Subgroups — C₁₉×#9650 #18015609

Order 4864.

656 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#324	C₂	1	4	yes	maximal
5	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
6	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
7	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
10	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₉	—	2	1	no	—
13	C₁₉×#389	—	2	1	no	—
14	C₁₉×#389	—	2	1	no	—
15	C₁₉×#389	—	2	1	no	—
16	C₁₉×#389	—	2	1	no	—
17	C₂×C₁₉×#95	C₄	1	2	yes	—
18	C₁₉×#336	—	2	1	no	—
19	C₁₉×#336	—	2	1	no	—
20	C₁₉×#324	—	2	8	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
38	C₂×C₄⋊C₄×C₁₉	C₈	1	4	yes	complemented
39	C₂×C₄²×C₁₉	—	4	2	no	—
40	C₂×C₄²×C₁₉	D₄	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	C₁₉×C₄⋊C₈	—	4	2	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₁₉×C₂²⋊C₈	—	2	4	no	—
47	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
48	C₄×C₈×C₁₉	—	4	2	no	—
49	C₁₉×#95	—	2	2	no	—
50	C₁₉×#95	—	2	2	no	—
51	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	4	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	4	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	4	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	—	4	2	no	—
67	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
72	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
73	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₉	#41	1	2	yes	—
78	C₂×C₈×C₁₉	—	2	4	no	—
79	C₂×C₈×C₁₉	—	4	2	no	—
80	C₂×C₈×C₁₉	—	4	2	no	—
81	C₂×C₈×C₁₉	—	4	2	no	—
82	C₂×C₈×C₁₉	—	4	2	no	—
83	C₂×C₈×C₁₉	—	4	2	no	—
84	C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₄⋊C₄×C₁₉	—	2	4	no	—
86	C₄⋊C₄×C₁₉	—	4	2	no	—
87	C₄⋊C₄×C₁₉	—	4	2	no	—
88	C₄⋊C₄×C₁₉	—	4	4	no	—
89	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₄²×C₁₉	—	2	2	no	—
92	C₄²×C₁₉	—	2	2	no	—
93	C₄²×C₁₉	—	4	1	no	—
94	C₄²×C₁₉	—	4	1	no	—
95	#9650	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	—	2	1	no	—
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂³×C₁₉	C₄×D₄	1	2	yes	—
102	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
103	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
104	C₂³×C₁₉	#131	1	2	yes	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	4	no	—
114	C₂×C₄×C₁₉	—	2	4	no	—
115	C₂×C₄×C₁₉	—	2	4	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	8	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	4	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	8	4	no	—
130	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
131	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
132	C₂×C₄×C₁₉	#99	1	2	yes	—
133	C₂×C₄×C₁₉	#101	1	2	yes	—
134	C₂×C₄×C₁₉	#101	1	2	yes	—
135	C₂×C₄×C₁₉	#121	1	2	yes	—
136	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
138	C₈×C₁₉	—	4	4	no	—
139	C₈×C₁₉	—	8	2	no	—
140	C₂×#389	C₂×C₁₉	1	1	yes	characteristic
141	#1797	C₂×C₁₉	1	1	yes	characteristic
142	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic
143	C₂×#324	C₂×C₁₉	1	4	yes	—
144	C₂²×C₁₉	—	2	2	no	—
145	C₂²×C₁₉	—	2	2	no	—
146	C₂²×C₁₉	—	2	1	no	—
147	C₂²×C₁₉	—	2	1	no	—
148	C₂²×C₁₉	—	2	1	no	—
149	C₂²×C₁₉	—	2	1	no	—
150	C₂²×C₁₉	—	2	2	no	—
151	C₂²×C₁₉	—	2	2	no	—
152	C₂²×C₁₉	#390	1	1	yes	characteristic
153	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
154	C₂²×C₁₉	#408	1	1	yes	characteristic
155	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
156	C₂²×C₁₉	#410	1	1	yes	characteristic
157	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
158	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
159	C₂²×C₁₉	C₈×D₄	1	2	yes	—
160	C₂²×C₁₉	#436	1	2	yes	—
161	C₄×C₁₉	—	2	2	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	2	1	no	—
164	C₄×C₁₉	—	2	2	no	—
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	4	4	no	—
167	C₄×C₁₉	—	4	1	no	—
168	C₄×C₁₉	—	8	2	no	—
169	C₄×C₁₉	#324	1	4	yes	complemented
170	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic
172	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
173	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
174	C₂×C₄⋊C₈	—	2	1	no	—
175	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
177	C₂×C₄×C₈	—	2	1	no	—
178	#389	—	2	1	no	—
179	#389	—	2	1	no	—
180	#389	—	2	1	no	—
181	#389	—	2	1	no	—
182	C₂×#95	C₄×C₁₉	1	2	yes	—
183	#336	—	2	1	no	—
