Subgroups — C₁₉×#10073 #18016032

Order 4864.

566 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2567	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1981	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#487	—	2	2	no	—
12	C₁₉×#487	—	2	2	no	—
13	C₁₉×#475	—	2	2	no	—
14	C₁₉×#475	—	2	2	no	—
15	C₂×C₁₉×#106	—	2	1	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#103	—	2	1	no	—
19	C₂×C₁₉×#103	—	2	2	no	—
20	C₂×C₁₉×#103	—	2	2	no	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#395	—	2	2	no	—
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#389	—	2	2	no	—
25	C₁₉×#384	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#333	—	2	2	no	—
28	C₁₉×Q₈⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×C₄⋊Q₈	—	2	1	no	—
42	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₄×Q₈×C₁₉	—	2	1	no	—
45	C₄×Q₈×C₁₉	—	2	1	no	—
46	C₄×Q₈×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₄²×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#106	—	2	4	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
63	C₁₉×#103	—	2	4	no	—
64	C₁₉×#103	—	2	8	no	—
65	C₁₉×#103	—	4	4	no	—
66	C₄×C₈×C₁₉	—	2	1	no	—
67	C₄×C₈×C₁₉	D₄	1	2	yes	—
68	C₁₉×#95	—	2	4	no	—
69	C₁₉×#95	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	2	no	—
73	C₂×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	—	2	2	no	—
75	C₂×Q₈×C₁₉	—	2	2	no	—
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	4	4	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	2	no	—
81	C₂×Q₈×C₁₉	—	4	2	no	—
82	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	4	2	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	8	4	no	—
112	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	—
113	C₄²×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	#41	1	1	yes	characteristic
121	#10073	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	#120	1	1	yes	characteristic
123	Q₈×C₁₉	—	2	2	no	—
124	Q₈×C₁₉	—	2	2	no	—
125	Q₈×C₁₉	—	4	4	no	—
126	Q₈×C₁₉	—	4	1	no	—
127	Q₈×C₁₉	—	4	1	no	—
128	Q₈×C₁₉	—	4	4	no	—
129	Q₈×C₁₉	—	8	2	no	—
130	Q₈×C₁₉	—	8	1	no	—
131	Q₈×C₁₉	—	8	1	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	8	2	no	—
145	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#137	1	2	yes	—
157	C₈×C₁₉	—	4	2	no	—
158	C₈×C₁₉	—	4	2	no	—
159	C₈×C₁₉	—	8	1	no	—
160	C₂×#487	C₂×C₁₉	1	1	yes	characteristic
161	C₂×#475	C₂×C₁₉	1	1	yes	characteristic
162	#2567	C₂×C₁₉	1	1	yes	characteristic
163	#1981	C₂×C₁₉	1	1	yes	characteristic
164	C₂×#333	C₂×C₁₉	1	1	yes	characteristic
165	C₂×Q₈⋊C₈	C₂×C₁₉	1	1	yes	characteristic
166	#1279	C₂×C₁₉	1	1	yes	characteristic
167	C₂²×C₁₉	#392	1	1	yes	characteristic
168	C₂²×C₁₉	#448	1	2	yes	—
169	C₂²×C₁₉	#451	1	1	yes	characteristic
170	C₂²×C₁₉	#452	1	1	yes	characteristic
171	C₂²×C₁₉	#455	1	2	yes	—
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	4	4	no	—
175	C₄×C₁₉	—	4	2	no	—
176	C₄×C₁₉	—	8	1	no	—
177	C₄×C₁₉	—	8	2	no	—
178	C₄×C₁₉	—	8	2	no	—
179	C₄×C₁₉	#451	1	1	yes	characteristic
180	C₄×C₁₉	#452	1	1	yes	characteristic
181	C₄×C₁₉	#461	1	2	yes	—
182	C₄×C₁₉	#467	1	1	yes	characteristic
183	C₄×C₁₉	#470	1	1	yes	characteristic
184	C₄×C₁₉	#492	1	1	yes	characteristic
185	C₄×C₁₉	#497	1	1	yes	characteristic
186	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
187	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
188	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
189	#487	—	2	2	no	—
190	#487	—	2	2	no	—
191	#475	—	2	2	no	—
192	#475	—	2	2	no	—
193	C₂×#106	—	2	1	no	—
194	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#103	—	2	1	no	—
197	C₂×#103	—	2	2	no	—
198	C₂×#103	—	2	2	no	—
199	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
200	#395	—	2	2	no	—
