Subgroups — C₁₉×#9688 #18015647

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2861	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1745	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#330	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#329	C₂	1	2	yes	maximal
6	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
9	C₂×C₁₉×#97	C₂²	1	2	yes	—
10	C₂×C₁₉×#97	C₂²	1	2	yes	—
11	C₁₉×#391	C₄	1	1	yes	characteristic
12	C₁₉×#391	C₄	1	1	yes	characteristic
13	C₁₉×#390	C₄	1	1	yes	characteristic
14	C₁₉×#390	C₄	1	1	yes	characteristic
15	C₁₉×#388	—	2	1	no	—
16	C₁₉×#388	—	2	1	no	—
17	C₁₉×#388	—	2	1	no	—
18	C₁₉×#388	—	2	1	no	—
19	C₄³×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#336	—	2	1	no	—
21	C₁₉×#336	—	2	1	no	—
22	C₁₉×#336	—	2	1	no	—
23	C₁₉×#330	—	2	4	no	—
24	C₁₉×#329	—	2	4	no	—
25	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₂²×C₈×C₁₉	—	2	2	no	—
29	C₁₉×#125	—	2	2	no	—
30	C₁₉×#125	—	2	2	no	—
31	C₁₉×#124	—	2	2	no	—
32	C₁₉×#124	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₄⋊C₈	—	2	4	no	—
51	C₁₉×#97	—	2	2	no	—
52	C₁₉×#97	—	2	2	no	—
53	C₁₉×#97	—	2	2	no	—
54	C₁₉×#97	D₄	1	4	yes	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	C₂⁴×C₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	4	1	no	—
62	C₂×Q₈×C₁₉	—	4	1	no	—
63	C₂×D₄×C₁₉	—	2	2	no	—
64	C₂×D₄×C₁₉	—	4	1	no	—
65	C₂×D₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₁₉	—	2	4	no	—
77	C₂×C₈×C₁₉	—	2	4	no	—
78	C₂×C₈×C₁₉	—	4	2	no	—
79	C₂×C₈×C₁₉	—	4	2	no	—
80	C₂×C₈×C₁₉	—	4	2	no	—
81	C₂×C₈×C₁₉	—	4	2	no	—
82	C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₄⋊C₄×C₁₉	—	4	2	no	—
85	C₄⋊C₄×C₁₉	—	4	1	no	—
86	C₄⋊C₄×C₁₉	—	4	1	no	—
87	C₂²⋊C₄×C₁₉	—	4	2	no	—
88	C₂²⋊C₄×C₁₉	—	4	2	no	—
89	C₂²⋊C₄×C₁₉	—	4	2	no	—
90	C₂²⋊C₄×C₁₉	—	4	2	no	—
91	C₂²⋊C₄×C₁₉	—	4	2	no	—
92	C₂²⋊C₄×C₁₉	—	4	1	no	—
93	C₂²⋊C₄×C₁₉	—	4	1	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	—	4	1	no	—
96	C₄²×C₁₉	—	4	1	no	—
97	C₄²×C₁₉	—	4	1	no	—
98	C₄²×C₁₉	—	4	1	no	—
99	C₄²×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	C₂×D₄	1	2	yes	—
101	C₄²×C₁₉	#41	1	2	yes	—
102	#9688	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂³×C₁₉	—	4	1	no	—
104	C₂³×C₁₉	—	4	1	no	—
105	C₂³×C₁₉	—	4	1	no	—
106	C₂³×C₁₉	—	4	1	no	—
107	C₂³×C₁₉	—	4	1	no	—
108	C₂³×C₁₉	—	4	1	no	—
109	C₂³×C₁₉	—	4	1	no	—
110	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	Q₈×C₁₉	—	8	2	no	—
112	D₄×C₁₉	—	8	2	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	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	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	#104	1	2	yes	—
140	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₁₉	#121	1	2	yes	—