184	#336	—	2	1	no	—
185	#324	—	2	8	no	—
186	C₂×C₁₉	—	2	2	no	—
187	C₂×C₁₉	—	2	2	no	—
188	C₂×C₁₉	C₂×#324	1	1	yes	characteristic
189	C₂×C₁₉	#1461	1	1	yes	characteristic
190	C₂×C₁₉	#1470	1	1	yes	characteristic
191	C₂×C₁₉	#1472	1	1	yes	characteristic
192	C₂×C₁₉	#1954	1	1	yes	characteristic
193	C₂×C₁₉	#1964	1	1	yes	characteristic
194	C₂×C₁₉	#1966	1	1	yes	characteristic
195	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
196	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
198	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
199	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	1	no	—
203	C₂×C₄⋊C₄	—	2	1	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	2	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	—	4	2	no	—
212	C₂×C₄⋊C₄	C₈×C₁₉	1	4	yes	complemented
213	C₂×C₄²	—	4	2	no	—
214	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
215	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
216	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
217	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
218	C₄⋊C₈	—	4	2	no	—
219	C₂²⋊C₈	—	2	2	no	—
220	C₂²⋊C₈	—	2	4	no	—
221	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
222	C₄×C₈	—	4	2	no	—
223	#95	—	2	2	no	—
224	#95	—	2	2	no	—
225	C₁₉	#9650	1	1	yes	characteristic, direct product factor, Sylow
226	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	4	1	no	—
238	C₂²×C₄	—	4	1	no	—
239	C₂²×C₄	—	4	1	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₈×C₁₉	1	4	yes	—
247	C₂²×C₄	C₂×C₈×C₁₉	1	2	yes	—
248	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
249	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
251	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
252	C₂²×C₄	#41×C₁₉	1	2	yes	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	4	2	no	—
256	C₂×C₈	—	4	2	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	2	no	—
259	C₄⋊C₄	—	2	4	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	4	2	no	—
262	C₄⋊C₄	—	4	4	no	—
263	C₄⋊C₄	—	4	2	no	—
264	C₄⋊C₄	—	4	2	no	—
265	C₄⋊C₄	—	4	2	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	2	2	no	—
268	C₄²	—	4	1	no	—
269	C₄²	—	4	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
275	C₂³	C₄×D₄×C₁₉	1	2	yes	—
276	C₂³	C₂²×C₈×C₁₉	1	1	yes	characteristic
277	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
278	C₂³	C₁₉×#131	1	2	yes	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	8	4	no	—
304	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
305	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
306	C₂×C₄	C₁₉×#99	1	2	yes	—
307	C₂×C₄	C₁₉×#101	1	2	yes	—
308	C₂×C₄	C₁₉×#101	1	2	yes	—
309	C₂×C₄	C₁₉×#121	1	2	yes	—
310	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
311	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
312	C₈	—	4	4	no	—
313	C₈	—	8	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	C₁₉×#390	1	1	yes	characteristic
323	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
324	C₂²	C₁₉×#408	1	1	yes	characteristic
325	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
326	C₂²	C₁₉×#410	1	1	yes	characteristic
327	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
328	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
329	C₂²	C₈×D₄×C₁₉	1	2	yes	—
330	C₂²	C₁₉×#436	1	2	yes	—
331	C₄	—	2	2	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	4	no	—
337	C₄	—	4	1	no	—
338	C₄	—	8	2	no	—
339	C₄	C₁₉×#324	1	4	yes	complemented
340	C₂	—	2	2	no	—
341	C₂	—	2	2	no	—
342	C₂	C₂×C₁₉×#324	1	1	yes	characteristic
343	C₂	C₁₉×#1461	1	1	yes	characteristic
344	C₂	C₁₉×#1470	1	1	yes	characteristic
345	C₂	C₁₉×#1472	1	1	yes	characteristic
346	C₂	C₁₉×#1954	1	1	yes	characteristic
347	C₂	C₁₉×#1964	1	1	yes	characteristic
348	C₂	C₁₉×#1966	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×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
38. C₂×C₄⋊C₄×C₁₉	C₈	semidirect
95. #9650	C₁₉	direct (N × H)
169. C₄×C₁₉	#324	semidirect
212. C₂×C₄⋊C₄	C₈×C₁₉	semidirect
225. C₁₉	#9650	direct (N × H)
339. C₄	C₁₉×#324	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#389	2
C₁₉×#1797	2
C₄×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#324	2
#9650	19

Subgroups — C19×#9650 #18015609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9650 #18015609