201	#391	—	2	1	no	—
202	#389	—	2	2	no	—
203	#384	—	2	1	no	—
204	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
205	#333	—	2	2	no	—
206	Q₈⋊C₈	—	2	2	no	—
207	C₂×C₁₉	#1643	1	2	yes	—
208	C₂×C₁₉	#1645	1	2	yes	—
209	C₂×C₁₉	#2001	1	1	yes	characteristic
210	C₂×C₁₉	#2004	1	1	yes	characteristic
211	C₂×C₁₉	#2013	1	1	yes	characteristic
212	C₂²×Q₈	—	2	1	no	—
213	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
214	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	2	1	no	—
218	C₄⋊Q₈	—	2	1	no	—
219	C₄⋊Q₈	—	2	1	no	—
220	C₄⋊Q₈	—	2	1	no	—
221	C₄⋊Q₈	—	2	1	no	—
222	C₄⋊Q₈	—	2	1	no	—
223	C₄⋊Q₈	—	2	1	no	—
224	C₄⋊Q₈	—	2	1	no	—
225	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	2	1	no	—
240	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
241	#106	—	2	4	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
246	#103	—	2	4	no	—
247	#103	—	2	8	no	—
248	#103	—	4	4	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	D₄×C₁₉	1	2	yes	—
251	#95	—	2	4	no	—
252	#95	—	2	1	no	—
253	C₁₉	#10073	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	4	4	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	Q₁₆×C₁₉	1	2	yes	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	4	2	no	—
278	C₂×C₈	—	4	1	no	—
279	C₂×C₈	—	4	1	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	4	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	8	4	no	—
296	C₄⋊C₄	SD₁₆×C₁₉	1	4	yes	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	1	no	—
300	C₄²	—	4	1	no	—
301	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₄²	#41×C₁₉	1	1	yes	characteristic
305	C₂³	C₁₉×#120	1	1	yes	characteristic
306	Q₈	—	2	2	no	—
307	Q₈	—	2	2	no	—
308	Q₈	—	4	4	no	—
309	Q₈	—	4	1	no	—
310	Q₈	—	4	1	no	—
311	Q₈	—	4	4	no	—
312	Q₈	—	8	2	no	—
313	Q₈	—	8	1	no	—
314	Q₈	—	8	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	8	2	no	—
328	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
329	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
330	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
331	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
332	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
333	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
334	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
335	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
336	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
337	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
338	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
339	C₂×C₄	C₁₉×#137	1	2	yes	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	8	1	no	—
343	C₂²	C₁₉×#392	1	1	yes	characteristic
344	C₂²	C₁₉×#448	1	2	yes	—
345	C₂²	C₁₉×#451	1	1	yes	characteristic
346	C₂²	C₁₉×#452	1	1	yes	characteristic
347	C₂²	C₁₉×#455	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	4	no	—
351	C₄	—	4	2	no	—
352	C₄	—	8	2	no	—
353	C₄	—	8	1	no	—
354	C₄	—	8	2	no	—
355	C₄	C₁₉×#451	1	1	yes	characteristic
356	C₄	C₁₉×#452	1	1	yes	characteristic
357	C₄	C₁₉×#461	1	2	yes	—
358	C₄	C₁₉×#467	1	1	yes	characteristic
359	C₄	C₁₉×#470	1	1	yes	characteristic
360	C₄	C₁₉×#492	1	1	yes	characteristic
361	C₄	C₁₉×#497	1	1	yes	characteristic
362	C₂	C₁₉×#1643	1	2	yes	—
363	C₂	C₁₉×#1645	1	2	yes	—
364	C₂	C₁₉×#2001	1	1	yes	characteristic
365	C₂	C₁₉×#2004	1	1	yes	characteristic
366	C₂	C₁₉×#2013	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
121. #10073	C₁₉	direct (N × H)
253. C₁₉	#10073	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×#487	2
C₂×C₁₉×#475	2
C₁₉×#2567	2
C₁₉×#1981	2
C₂×C₁₉×#333	2
C₂×C₁₉×Q₈⋊C₈	2
C₁₉×#1279	2
#10073	19

Subgroups — C19×#10073 #18016032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10073 #18016032