142	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
144	C₈×C₁₉	—	4	4	no	—
145	C₈×C₁₉	—	4	4	no	—
146	#2861	C₂×C₁₉	1	1	yes	characteristic
147	#1767	C₂×C₁₉	1	1	yes	characteristic, complemented
148	#1745	C₂×C₁₉	1	1	yes	characteristic, complemented
149	C₂×#330	C₂×C₁₉	1	2	yes	complemented
150	C₂×#329	C₂×C₁₉	1	2	yes	—
151	C₂²×C₁₉	—	8	1	no	—
152	C₂²×C₁₉	—	8	1	no	—
153	C₂²×C₁₉	—	8	1	no	—
154	C₂²×C₁₉	—	8	1	no	—
155	C₂²×C₁₉	—	8	1	no	—
156	C₂²×C₁₉	—	8	1	no	—
157	C₂²×C₁₉	—	8	1	no	—
158	C₂²×C₁₉	#390	1	1	yes	characteristic
159	C₂²×C₁₉	#413	1	1	yes	characteristic
160	C₂²×C₁₉	#413	1	1	yes	characteristic
161	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
162	C₂²×C₁₉	#421	1	1	yes	characteristic
163	C₂²×C₁₉	#421	1	1	yes	characteristic
164	C₂²×C₁₉	#421	1	1	yes	characteristic
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	2	2	no	—
167	C₄×C₁₉	—	2	1	no	—
168	C₄×C₁₉	—	2	1	no	—
169	C₄×C₁₉	—	2	2	no	—
170	C₄×C₁₉	—	4	1	no	—
171	C₄×C₁₉	—	4	1	no	—
172	C₄×C₁₉	—	4	1	no	—
173	C₄×C₁₉	—	8	1	no	—
174	C₄×C₁₉	—	8	1	no	—
175	C₄×C₁₉	—	8	1	no	—
176	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
177	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
178	C₂×C₄⋊C₈	—	2	1	no	—
179	C₂×#97	C₂²×C₁₉	1	2	yes	—
180	C₂×#97	C₂²×C₁₉	1	2	yes	—
181	#391	C₄×C₁₉	1	1	yes	characteristic
182	#391	C₄×C₁₉	1	1	yes	characteristic
183	#390	C₄×C₁₉	1	1	yes	characteristic
184	#390	C₄×C₁₉	1	1	yes	characteristic
185	#388	—	2	1	no	—
186	#388	—	2	1	no	—
187	#388	—	2	1	no	—
188	#388	—	2	1	no	—
189	C₄³	C₂²×C₁₉	1	1	yes	characteristic
190	#336	—	2	1	no	—
191	#336	—	2	1	no	—
192	#336	—	2	1	no	—
193	#330	—	2	4	no	—
194	#329	—	2	4	no	—
195	C₂×C₁₉	—	16	1	no	—
196	C₂×C₁₉	#1529	1	1	yes	characteristic
197	C₂×C₁₉	#1532	1	1	yes	characteristic
198	C₂×C₁₉	#1535	1	1	yes	characteristic
199	C₂×C₁₉	#1535	1	1	yes	characteristic
200	C₂×C₁₉	#1963	1	1	yes	characteristic
201	C₂×C₁₉	#1967	1	1	yes	characteristic
202	C₂×C₁₉	#1980	1	1	yes	characteristic
203	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
204	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	#125	—	2	2	no	—
208	#125	—	2	2	no	—
209	#124	—	2	2	no	—
210	#124	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	1	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	—	2	1	no	—
216	C₂×C₂²⋊C₄	—	2	1	no	—
217	C₂×C₂²⋊C₄	—	2	1	no	—
218	C₂×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
223	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
224	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
225	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
226	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
228	C₄⋊C₈	—	2	4	no	—
229	#97	—	2	2	no	—
230	#97	—	2	2	no	—
231	#97	—	2	2	no	—
232	#97	D₄×C₁₉	1	4	yes	—
