Subgroups — C₂×C₁₉×#1891 #18026922

Order 4864.

1870 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#407	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1891	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#344	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#568	—	2	2	no	—
10	C₁₉×#568	—	2	4	no	—
11	C₁₉×#568	C₂²	1	4	yes	complemented
12	C₂×C₁₉×#131	—	2	4	no	—
13	C₂²×M₁₆×C₁₉	—	2	2	no	—
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#525	—	2	2	no	—
17	C₁₉×#525	—	2	2	no	—
18	C₁₉×#525	C₄	1	4	yes	—
19	C₁₉×#525	C₂²	1	4	yes	—
20	C₂×C₁₉×#123	C₄	1	2	yes	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₉×#121	—	2	1	no	—
23	C₂×C₁₉×#120	C₄	1	2	yes	—
24	C₂×C₄×D₄×C₁₉	—	2	2	no	—
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₁₉×#413	—	2	2	no	—
27	C₁₉×#413	C₂²	1	4	yes	complemented
28	C₂×C₁₉×#101	—	2	1	no	—
29	C₂×C₁₉×#100	—	2	1	no	—
30	C₁₉×#407	—	2	4	no	—
31	C₁₉×#407	C₂²	1	8	yes	complemented
32	C₂×C₁₉×C₂²⋊C₈	—	2	4	no	—
33	C₁₉×#344	C₂²	1	8	yes	complemented
34	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×#41×C₁₉	D₄	1	2	yes	—
41	C₂×#41×C₁₉	D₄	1	2	yes	—
42	C₂×#41×C₁₉	C₂³	1	2	yes	—
43	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
46	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	—	2	2	no	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	—	2	2	no	—
55	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₁₉	D₄	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×#131	—	2	16	no	—
61	C₁₉×#131	—	2	16	no	—
62	C₂×M₁₆×C₁₉	—	2	4	no	—
63	C₂×M₁₆×C₁₉	—	2	8	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₂×M₁₆×C₁₉	—	2	8	no	—
66	C₂×M₁₆×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	2	2	no	—
69	C₂×M₁₆×C₁₉	—	2	2	no	—
70	C₂×M₁₆×C₁₉	—	2	2	no	—
71	C₂×M₁₆×C₁₉	—	2	2	no	—
72	C₂×M₁₆×C₁₉	—	2	2	no	—
73	C₂×M₁₆×C₁₉	—	2	2	no	—
74	C₂×M₁₆×C₁₉	D₄	1	4	yes	complemented
75	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
76	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
77	C₂²×C₈×C₁₉	—	2	4	no	—
78	C₂²×C₈×C₁₉	—	2	2	no	—
79	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
80	C₁₉×#123	—	2	4	no	—
81	C₁₉×#123	C₂×C₄	1	8	yes	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	—	2	4	no	—
84	C₁₉×#121	—	2	4	no	—
85	C₁₉×#121	—	2	4	no	—
86	C₁₉×#120	—	2	4	no	—
87	C₁₉×#120	C₂×C₄	1	8	yes	—
88	C₄×D₄×C₁₉	—	2	8	no	—
89	C₄×D₄×C₁₉	—	2	8	no	—
90	C₁₉×#117	—	2	1	no	—
91	C₁₉×#117	—	2	1	no	—
92	C₁₉×#117	C₂×C₄	1	2	yes	—
93	C₁₉×#117	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₁₉×#101	—	2	4	no	—
101	C₁₉×#100	—	2	4	no	—
102	C₁₉×C₂²⋊C₈	—	2	16	no	—
103	C₂⁴×C₁₉	—	2	1	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	2	1	no	—
106	C₂⁴×C₁₉	—	2	2	no	—
107	C₂⁴×C₁₉	—	4	4	no	—
108	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
109	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
110	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	#41×C₁₉	—	2	4	no	—
112	#41×C₁₉	—	2	4	no	—
113	#41×C₁₉	—	2	4	no	—
114	#41×C₁₉	—	2	4	no	—
115	#41×C₁₉	—	2	4	no	—
116	#41×C₁₉	—	2	4	no	—
117	#41×C₁₉	—	2	4	no	—
118	#41×C₁₉	—	2	4	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
122	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	4	no	—
125	C₂×D₄×C₁₉	—	2	8	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	4	8	no	—
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
130	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	4	2	no	—
151	C₂²×C₄×C₁₉	—	4	1	no	—
152	C₂²×C₄×C₁₉	—	4	1	no	—
153	C₂²×C₄×C₁₉	—	4	2	no	—
154	C₂²×C₄×C₁₉	—	4	2	no	—
155	C₂²×C₄×C₁₉	—	4	2	no	—
156	C₂²×C₄×C₁₉	—	4	2	no	—
157	C₂²×C₄×C₁₉	—	4	1	no	—
