Subgroups — C₁₉×#9529 #18015488

Order 4864.

468 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3109	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1287	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#532	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#481	C₄	1	2	yes	—
11	C₁₉×#476	—	2	1	no	—
12	C₁₉×#459	—	2	1	no	—
13	C₁₉×#447	C₄	1	2	yes	—
14	C₁₉×#442	—	2	2	no	—
15	C₁₉×#436	—	2	1	no	—
16	C₁₉×#435	—	2	2	no	—
17	C₈×D₄×C₁₉	—	2	1	no	—
18	C₁₉×#432	C₂²	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	1	yes	characteristic
20	C₁₉×#432	C₂²	1	1	yes	characteristic
21	C₁₉×#431	C₂²	1	1	yes	characteristic
22	C₁₉×#423	C₂²	1	1	yes	characteristic
23	C₁₉×#408	—	2	2	no	—
24	C₁₉×#332	—	2	1	no	—
25	C₁₉×#331	—	2	1	no	—
26	C₁₉×D₄⋊C₈	—	2	1	no	—
27	C₁₉×D₄⋊C₈	—	2	1	no	—
28	C₁₉×#323	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂×D₈×C₁₉	—	2	2	no	—
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	2	no	—
36	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
37	C₁₉×#127	D₄	1	1	yes	characteristic
38	C₁₉×#124	—	2	1	no	—
39	C₁₉×#121	—	2	1	no	—
40	C₁₉×#121	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×#106	—	2	2	no	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×#102	—	2	2	no	—
58	C₁₉×#102	—	2	2	no	—
59	C₁₉×C₂²⋊C₈	—	2	2	no	—
60	C₁₉×C₂²⋊C₈	—	2	2	no	—
61	C₁₉×C₂²⋊C₈	—	2	1	no	—
62	C₁₉×C₂²⋊C₈	—	2	1	no	—
63	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
65	C₁₉×#97	—	2	1	no	—
66	C₁₉×#97	—	2	1	no	—
67	C₁₉×#97	—	2	1	no	—
68	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
69	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
70	C₂⁴×C₁₉	—	2	1	no	—
71	#41×C₁₉	—	8	2	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	8	1	no	—
85	C₂²×C₄×C₁₉	—	8	1	no	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	D₈×C₁₉	—	4	4	no	—
90	M₁₆×C₁₉	—	8	2	no	—
91	M₁₆×C₁₉	—	8	1	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	8	2	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
103	C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₉	—	4	1	no	—
106	C₂²⋊C₄×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	#9529	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	4	1	no	—
115	C₂³×C₁₉	—	4	1	no	—
116	C₂³×C₁₉	—	8	1	no	—
117	C₂³×C₁₉	—	8	1	no	—
118	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
119	Q₈×C₁₉	—	8	1	no	—
120	D₄×C₁₉	—	2	2	no	—
121	D₄×C₁₉	—	2	2	no	—
122	D₄×C₁₉	—	4	2	no	—
123	D₄×C₁₉	—	4	1	no	—
124	D₄×C₁₉	—	4	1	no	—
125	D₄×C₁₉	—	4	1	no	—
126	D₄×C₁₉	—	4	1	no	—
127	D₄×C₁₉	—	8	1	no	—
128	D₄×C₁₉	—	8	2	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	8	2	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
147	C₈×C₁₉	—	4	1	no	—
148	C₈×C₁₉	—	4	2	no	—
149	C₈×C₁₉	—	4	1	no	—
150	C₈×C₁₉	—	4	2	no	—
151	C₈×C₁₉	—	8	1	no	—
152	C₈×C₁₉	—	8	1	no	—
153	#3109	C₂×C₁₉	1	1	yes	characteristic
154	#2981	C₂×C₁₉	1	1	yes	characteristic, complemented
155	#1557	C₂×C₁₉	1	1	yes	characteristic, complemented
156	#1486	C₂×C₁₉	1	1	yes	characteristic, complemented
157	#1466	C₂×C₁₉	1	1	yes	characteristic, complemented
158	#1307	C₂×C₁₉	1	1	yes	characteristic, complemented
159	#1287	C₂×C₁₉	1	1	yes	characteristic, complemented
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	4	2	no	—
164	C₂²×C₁₉	—	4	2	no	—
165	C₂²×C₁₉	—	4	2	no	—
166	C₂²×C₁₉	—	4	2	no	—
167	C₂²×C₁₉	—	8	2	no	—
168	C₂²×C₁₉	—	8	2	no	—
169	C₂²×C₁₉	—	8	1	no	—
170	C₂²×C₁₉	—	8	1	no	—
171	C₂²×C₁₉	#386	1	1	yes	characteristic
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	4	2	no	—
178	C₄×C₁₉	—	8	1	no	—
179	C₄×C₁₉	#471	1	1	yes	characteristic
180	C₄×C₁₉	#472	1	1	yes	characteristic
181	#532	C₂²×C₁₉	1	1	yes	characteristic
182	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
183	#481	C₄×C₁₉	1	2	yes	—
184	#476	—	2	1	no	—
185	#459	—	2	1	no	—
186	#447	C₄×C₁₉	1	2	yes	—
187	#442	—	2	2	no	—
188	#436	—	2	1	no	—
189	#435	—	2	2	no	—
190	C₈×D₄	—	2	1	no	—
191	#432	C₂²×C₁₉	1	1	yes	characteristic
192	#432	C₂²×C₁₉	1	1	yes	characteristic
193	#432	C₂²×C₁₉	1	1	yes	characteristic
194	#431	C₂²×C₁₉	1	1	yes	characteristic
195	#423	C₂²×C₁₉	1	1	yes	characteristic
196	#408	—	2	2	no	—
197	#332	—	2	1	no	—
198	#331	—	2	1	no	—
