Subgroups — C₂×C₁₉×#1473 #18023338

Order 4864.

1066 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#126	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1473	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#324	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#323	C₂	1	2	yes	maximal
7	C₂×C₁₉×#126	—	2	1	no	—
8	C₂×C₁₉×#126	—	2	1	no	—
9	C₂×C₁₉×#126	—	2	1	no	—
10	C₂×C₁₉×#126	—	2	1	no	—
11	C₂×C₁₉×#126	—	2	2	no	—
12	C₂×C₁₉×#126	—	2	2	no	—
13	C₂×C₁₉×#126	C₄	1	4	yes	—
14	C₂×C₁₉×#126	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₉	C₄	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#432	—	2	2	no	—
23	C₁₉×#432	C₂²	1	4	yes	complemented
24	C₁₉×#431	—	2	2	no	—
25	C₁₉×#431	C₂²	1	4	yes	complemented
26	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
27	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₁₉×#97	—	2	1	no	—
31	C₂×C₄×C₈×C₁₉	—	2	1	no	—
32	C₁₉×#324	C₂²	1	8	yes	complemented
33	C₁₉×#323	C₂²	1	8	yes	—
34	C₂⁵×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	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₁₉×#126	—	2	4	no	—
44	C₁₉×#126	—	2	4	no	—
45	C₁₉×#126	—	2	4	no	—
46	C₁₉×#126	—	2	4	no	—
47	C₁₉×#126	—	2	4	no	—
48	C₁₉×#126	—	2	4	no	—
49	C₁₉×#126	—	2	4	no	—
50	C₁₉×#126	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₉	D₄	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
87	C₁₉×C₄⋊C₈	—	2	4	no	—
88	C₁₉×C₄⋊C₈	—	2	4	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×C₂²⋊C₈	—	2	2	no	—
91	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
92	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
93	C₁₉×#97	—	2	4	no	—
94	C₄×C₈×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	—	2	4	no	—
98	C₂⁴×C₁₉	—	4	2	no	—
99	C₂⁴×C₁₉	—	4	2	no	—
100	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₂×C₈×C₁₉	—	4	4	no	—
134	C₂×C₈×C₁₉	—	4	4	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₉	—	2	2	no	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
153	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
154	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
155	C₄²×C₁₉	C₂×D₄	1	2	yes	—
156	C₄²×C₁₉	C₂×D₄	1	2	yes	—
157	C₄²×C₁₉	C₂×D₄	1	2	yes	—
158	C₄²×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×#1473	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	4	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	2	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	4	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	8	8	no	—
173	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂³×C₁₉	#131	1	4	yes	—
176	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	C₈×C₁₉	—	4	4	no	—
212	C₈×C₁₉	—	4	4	no	—
213	C₂²×#126	C₂×C₁₉	1	1	yes	characteristic
214	C₂×#432	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂×#431	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1473	C₂×C₁₉	1	8	yes	direct product factor
217	C₂×#324	C₂×C₁₉	1	2	yes	complemented
218	C₂×#323	C₂×C₁₉	1	2	yes	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	8	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	2	no	—
227	C₂²×C₁₉	—	8	4	no	—
228	C₂²×C₁₉	—	8	4	no	—
229	C₂²×C₁₉	—	8	4	no	—
230	C₂²×C₁₉	#408	1	2	yes	—
231	C₂²×C₁₉	#408	1	2	yes	—
232	C₂²×C₁₉	#410	1	2	yes	—
233	C₂²×C₁₉	#413	1	2	yes	—
234	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₁₉	C₂×#131	1	2	yes	—
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	2	2	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₂×#126	—	2	1	no	—
248	C₂×#126	—	2	1	no	—
249	C₂×#126	—	2	1	no	—
250	C₂×#126	—	2	1	no	—
251	C₂×#126	—	2	2	no	—
252	C₂×#126	—	2	2	no	—
253	C₂×#126	C₄×C₁₉	1	4	yes	—
254	C₂×#126	C₂²×C₁₉	1	4	yes	—
255	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₄×C₁₉	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
262	#432	—	2	2	no	—
263	#432	C₂²×C₁₉	1	4	yes	complemented
264	#431	—	2	2	no	—
265	#431	C₂²×C₁₉	1	4	yes	complemented
266	C₂×C₄⋊C₈	—	2	1	no	—
267	C₂×C₄⋊C₈	—	2	1	no	—