158	C₂²×C₄×C₁₉	—	4	1	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
162	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	#41	1	2	yes	—
172	C₂²×C₄×C₁₉	#41	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₁₉	—	2	16	no	—
175	M₁₆×C₁₉	—	2	4	no	—
176	M₁₆×C₁₉	—	2	4	no	—
177	M₁₆×C₁₉	—	2	4	no	—
178	M₁₆×C₁₉	—	2	4	no	—
179	M₁₆×C₁₉	—	2	4	no	—
180	M₁₆×C₁₉	—	2	4	no	—
181	M₁₆×C₁₉	—	4	2	no	—
182	M₁₆×C₁₉	—	4	2	no	—
183	C₂×C₈×C₁₉	—	2	16	no	—
184	C₂×C₈×C₁₉	—	2	4	no	—
185	C₂×C₈×C₁₉	—	2	4	no	—
186	C₂×C₈×C₁₉	—	2	4	no	—
187	C₂×C₈×C₁₉	—	4	2	no	—
188	C₂×C₈×C₁₉	—	4	2	no	—
189	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	complemented
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	8	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	8	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₂×#1891	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₁₉	—	2	4	no	—
201	C₂³×C₁₉	—	2	8	no	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	4	4	no	—
210	C₂³×C₁₉	—	4	4	no	—
211	C₂³×C₁₉	—	4	8	no	—
212	C₂³×C₁₉	—	4	4	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
218	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×C₁₉	C₄×D₄	1	2	yes	—
220	C₂³×C₁₉	C₄×D₄	1	2	yes	—
221	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
222	Q₈×C₁₉	—	2	4	no	—
223	Q₈×C₁₉	—	2	4	no	—
224	D₄×C₁₉	—	2	8	no	—
225	D₄×C₁₉	—	2	8	no	—
226	D₄×C₁₉	—	2	4	no	—
227	D₄×C₁₉	—	2	4	no	—
228	D₄×C₁₉	—	4	16	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	4	4	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	4	no	—
248	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
249	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
252	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₁₉	#120	1	2	yes	—
254	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	2	yes	—
257	C₂×C₄×C₁₉	#121	1	2	yes	—
258	C₂×C₄×C₁₉	#121	1	2	yes	—
259	C₂×C₄×C₁₉	#121	1	2	yes	—
260	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#123	1	2	yes	—
263	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
267	C₈×C₁₉	—	2	8	no	—
268	C₈×C₁₉	—	4	4	no	—
269	C₂×#568	C₂×C₁₉	1	1	yes	characteristic, complemented
270	C₂×#525	C₂×C₁₉	1	1	yes	characteristic
271	C₂×#413	C₂×C₁₉	1	1	yes	characteristic, complemented
272	C₂×#407	C₂×C₁₉	1	2	yes	complemented
273	#1891	C₂×C₁₉	1	8	yes	direct product factor
274	C₂×#344	C₂×C₁₉	1	2	yes	complemented
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	4	no	—
277	C₂²×C₁₉	—	2	4	no	—
278	C₂²×C₁₉	—	2	8	no	—
279	C₂²×C₁₉	—	2	4	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	4	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	4	no	—
286	C₂²×C₁₉	—	4	4	no	—
287	C₂²×C₁₉	—	4	8	no	—
288	C₂²×C₁₉	—	4	4	no	—
289	C₂²×C₁₉	—	4	4	no	—
290	C₂²×C₁₉	—	4	2	no	—
291	C₂²×C₁₉	—	8	2	no	—
292	C₂²×C₁₉	#386	1	1	yes	characteristic
293	C₂²×C₁₉	#386	1	2	yes	—
294	C₂²×C₁₉	#386	1	1	yes	characteristic
295	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
297	C₄×C₁₉	—	2	4	no	—
298	C₄×C₁₉	—	4	4	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	#386	1	1	yes	characteristic
301	C₄×C₁₉	#386	1	1	yes	characteristic
302	C₄×C₁₉	#386	1	2	yes	—
303	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
304	C₄×C₁₉	C₂×#121	1	2	yes	—
305	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
306	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
307	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
308	#568	—	2	2	no	—
309	#568	—	2	4	no	—
310	#568	C₂²×C₁₉	1	4	yes	complemented
311	C₂×#131	—	2	4	no	—
312	C₂²×M₁₆	—	2	2	no	—
313	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
