Subgroups — C₂×C₁₉×#1472 #18023337

Order 4864.

1426 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#407	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1472	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#324	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₉	—	2	1	no	—
9	C₂³×C₈×C₁₉	—	2	1	no	—
10	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
16	C₂×C₁₉×C₂²⋊Q₈	C₄	1	4	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
21	C₁₉×#407	—	2	2	no	—
22	C₁₉×#407	C₂²	1	4	yes	—
23	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
24	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
29	C₁₉×#324	C₂²	1	16	yes	complemented
30	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	—	2	1	no	—
34	C₂²×Q₈×C₁₉	—	4	4	no	—
35	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₉	—	4	4	no	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	D₄	1	2	yes	—
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	D₄	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	—	4	4	no	—
51	C₂²×C₈×C₁₉	—	2	4	no	—
52	C₂²×C₈×C₁₉	—	2	2	no	—
53	C₂²×C₈×C₁₉	—	2	2	no	—
54	C₂²×C₈×C₁₉	—	4	4	no	—
55	C₁₉×C₂²⋊Q₈	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	4	no	—
60	C₁₉×C₂²⋊Q₈	—	2	4	no	—
61	C₁₉×C₂²⋊Q₈	—	2	4	no	—
62	C₁₉×C₂²⋊Q₈	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
77	C₁₉×C₂²⋊C₈	—	2	2	no	—
78	C₁₉×C₂²⋊C₈	—	2	4	no	—
79	C₁₉×C₂²⋊C₈	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	—	2	2	no	—
81	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
82	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	4	2	no	—
86	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
90	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂×Q₈×C₁₉	—	2	4	no	—
92	C₂×Q₈×C₁₉	—	2	4	no	—
93	C₂×Q₈×C₁₉	—	4	8	no	—
94	C₂×Q₈×C₁₉	—	4	4	no	—
95	C₂×Q₈×C₁₉	—	4	8	no	—
96	C₂×Q₈×C₁₉	—	4	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	8	no	—
105	C₂²×C₄×C₁₉	—	4	4	no	—
106	C₂²×C₄×C₁₉	—	4	4	no	—
107	C₂²×C₄×C₁₉	—	4	4	no	—
108	C₂²×C₄×C₁₉	—	4	4	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	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	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	M₁₆×C₁₉	—	4	8	no	—
134	C₂×C₈×C₁₉	—	2	4	no	—
135	C₂×C₈×C₁₉	—	2	4	no	—
136	C₂×C₈×C₁₉	—	4	4	no	—
137	C₂×C₈×C₁₉	—	4	8	no	—
138	C₂×C₈×C₁₉	—	4	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	2	8	no	—
146	C₂²⋊C₄×C₁₉	—	2	8	no	—
147	C₂×#1472	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	4	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	4	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	16	no	—
162	C₂³×C₁₉	#101	1	4	yes	—
163	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₁₉	#131	1	4	yes	—
168	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
169	Q₈×C₁₉	—	4	8	no	—
170	Q₈×C₁₉	—	4	8	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	1	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	#99	1	4	yes	—
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₁₉	—	4	4	no	—
204	C₈×C₁₉	—	4	4	no	—
205	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
206	C₂×#407	C₂×C₁₉	1	1	yes	characteristic
207	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
208	#1472	C₂×C₁₉	1	8	yes	direct product factor
209	C₂×#324	C₂×C₁₉	1	4	yes	complemented
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	1	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	1	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	8	no	—
217	C₂²×C₁₉	—	2	8	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	2	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	4	8	no	—
222	C₂²×C₁₉	—	4	8	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	#408	1	2	yes	—
225	C₂²×C₁₉	#408	1	2	yes	—
226	C₂²×C₁₉	C₂×#99	1	2	yes	—
227	C₂²×C₁₉	C₂×#101	1	4	yes	—
228	C₂²×C₁₉	C₂×#101	1	2	yes	—
229	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#131	1	2	yes	—
231	C₄×C₁₉	—	2	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	4	4	no	—
238	C₄×C₁₉	C₂×#99	1	4	yes	—
239	C₂³×Q₈	C₄×C₁₉	1	1	yes	characteristic
240	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
241	C₂²×M₁₆	—	2	1	no	—
242	C₂³×C₈	—	2	1	no	—
243	C₂×C₂²⋊Q₈	—	2	1	no	—
244	C₂×C₂²⋊Q₈	—	2	1	no	—
245	C₂×C₂²⋊Q₈	—	2	1	no	—
246	C₂×C₂²⋊Q₈	—	2	2	no	—
247	C₂×C₂²⋊Q₈	—	2	1	no	—
248	C₂×C₂²⋊Q₈	—	2	2	no	—
249	C₂×C₂²⋊Q₈	C₄×C₁₉	1	4	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
