Subgroups — C₁₉×#17793 #18023752

Order 4864.

762 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	C₁₉×#2920	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1568	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1567	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1566	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1564	C₂	1	4	yes	maximal, complemented
7	C₂³×C₈×C₁₉	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#432	—	2	2	no	—
10	C₁₉×#432	C₂²	1	4	yes	—
11	C₁₉×#431	—	2	2	no	—
12	C₁₉×#431	C₂²	1	4	yes	—
13	C₁₉×#423	C₂²	1	4	yes	—
14	C₁₉×#407	—	2	2	no	—
15	C₄×M₁₆×C₁₉	—	2	2	no	—
16	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#335	C₂²	1	8	yes	complemented
26	C₁₉×#334	C₂²	1	8	yes	complemented
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₁₉	—	2	4	no	—
31	C₂²×C₈×C₁₉	—	2	8	no	—
32	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₄⋊C₈	—	2	4	no	—
51	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
52	C₁₉×C₂²⋊C₈	—	2	4	no	—
53	C₁₉×C₂²⋊C₈	—	2	4	no	—
54	C₁₉×#97	—	2	4	no	—
55	C₄×C₈×C₁₉	—	2	4	no	—
56	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
61	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
64	C₄×C₈×C₁₉	C₂³	1	2	yes	—
65	C₄×C₈×C₁₉	C₂³	1	2	yes	—
66	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	2	4	no	—
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
88	M₁₆×C₁₉	—	4	8	no	—
89	C₂×C₈×C₁₉	—	2	4	no	—
90	C₂×C₈×C₁₉	—	2	4	no	—
91	C₂×C₈×C₁₉	—	2	4	no	—
92	C₂×C₈×C₁₉	—	2	4	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	8	no	—
95	C₂×C₈×C₁₉	M₁₆	1	8	yes	complemented
96	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
100	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
116	#17793	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	#108	1	4	yes	—
139	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
149	C₂×C₄×C₁₉	#135	1	4	yes	—
150	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
153	C₈×C₁₉	—	2	2	no	—
154	C₈×C₁₉	—	2	2	no	—
155	C₈×C₁₉	—	4	8	no	—
156	C₈×C₁₉	C₂×M₁₆	1	4	yes	—
157	C₈×C₁₉	C₂×M₁₆	1	4	yes	—
158	#2920	C₂×C₁₉	1	2	yes	—
159	C₂²×C₄×C₈	C₂×C₁₉	1	1	yes	characteristic
160	#1568	C₂×C₁₉	1	4	yes	complemented
161	#1567	C₂×C₁₉	1	2	yes	complemented
162	#1566	C₂×C₁₉	1	2	yes	complemented
163	#1564	C₂×C₁₉	1	4	yes	complemented
164	C₂²×C₁₉	—	2	8	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	#423	1	2	yes	—
172	C₂²×C₁₉	#427	1	2	yes	—
173	C₂²×C₁₉	C₂×#108	1	2	yes	—
174	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	#423	1	2	yes	—
182	C₄×C₁₉	#427	1	2	yes	—
183	C₄×C₁₉	C₂×#108	1	2	yes	—
184	C₄×C₁₉	C₂×#108	1	2	yes	—
185	C₄×C₁₉	C₂²×M₁₆	1	2	yes	—
186	C₄×C₁₉	C₂×#135	1	2	yes	—
187	C₂³×C₈	C₄×C₁₉	1	2	yes	—
188	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
189	#432	—	2	2	no	—
190	#432	C₂²×C₁₉	1	4	yes	—
191	#431	—	2	2	no	—
192	#431	C₂²×C₁₉	1	4	yes	—
193	#423	C₂²×C₁₉	1	4	yes	—
194	#407	—	2	2	no	—
195	C₄×M₁₆	—	2	2	no	—
196	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
197	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
198	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
199	C₂×C₄×C₈	C₄×C₁₉	1	2	yes	—
200	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
205	#335	C₂²×C₁₉	1	8	yes	complemented
206	#334	C₂²×C₁₉	1	8	yes	complemented
207	C₂×C₁₉	—	2	2	no	—
208	C₂×C₁₉	—	2	2	no	—
209	C₂×C₁₉	—	2	2	no	—
210	C₂×C₁₉	C₂×#423	1	1	yes	characteristic
211	C₂×C₁₉	C₂×#427	1	1	yes	characteristic
212	C₂×C₁₉	C₂²×#108	1	1	yes	characteristic
213	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
215	C₂³×C₄	Q₈×C₁₉	1	1	yes	characteristic
216	C₂×M₁₆	—	2	4	no	—
217	C₂²×C₈	—	2	8	no	—
218	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
219	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