314	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
315	#525	—	2	2	no	—
316	#525	—	2	2	no	—
317	#525	C₄×C₁₉	1	4	yes	—
318	#525	C₂²×C₁₉	1	4	yes	—
319	C₂×#123	C₄×C₁₉	1	2	yes	—
320	C₂×C₂²⋊Q₈	—	2	1	no	—
321	C₂×#121	—	2	1	no	—
322	C₂×#120	C₄×C₁₉	1	2	yes	—
323	C₂×C₄×D₄	—	2	2	no	—
324	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
325	#413	—	2	2	no	—
326	#413	C₂²×C₁₉	1	4	yes	complemented
327	C₂×#101	—	2	1	no	—
328	C₂×#100	—	2	1	no	—
329	#407	—	2	4	no	—
330	#407	C₂²×C₁₉	1	8	yes	complemented
331	C₂×C₂²⋊C₈	—	2	4	no	—
332	#344	C₂²×C₁₉	1	8	yes	complemented
333	C₂×C₁₉	—	2	1	no	—
334	C₂×C₁₉	—	2	2	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	2	no	—
337	C₂×C₁₉	—	4	4	no	—
338	C₂×C₁₉	—	4	4	no	—
339	C₂×C₁₉	#1891	1	2	yes	direct product factor
340	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
341	C₂⁵	C₂×C₄×C₁₉	1	1	yes	characteristic
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
347	C₂×#41	D₄×C₁₉	1	2	yes	—
348	C₂×#41	D₄×C₁₉	1	2	yes	—
349	C₂×#41	C₂³×C₁₉	1	2	yes	—
350	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
353	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	—	2	2	no	—
359	C₂³×C₄	—	2	2	no	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	—	2	2	no	—
362	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
363	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
364	C₂³×C₄	D₄×C₁₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
367	#131	—	2	16	no	—
368	#131	—	2	16	no	—
369	C₂×M₁₆	—	2	4	no	—
370	C₂×M₁₆	—	2	8	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	8	no	—
373	C₂×M₁₆	—	2	2	no	—
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	2	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	D₄×C₁₉	1	4	yes	complemented
382	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
383	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
384	C₂²×C₈	—	2	4	no	—
385	C₂²×C₈	—	2	2	no	—
386	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
387	#123	—	2	4	no	—
388	#123	C₂×C₄×C₁₉	1	8	yes	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	4	no	—
391	#121	—	2	4	no	—
392	#121	—	2	4	no	—
393	#120	—	2	4	no	—
394	#120	C₂×C₄×C₁₉	1	8	yes	—
395	C₄×D₄	—	2	8	no	—
396	C₄×D₄	—	2	8	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	C₂×C₄×C₁₉	1	2	yes	—
400	#117	C₂³×C₁₉	1	2	yes	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
406	C₂×C₄²	—	2	1	no	—
407	#101	—	2	4	no	—
408	#100	—	2	4	no	—
409	C₂²⋊C₈	—	2	16	no	—
410	C₁₉	C₂×#1891	1	1	yes	characteristic, direct product factor, Sylow
411	C₂⁴	—	2	1	no	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	4	4	no	—
416	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
417	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
418	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
419	#41	—	2	4	no	—
420	#41	—	2	4	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
430	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
438	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
439	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
440	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
469	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
470	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
471	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
479	C₂²×C₄	#41×C₁₉	1	2	yes	—
480	C₂²×C₄	#41×C₁₉	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
482	M₁₆	—	2	16	no	—
483	M₁₆	—	2	4	no	—
484	M₁₆	—	2	4	no	—
485	M₁₆	—	2	4	no	—
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	4	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	4	2	no	—
490	M₁₆	—	4	2	no	—