251	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
254	#407	—	2	2	no	—
255	#407	C₂²×C₁₉	1	4	yes	—
256	C₂×C₂²⋊C₈	—	2	2	no	—
257	C₂×C₂²⋊C₈	—	2	1	no	—
258	C₂×C₂²⋊C₈	—	2	1	no	—
259	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
262	#324	C₂²×C₁₉	1	16	yes	complemented
263	C₂×C₁₉	—	2	2	no	—
264	C₂×C₁₉	—	2	2	no	—
265	C₂×C₁₉	—	2	4	no	—
266	C₂×C₁₉	—	4	2	no	—
267	C₂×C₁₉	#1472	1	4	yes	direct product factor
268	C₂×C₁₉	C₂×#408	1	1	yes	characteristic
269	C₂×C₁₉	C₂²×#99	1	1	yes	characteristic
270	C₂×C₁₉	C₂²×#101	1	1	yes	characteristic
271	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	—	4	4	no	—
276	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
277	C₂³×C₄	—	4	4	no	—
278	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
279	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
280	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
281	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
282	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
283	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₁₉	1	2	yes	—
285	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₁₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×M₁₆	—	2	4	no	—
291	C₂×M₁₆	—	4	4	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	4	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	4	4	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	4	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	4	no	—
320	C₂²⋊C₈	—	2	4	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
323	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
324	C₁₉	C₂×#1472	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	4	2	no	—
328	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
329	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
330	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
331	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
332	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	4	8	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×Q₈	—	4	8	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
358	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
359	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
365	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
375	M₁₆	—	4	8	no	—
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	4	4	no	—
379	C₂×C₈	—	4	8	no	—
380	C₂×C₈	—	4	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	16	no	—
403	C₂³	C₁₉×#101	1	4	yes	—
404	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
405	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
406	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
407	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
408	C₂³	C₁₉×#131	1	4	yes	—
409	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
410	Q₈	—	4	8	no	—
411	Q₈	—	4	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	C₁₉×#99	1	4	yes	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
441	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
444	C₈	—	4	4	no	—
445	C₈	—	4	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	8	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	4	4	no	—
460	C₂²	C₁₉×#408	1	2	yes	—
461	C₂²	C₁₉×#408	1	2	yes	—
462	C₂²	C₂×C₁₉×#99	1	2	yes	—
463	C₂²	C₂×C₁₉×#101	1	4	yes	—
464	C₂²	C₂×C₁₉×#101	1	2	yes	—
465	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
466	C₂²	C₂×C₁₉×#131	1	2	yes	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	4	no	—
474	C₄	C₂×C₁₉×#99	1	4	yes	—
475	C₂	—	2	2	no	—
476	C₂	—	2	4	no	—
477	C₂	—	2	2	no	—
478	C₂	—	4	2	no	—
479	C₂	C₁₉×#1472	1	4	yes	direct product factor
480	C₂	C₂×C₁₉×#408	1	1	yes	characteristic
481	C₂	C₂²×C₁₉×#99	1	1	yes	characteristic
482	C₂	C₂²×C₁₉×#101	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 ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1472	C₂	direct (N × H)
5. C₂×C₁₉×#324	C₂	semidirect
29. C₁₉×#324	C₂²	semidirect
147. C₂×#1472	C₁₉	direct (N × H)
208. #1472	C₂×C₁₉	direct (N × H)
209. C₂×#324	C₂×C₁₉	semidirect
262. #324	C₂²×C₁₉	semidirect
267. C₂×C₁₉	#1472	direct (N × H)
324. C₁₉	C₂×#1472	direct (N × H)
479. C₂	C₁₉×#1472	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×C₂²⋊Q₈	2
C₂×C₁₉×#407	2
C₂²×C₁₉×C₂²⋊C₈	2
C₁₉×#1472	2
C₂×C₁₉×#324	2
C₂×#1472	19

Subgroups — C2×C19×#1472 #18023337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1472 #18023337