Subgroups — C₁₉×#9543 #18015502

Order 4864.

408 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#334	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#103	C₄	1	1	yes	characteristic
12	C₂×C₁₉×#103	C₄	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	—	2	1	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#340	C₄	1	1	yes	characteristic
19	C₁₉×#340	C₄	1	1	yes	characteristic
20	C₁₉×#336	—	2	1	no	—
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#334	—	2	2	no	—
24	C₁₉×Q₈⋊C₈	—	2	2	no	—
25	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₁₉×C₄⋊C₈	—	2	1	no	—
45	C₁₉×C₄⋊C₈	—	2	1	no	—
46	C₁₉×C₄⋊C₈	—	2	1	no	—
47	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
48	C₁₉×#103	—	2	2	no	—
49	C₁₉×#103	C₈	1	4	yes	complemented
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₄×C₈×C₁₉	—	2	1	no	—
53	C₄×C₈×C₁₉	—	2	1	no	—
54	C₄×C₈×C₁₉	—	2	1	no	—
55	C₄×C₈×C₁₉	—	2	1	no	—
56	C₄×C₈×C₁₉	—	4	2	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₂×Q₈×C₁₉	—	2	1	no	—
59	C₂×Q₈×C₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	—	2	1	no	—
61	C₂×Q₈×C₁₉	—	2	1	no	—
62	C₂×Q₈×C₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
71	C₂×C₈×C₁₉	—	2	1	no	—
72	C₂×C₈×C₁₉	—	2	1	no	—
73	C₂×C₈×C₁₉	—	2	1	no	—
74	C₂×C₈×C₁₉	—	2	1	no	—
75	C₂×C₈×C₁₉	—	2	2	no	—
76	C₂×C₈×C₁₉	—	2	1	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	1	no	—
79	C₂×C₈×C₁₉	—	2	1	no	—
80	C₂×C₈×C₁₉	—	2	1	no	—
81	C₂×C₈×C₁₉	—	2	1	no	—
82	C₂×C₈×C₁₉	—	2	1	no	—
83	C₂×C₈×C₁₉	—	4	1	no	—
84	C₂×C₈×C₁₉	—	4	1	no	—
85	C₂×C₈×C₁₉	—	4	1	no	—
86	C₂×C₈×C₁₉	—	4	1	no	—
87	C₂×C₈×C₁₉	—	4	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
91	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
92	C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
99	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	4	1	no	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	#9543	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
110	Q₈×C₁₉	—	2	2	no	—
111	Q₈×C₁₉	—	2	2	no	—
112	Q₈×C₁₉	—	4	1	no	—
113	Q₈×C₁₉	—	4	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	2	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	4	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
142	C₈×C₁₉	—	2	2	no	—
143	C₈×C₁₉	—	2	2	no	—
144	C₈×C₁₉	—	4	2	no	—
145	C₈×C₁₉	—	4	1	no	—
146	C₈×C₁₉	—	4	2	no	—
147	C₈×C₁₉	—	4	1	no	—
148	C₈×C₁₉	—	8	1	no	—
149	#1984	C₂×C₁₉	1	1	yes	characteristic
150	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
151	C₄×#103	C₂×C₁₉	1	1	yes	characteristic
152	C₂×#334	C₂×C₁₉	1	1	yes	characteristic
153	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic
154	#1279	C₂×C₁₉	1	1	yes	characteristic
155	#1273	C₂×C₁₉	1	1	yes	characteristic
156	C₂²×C₁₉	#388	1	1	yes	characteristic
157	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
158	C₂²×C₁₉	#435	1	1	yes	characteristic
159	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
160	C₂²×C₁₉	#441	1	1	yes	characteristic
161	C₂²×C₁₉	#443	1	1	yes	characteristic
162	C₂²×C₁₉	#444	1	1	yes	characteristic
163	C₄×C₁₉	—	2	1	no	—
164	C₄×C₁₉	—	2	1	no	—
165	C₄×C₁₉	—	4	2	no	—
166	C₄×C₁₉	—	4	2	no	—
167	C₄×C₁₉	—	4	2	no	—
168	C₄×C₁₉	—	8	1	no	—
169	C₄×C₁₉	#431	1	1	yes	characteristic
170	C₄×C₁₉	#433	1	1	yes	characteristic
171	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
172	C₄×C₁₉	#436	1	1	yes	characteristic
173	C₄×C₁₉	#461	1	1	yes	characteristic
174	C₄×C₁₉	#464	1	1	yes	characteristic
175	C₄×C₁₉	#483	1	1	yes	characteristic
176	C₄×C₁₉	#485	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
180	C₂×#103	C₄×C₁₉	1	1	yes	characteristic
181	C₂×#103	C₄×C₁₉	1	1	yes	characteristic
182	C₂×C₄×C₈	—	2	1	no	—
183	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
187	#340	C₄×C₁₉	1	1	yes	characteristic
188	#340	C₄×C₁₉	1	1	yes	characteristic
189	#336	—	2	1	no	—
190	#336	—	2	1	no	—
191	#336	—	2	1	no	—
192	#334	—	2	2	no	—
193	Q₈⋊C₈	—	2	2	no	—
194	C₂×C₁₉	C₈×SD₁₆	1	1	yes	characteristic
195	C₂×C₁₉	#1579	1	1	yes	characteristic
196	C₂×C₁₉	#1582	1	1	yes	characteristic
197	C₂×C₁₉	#1587	1	1	yes	characteristic
198	C₂×C₁₉	#1923	1	1	yes	characteristic
199	C₂×C₁₉	#1927	1	1	yes	characteristic
200	C₂×C₁₉	#1929	1	1	yes	characteristic
201	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
202	C₂²×C₈	—	2	1	no	—
203	C₂²×C₈	—	2	1	no	—
204	C₂²×C₈	—	2	1	no	—