268	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
270	C₂×#97	—	2	1	no	—
271	C₂×C₄×C₈	—	2	1	no	—
272	#324	C₂²×C₁₉	1	8	yes	complemented
273	#323	C₂²×C₁₉	1	8	yes	—
274	C₂×C₁₉	—	2	2	no	—
275	C₂×C₁₉	—	2	2	no	—
276	C₂×C₁₉	—	8	2	no	—
277	C₂×C₁₉	#1473	1	4	yes	direct product factor
278	C₂×C₁₉	C₂×#408	1	1	yes	characteristic
279	C₂×C₁₉	C₂×#410	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#413	1	1	yes	characteristic
281	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
282	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
283	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	#126	—	2	4	no	—
291	#126	—	2	4	no	—
292	#126	—	2	4	no	—
293	#126	—	2	4	no	—
294	#126	—	2	4	no	—
295	#126	—	2	4	no	—
296	#126	—	2	4	no	—
297	#126	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
326	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
327	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
330	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
331	C₂×C₄²	D₄×C₁₉	1	2	yes	—
332	C₂×C₄²	D₄×C₁₉	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
334	C₄⋊C₈	—	2	4	no	—
335	C₄⋊C₈	—	2	4	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
339	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
340	#97	—	2	4	no	—
341	C₄×C₈	—	2	4	no	—
342	C₁₉	C₂×#1473	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	—	2	1	no	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	4	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
349	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
371	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	4	4	no	—
382	C₂×C₈	—	4	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
400	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
401	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
402	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
403	C₄²	C₂×D₄×C₁₉	1	2	yes	—
404	C₄²	C₂×D₄×C₁₉	1	2	yes	—
405	C₄²	C₂×D₄×C₁₉	1	2	yes	—
406	C₄²	C₂×D₄×C₁₉	1	2	yes	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	8	8	no	—
420	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
421	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
422	C₂³	C₁₉×#131	1	4	yes	—
423	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
452	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
453	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
454	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
455	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
458	C₈	—	4	4	no	—
459	C₈	—	4	4	no	—
460	C₂²	—	2	8	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	8	4	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	C₁₉×#408	1	2	yes	—
472	C₂²	C₁₉×#408	1	2	yes	—
473	C₂²	C₁₉×#410	1	2	yes	—
474	C₂²	C₁₉×#413	1	2	yes	—
475	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
476	C₂²	C₂×C₁₉×#131	1	2	yes	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₂	—	2	2	no	—
489	C₂	—	2	2	no	—
490	C₂	—	8	2	no	—
491	C₂	C₁₉×#1473	1	4	yes	direct product factor
492	C₂	C₂×C₁₉×#408	1	1	yes	characteristic
493	C₂	C₂×C₁₉×#410	1	1	yes	characteristic
494	C₂	C₂×C₁₉×#413	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#432	C₂	semidirect
3. C₂×C₁₉×#431	C₂	semidirect
4. C₁₉×#1473	C₂	direct (N × H)
5. C₂×C₁₉×#324	C₂	semidirect
23. C₁₉×#432	C₂²	semidirect
25. C₁₉×#431	C₂²	semidirect
32. C₁₉×#324	C₂²	semidirect
159. C₂×#1473	C₁₉	direct (N × H)
214. C₂×#432	C₂×C₁₉	semidirect
215. C₂×#431	C₂×C₁₉	semidirect
216. #1473	C₂×C₁₉	direct (N × H)
217. C₂×#324	C₂×C₁₉	semidirect
263. #432	C₂²×C₁₉	semidirect
265. #431	C₂²×C₁₉	semidirect
272. #324	C₂²×C₁₉	semidirect
277. C₂×C₁₉	#1473	direct (N × H)
342. C₁₉	C₂×#1473	direct (N × H)
491. C₂	C₁₉×#1473	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#126	2
C₂×C₁₉×#432	2
C₂×C₁₉×#431	2
C₁₉×#1473	2
C₂×C₁₉×#324	2
C₂×C₁₉×#323	2
C₂×#1473	19

Subgroups — C2×C19×#1473 #18023338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1473 #18023338