199	D₄⋊C₈	—	2	1	no	—
200	D₄⋊C₈	—	2	1	no	—
201	#323	—	2	2	no	—
202	C₂×C₁₉	—	4	1	no	—
203	C₂×C₁₉	—	8	2	no	—
204	C₂×C₁₉	—	8	2	no	—
205	C₂×C₁₉	#1891	1	1	yes	characteristic
206	C₂×C₁₉	#1904	1	1	yes	characteristic
207	C₂×C₁₉	#1907	1	1	yes	characteristic
208	C₂×#41	—	2	1	no	—
209	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
210	C₂³×C₄	—	2	1	no	—
211	C₂×D₈	—	2	2	no	—
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	1	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
216	#127	D₄×C₁₉	1	1	yes	characteristic
217	#124	—	2	1	no	—
218	#121	—	2	1	no	—
219	#121	C₂×C₄×C₁₉	1	2	yes	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	D₄×C₁₉	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
229	#106	—	2	2	no	—
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	—	2	1	no	—
232	C₄⋊C₈	—	2	1	no	—
233	C₄⋊C₈	—	2	1	no	—
234	C₄⋊C₈	—	2	1	no	—
235	C₄⋊C₈	—	2	1	no	—
236	#102	—	2	2	no	—
237	#102	—	2	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	—	2	1	no	—
241	C₂²⋊C₈	—	2	1	no	—
242	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
243	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
244	#97	—	2	1	no	—
245	#97	—	2	1	no	—
246	#97	—	2	1	no	—
247	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
248	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
249	C₁₉	#9529	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁴	—	2	1	no	—
251	#41	—	8	2	no	—
252	C₂×Q₈	—	2	1	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	4	2	no	—
259	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	8	1	no	—
265	C₂²×C₄	—	8	1	no	—
266	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
268	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
269	D₈	—	4	4	no	—
270	M₁₆	—	8	2	no	—
271	M₁₆	—	8	1	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	—	4	1	no	—
278	C₂×C₈	—	8	2	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	2	2	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	4	1	no	—
287	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₄²	#41×C₁₉	1	1	yes	characteristic
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	4	1	no	—
294	C₂³	—	4	1	no	—
295	C₂³	—	8	1	no	—
296	C₂³	—	8	1	no	—
297	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
298	Q₈	—	8	1	no	—
299	D₄	—	2	2	no	—
300	D₄	—	2	2	no	—
301	D₄	—	4	2	no	—
302	D₄	—	4	1	no	—
303	D₄	—	4	1	no	—
304	D₄	—	4	1	no	—
305	D₄	—	4	1	no	—
306	D₄	—	8	1	no	—
307	D₄	—	8	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	8	2	no	—
317	C₂×C₄	—	8	1	no	—
318	C₂×C₄	—	8	1	no	—
319	C₂×C₄	—	8	1	no	—
320	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
322	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
323	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
324	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
325	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
326	C₈	—	4	1	no	—
327	C₈	—	4	2	no	—
328	C₈	—	4	1	no	—
329	C₈	—	4	2	no	—
330	C₈	—	8	1	no	—
331	C₈	—	8	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	8	2	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	1	no	—
342	C₂²	—	8	1	no	—
343	C₂²	C₁₉×#386	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	8	1	no	—
351	C₄	C₁₉×#471	1	1	yes	characteristic
352	C₄	C₁₉×#472	1	1	yes	characteristic
353	C₂	—	4	1	no	—
354	C₂	—	8	2	no	—
355	C₂	—	8	2	no	—
356	C₂	C₁₉×#1891	1	1	yes	characteristic
357	C₂	C₁₉×#1904	1	1	yes	characteristic
358	C₂	C₁₉×#1907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3109	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2981	C₂	semidirect
3. C₁₉×#1557	C₂	semidirect
4. C₁₉×#1486	C₂	semidirect
5. C₁₉×#1466	C₂	semidirect
6. C₁₉×#1307	C₂	semidirect
7. C₁₉×#1287	C₂	semidirect
111. #9529	C₁₉	direct (N × H)
154. #2981	C₂×C₁₉	semidirect
155. #1557	C₂×C₁₉	semidirect
156. #1486	C₂×C₁₉	semidirect
157. #1466	C₂×C₁₉	semidirect
158. #1307	C₂×C₁₉	semidirect
159. #1287	C₂×C₁₉	semidirect
249. C₁₉	#9529	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×#3109	2
C₁₉×#2981	2
C₁₉×#1557	2
C₁₉×#1486	2
C₁₉×#1466	2
C₁₉×#1307	2
C₁₉×#1287	2
#9529	19

Subgroups — C19×#9529 #18015488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9529 #18015488