205	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
207	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
208	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
209	C₄×Q₈	—	2	1	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	—	2	1	no	—
212	C₄×Q₈	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
217	C₂×C₄²	—	2	1	no	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
220	C₄⋊C₈	—	2	1	no	—
221	C₄⋊C₈	—	2	1	no	—
222	C₄⋊C₈	—	2	1	no	—
223	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
224	#103	—	2	2	no	—
225	#103	C₈×C₁₉	1	4	yes	complemented
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	4	2	no	—
233	#95	—	2	1	no	—
234	C₁₉	#9543	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×Q₈	—	2	1	no	—
236	C₂×Q₈	—	2	1	no	—
237	C₂×Q₈	—	2	1	no	—
238	C₂×Q₈	—	2	1	no	—
239	C₂×Q₈	—	2	1	no	—
240	C₂×Q₈	C₂×C₈×C₁₉	1	2	yes	—
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
247	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
248	C₂×C₈	—	2	1	no	—
249	C₂×C₈	—	2	1	no	—
250	C₂×C₈	—	2	1	no	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	4	1	no	—
261	C₂×C₈	—	4	1	no	—
262	C₂×C₈	—	4	1	no	—
263	C₂×C₈	—	4	1	no	—
264	C₂×C₈	—	4	1	no	—
265	C₂×C₈	—	4	1	no	—
266	C₂×C₈	—	4	1	no	—
267	C₂×C₈	C₂×C₈×C₁₉	1	2	yes	—
268	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	2	1	no	—
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	4	1	no	—
274	C₄⋊C₄	—	4	1	no	—
275	C₄⋊C₄	C₂×C₈×C₁₉	1	2	yes	—
276	C₄⋊C₄	M₁₆×C₁₉	1	2	yes	—
277	C₄²	—	4	1	no	—
278	C₄²	—	4	1	no	—
279	C₄²	—	4	1	no	—
280	C₄²	—	4	1	no	—
281	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
282	C₄²	#41×C₁₉	1	1	yes	characteristic
283	C₄²	#41×C₁₉	1	1	yes	characteristic
284	C₄²	#41×C₁₉	1	1	yes	characteristic
285	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
286	Q₈	—	2	2	no	—
287	Q₈	—	2	2	no	—
288	Q₈	—	4	1	no	—
289	Q₈	—	4	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	1	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
305	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
306	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
307	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
308	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
309	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
310	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
311	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
312	C₂×C₄	C₁₉×#131	1	1	yes	characteristic
313	C₂×C₄	C₁₉×#131	1	1	yes	characteristic
314	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
315	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
316	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
317	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
318	C₈	—	2	2	no	—
319	C₈	—	2	2	no	—
320	C₈	—	4	2	no	—
321	C₈	—	4	1	no	—
322	C₈	—	4	2	no	—
323	C₈	—	4	1	no	—
324	C₈	—	8	1	no	—
325	C₂²	C₁₉×#388	1	1	yes	characteristic
326	C₂²	C₈×D₄×C₁₉	1	1	yes	characteristic
327	C₂²	C₁₉×#435	1	1	yes	characteristic
328	C₂²	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
329	C₂²	C₁₉×#441	1	1	yes	characteristic
330	C₂²	C₁₉×#443	1	1	yes	characteristic
331	C₂²	C₁₉×#444	1	1	yes	characteristic
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	4	2	no	—
335	C₄	—	4	2	no	—
336	C₄	—	4	2	no	—
337	C₄	—	8	1	no	—
338	C₄	C₁₉×#431	1	1	yes	characteristic
339	C₄	C₁₉×#433	1	1	yes	characteristic
340	C₄	C₈×D₄×C₁₉	1	1	yes	characteristic
341	C₄	C₁₉×#436	1	1	yes	characteristic
342	C₄	C₁₉×#461	1	1	yes	characteristic
343	C₄	C₁₉×#464	1	1	yes	characteristic
344	C₄	C₁₉×#483	1	1	yes	characteristic
345	C₄	C₁₉×#485	1	1	yes	characteristic
346	C₂	C₈×SD₁₆×C₁₉	1	1	yes	characteristic
347	C₂	C₁₉×#1579	1	1	yes	characteristic
348	C₂	C₁₉×#1582	1	1	yes	characteristic
349	C₂	C₁₉×#1587	1	1	yes	characteristic
350	C₂	C₁₉×#1923	1	1	yes	characteristic
351	C₂	C₁₉×#1927	1	1	yes	characteristic
352	C₂	C₁₉×#1929	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
49. C₁₉×#103	C₈	semidirect
108. #9543	C₁₉	direct (N × H)
225. #103	C₈×C₁₉	semidirect
234. C₁₉	#9543	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#1984	2
C₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×#103	2
C₂×C₁₉×#334	2
C₂×C₁₉×Q₈⋊C₈	2
C₁₉×#1279	2
C₁₉×#1273	2
#9543	19

Subgroups — C19×#9543 #18015502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9543 #18015502