220	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
221	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
222	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
223	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
230	C₂×C₄²	Q₈×C₁₉	1	1	yes	characteristic
231	C₂×C₄²	Q₈×C₁₉	1	1	yes	characteristic
232	C₂×C₄²	Q₈×C₁₉	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
238	C₂²⋊C₈	—	2	4	no	—
239	C₂²⋊C₈	—	2	4	no	—
240	#97	—	2	4	no	—
241	C₄×C₈	—	2	4	no	—
242	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
243	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
244	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
245	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
246	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
247	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
248	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
249	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
250	C₄×C₈	C₂³×C₁₉	1	2	yes	—
251	C₄×C₈	C₂³×C₁₉	1	2	yes	—
252	C₁₉	#17793	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	C₄⋊C₄×C₁₉	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
275	M₁₆	—	4	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	M₁₆×C₁₉	1	8	yes	complemented
283	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
284	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
285	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
286	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
287	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
288	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
293	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
294	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
295	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
296	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
299	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
300	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
301	C₄²	C₂×Q₈×C₁₉	1	1	yes	characteristic
302	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
307	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	C₁₉×#108	1	4	yes	—
325	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
334	C₂×C₄	C₂×M₁₆×C₁₉	1	4	yes	—
335	C₂×C₄	C₁₉×#135	1	4	yes	—
336	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
338	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	4	8	no	—
342	C₈	C₂×M₁₆×C₁₉	1	4	yes	—
343	C₈	C₂×M₁₆×C₁₉	1	4	yes	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	C₁₉×#423	1	2	yes	—
352	C₂²	C₁₉×#427	1	2	yes	—
353	C₂²	C₂×C₁₉×#108	1	2	yes	—
354	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	C₁₉×#423	1	2	yes	—
362	C₄	C₁₉×#427	1	2	yes	—
363	C₄	C₂×C₁₉×#108	1	2	yes	—
364	C₄	C₂×C₁₉×#108	1	2	yes	—
365	C₄	C₂²×M₁₆×C₁₉	1	2	yes	—
366	C₄	C₂×C₁₉×#135	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	C₂×C₁₉×#423	1	1	yes	characteristic
371	C₂	C₂×C₁₉×#427	1	1	yes	characteristic
372	C₂	C₂²×C₁₉×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₉	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1568	C₂	semidirect
4. C₁₉×#1567	C₂	semidirect
5. C₁₉×#1566	C₂	semidirect
6. C₁₉×#1564	C₂	semidirect
25. C₁₉×#335	C₂²	semidirect
26. C₁₉×#334	C₂²	semidirect
95. C₂×C₈×C₁₉	M₁₆	semidirect
116. #17793	C₁₉	direct (N × H)
160. #1568	C₂×C₁₉	semidirect
161. #1567	C₂×C₁₉	semidirect
162. #1566	C₂×C₁₉	semidirect
163. #1564	C₂×C₁₉	semidirect
205. #335	C₂²×C₁₉	semidirect
206. #334	C₂²×C₁₉	semidirect
252. C₁₉	#17793	direct (N × H)
282. C₂×C₈	M₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2920	2
C₂²×C₄×C₈×C₁₉	2
C₁₉×#1568	2
C₁₉×#1567	2
C₁₉×#1566	2
C₁₉×#1564	2
#17793	19

Subgroups — C19×#17793 #18023752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17793 #18023752