
161. C₂×#343	C₂×C₁₉	semidirect
188. C₂²×M₁₆	C₄×C₁₉	semidirect
200. #343	C₂²×C₁₉	semidirect
205. C₂×C₁₉	#1742	direct (N × H)
227. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
247. C₁₉	C₂×#1742	direct (N × H)
370. C₂	C₁₉×#1742	direct (N × H)

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
C₂²×C₁₉×#117	2
C₁₉×#1742	2
C₂×C₁₉×#343	2
C₂×#1742	19

Subgroups — C2×C19×#1742 #18026316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1742 #18026316