233	#95	—	2	1	no	—
234	#95	—	2	1	no	—
235	#95	—	2	1	no	—
236	#95	—	2	1	no	—
237	C₁₉	#9688	1	1	yes	characteristic, direct product factor, Sylow
238	C₂⁴	—	2	1	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	4	1	no	—
241	C₂×Q₈	—	4	1	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	4	1	no	—
244	C₂×D₄	—	4	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
250	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	4	2	no	—
264	C₄⋊C₄	—	4	1	no	—
265	C₄⋊C₄	—	4	1	no	—
266	C₂²⋊C₄	—	4	2	no	—
267	C₂²⋊C₄	—	4	2	no	—
268	C₂²⋊C₄	—	4	2	no	—
269	C₂²⋊C₄	—	4	2	no	—
270	C₂²⋊C₄	—	4	1	no	—
271	C₂²⋊C₄	—	4	1	no	—
272	C₂²⋊C₄	—	4	2	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	4	1	no	—
275	C₄²	—	4	1	no	—
276	C₄²	—	4	1	no	—
277	C₄²	—	4	1	no	—
278	C₄²	—	4	1	no	—
279	C₄²	C₂×D₄×C₁₉	1	2	yes	—
280	C₄²	#41×C₁₉	1	2	yes	—
281	C₂³	—	4	1	no	—
282	C₂³	—	4	1	no	—
283	C₂³	—	4	1	no	—
284	C₂³	—	4	1	no	—
285	C₂³	—	4	1	no	—
286	C₂³	—	4	1	no	—
287	C₂³	—	4	1	no	—
288	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
289	Q₈	—	8	2	no	—
290	D₄	—	8	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	C₁₉×#104	1	2	yes	—
318	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
319	C₂×C₄	C₁₉×#121	1	2	yes	—
320	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
321	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
322	C₈	—	4	4	no	—
323	C₈	—	4	4	no	—
324	C₂²	—	8	1	no	—
325	C₂²	—	8	1	no	—
326	C₂²	—	8	1	no	—
327	C₂²	—	8	1	no	—
328	C₂²	—	8	1	no	—
329	C₂²	—	8	1	no	—
330	C₂²	—	8	1	no	—
331	C₂²	C₁₉×#390	1	1	yes	characteristic
332	C₂²	C₁₉×#413	1	1	yes	characteristic
333	C₂²	C₁₉×#413	1	1	yes	characteristic
334	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
335	C₂²	C₁₉×#421	1	1	yes	characteristic
336	C₂²	C₁₉×#421	1	1	yes	characteristic
337	C₂²	C₁₉×#421	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	1	no	—
346	C₄	—	8	1	no	—
347	C₄	—	8	1	no	—
348	C₄	—	8	1	no	—
349	C₂	—	16	1	no	—
350	C₂	C₁₉×#1529	1	1	yes	characteristic
351	C₂	C₁₉×#1532	1	1	yes	characteristic
352	C₂	C₁₉×#1535	1	1	yes	characteristic
353	C₂	C₁₉×#1535	1	1	yes	characteristic
354	C₂	C₁₉×#1963	1	1	yes	characteristic
355	C₂	C₁₉×#1967	1	1	yes	characteristic
356	C₂	C₁₉×#1980	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1767	C₂	semidirect
3. C₁₉×#1745	C₂	semidirect
4. C₂×C₁₉×#330	C₂	semidirect
102. #9688	C₁₉	direct (N × H)
147. #1767	C₂×C₁₉	semidirect
148. #1745	C₂×C₁₉	semidirect
149. C₂×#330	C₂×C₁₉	semidirect
237. C₁₉	#9688	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×#2861	2
C₁₉×#1767	2
C₁₉×#1745	2
C₂×C₁₉×#330	2
C₂×C₁₉×#329	2
#9688	19

Subgroups — C19×#9688 #18015647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9688 #18015647