491	C₂×C₈	—	2	16	no	—
492	C₂×C₈	—	2	4	no	—
493	C₂×C₈	—	2	4	no	—
494	C₂×C₈	—	2	4	no	—
495	C₂×C₈	—	4	2	no	—
496	C₂×C₈	—	4	2	no	—
497	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	complemented
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	8	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	4	4	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	1	no	—
523	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
524	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
525	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
526	C₂³	C₄×D₄×C₁₉	1	2	yes	—
527	C₂³	C₄×D₄×C₁₉	1	2	yes	—
528	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	D₄	—	2	8	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	4	no	—
535	D₄	—	4	16	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
556	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
557	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
558	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
559	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
560	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
561	C₂×C₄	C₁₉×#120	1	2	yes	—
562	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#121	1	2	yes	—
564	C₂×C₄	C₁₉×#121	1	2	yes	—
565	C₂×C₄	C₁₉×#121	1	2	yes	—
566	C₂×C₄	C₁₉×#121	1	2	yes	—
567	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
568	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#123	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
574	C₈	—	2	8	no	—
575	C₈	—	4	4	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	8	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	2	no	—
593	C₂²	C₁₉×#386	1	1	yes	characteristic
594	C₂²	C₁₉×#386	1	2	yes	—
595	C₂²	C₁₉×#386	1	1	yes	characteristic
596	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
597	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
598	C₄	—	2	4	no	—
599	C₄	—	4	4	no	—
600	C₄	—	4	2	no	—
601	C₄	C₁₉×#386	1	1	yes	characteristic
602	C₄	C₁₉×#386	1	1	yes	characteristic
603	C₄	C₁₉×#386	1	2	yes	—
604	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
605	C₄	C₂×C₁₉×#121	1	2	yes	—
606	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
607	C₂	—	2	1	no	—
608	C₂	—	2	2	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	2	no	—
611	C₂	—	4	4	no	—
612	C₂	—	4	4	no	—
613	C₂	C₁₉×#1891	1	2	yes	direct product factor
614	C₂	C₂×C₁₉×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#525	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#568	C₂	semidirect
3. C₂×C₁₉×#413	C₂	semidirect
4. C₂×C₁₉×#407	C₂	semidirect
5. C₁₉×#1891	C₂	direct (N × H)
6. C₂×C₁₉×#344	C₂	semidirect
11. C₁₉×#568	C₂²	semidirect
27. C₁₉×#413	C₂²	semidirect
31. C₁₉×#407	C₂²	semidirect
33. C₁₉×#344	C₂²	semidirect
74. C₂×M₁₆×C₁₉	D₄	semidirect
79. C₂²×C₈×C₁₉	D₄	semidirect
189. C₂×C₈×C₁₉	C₂×D₄	semidirect
199. C₂×#1891	C₁₉	direct (N × H)
269. C₂×#568	C₂×C₁₉	semidirect
271. C₂×#413	C₂×C₁₉	semidirect
272. C₂×#407	C₂×C₁₉	semidirect
273. #1891	C₂×C₁₉	direct (N × H)
274. C₂×#344	C₂×C₁₉	semidirect
310. #568	C₂²×C₁₉	semidirect
326. #413	C₂²×C₁₉	semidirect
330. #407	C₂²×C₁₉	semidirect
332. #344	C₂²×C₁₉	semidirect
339. C₂×C₁₉	#1891	direct (N × H)
381. C₂×M₁₆	D₄×C₁₉	semidirect
386. C₂²×C₈	D₄×C₁₉	semidirect
410. C₁₉	C₂×#1891	direct (N × H)
497. C₂×C₈	C₂×D₄×C₁₉	semidirect
613. C₂	C₁₉×#1891	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#568	2
C₂×C₁₉×#525	2
C₂×C₁₉×#413	2
C₂×C₁₉×#407	2
C₁₉×#1891	2
C₂×C₁₉×#344	2
C₂×#1891	19

Subgroups — C2×C19×#1891 #18026922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1891 #18026922