Subgroups — C₁₉×#10277 #18016236

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 356 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×#477	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#475	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#332	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1277	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×#477	—	2	2	no	—
14	C₁₉×#477	—	2	2	no	—
15	C₁₉×#475	—	2	2	no	—
16	C₁₉×#475	—	2	2	no	—
17	C₂×C₁₉×#107	—	2	1	no	—
18	C₂×C₁₉×#106	—	2	1	no	—
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	—	2	1	no	—
23	C₂×C₁₉×#103	—	2	1	no	—
24	C₂×C₁₉×#103	—	2	2	no	—
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#336	—	2	2	no	—
27	C₁₉×#333	—	2	2	no	—
28	C₁₉×#332	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	D₄	1	2	yes	—
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	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
44	C₄×Q₈×C₁₉	—	2	1	no	—
45	C₄×Q₈×C₁₉	—	2	1	no	—
46	C₄×Q₈×C₁₉	—	2	1	no	—
47	C₄×Q₈×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	1	no	—
53	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₉	—	2	1	no	—
55	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×#107	—	2	4	no	—
57	C₁₉×#106	—	2	4	no	—
58	C₁₉×C₄⋊C₈	—	2	1	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×C₄⋊C₈	D₄	1	2	yes	—
64	C₁₉×#103	—	2	4	no	—
65	C₁₉×#103	—	2	4	no	—
66	C₁₉×#103	—	2	8	no	—
67	C₄×C₈×C₁₉	—	2	1	no	—
68	C₄×C₈×C₁₉	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	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	2	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	4	2	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×Q₈×C₁₉	—	8	2	no	—
81	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂×C₈×C₁₉	—	2	2	no	—
90	C₂×C₈×C₁₉	—	2	2	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	2	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	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	2	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	—	4	1	no	—
112	C₄²×C₁₉	—	4	1	no	—
113	C₄²×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
118	#10277	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₁₉	#121	1	1	yes	characteristic
120	Q₈×C₁₉	—	2	2	no	—
121	Q₈×C₁₉	—	2	2	no	—
122	Q₈×C₁₉	—	4	1	no	—
123	Q₈×C₁₉	—	4	1	no	—
124	Q₈×C₁₉	—	4	4	no	—
125	Q₈×C₁₉	—	8	2	no	—
126	Q₈×C₁₉	—	8	2	no	—
127	Q₈×C₁₉	—	8	1	no	—
128	Q₈×C₁₉	—	8	1	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	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	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	8	2	no	—
138	C₂×C₄×C₁₉	—	8	2	no	—
139	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#135	1	2	yes	—
148	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#137	1	2	yes	—
151	C₈×C₁₉	—	4	2	no	—
152	C₈×C₁₉	—	4	2	no	—
153	C₈×C₁₉	—	4	2	no	—
154	C₈×C₁₉	—	8	1	no	—
155	C₂×#487	C₂×C₁₉	1	1	yes	characteristic
156	C₂×#477	C₂×C₁₉	1	1	yes	characteristic
157	C₂×#475	C₂×C₁₉	1	1	yes	characteristic
158	#1984	C₂×C₁₉	1	1	yes	characteristic
159	C₂×#333	C₂×C₁₉	1	1	yes	characteristic
160	C₂×#332	C₂×C₁₉	1	1	yes	characteristic
161	#1277	C₂×C₁₉	1	1	yes	characteristic
162	C₂²×C₁₉	#392	1	1	yes	characteristic
163	C₂²×C₁₉	#464	1	2	yes	—
164	C₂²×C₁₉	#467	1	1	yes	characteristic
165	C₂²×C₁₉	#470	1	1	yes	characteristic
166	C₂²×C₁₉	#471	1	2	yes	—
167	C₄×C₁₉	—	2	1	no	—
168	C₄×C₁₉	—	2	1	no	—
169	C₄×C₁₉	—	4	2	no	—
170	C₄×C₁₉	—	8	2	no	—
171	C₄×C₁₉	—	8	1	no	—
172	C₄×C₁₉	—	8	2	no	—
173	C₄×C₁₉	#451	1	1	yes	characteristic
174	C₄×C₁₉	#451	1	1	yes	characteristic
175	C₄×C₁₉	#452	1	1	yes	characteristic
176	C₄×C₁₉	#452	1	1	yes	characteristic
177	C₄×C₁₉	#452	1	2	yes	—
178	C₄×C₁₉	#495	1	1	yes	characteristic
179	C₄×C₁₉	#497	1	1	yes	characteristic
180	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
181	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
182	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
183	#487	—	2	2	no	—
184	#487	—	2	2	no	—
185	#477	—	2	2	no	—
186	#477	—	2	2	no	—
187	#475	—	2	2	no	—
188	#475	—	2	2	no	—
189	C₂×#107	—	2	1	no	—
190	C₂×#106	—	2	1	no	—
191	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
194	C₂×#103	—	2	1	no	—
195	C₂×#103	—	2	1	no	—
196	C₂×#103	—	2	2	no	—
197	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
198	#336	—	2	2	no	—
199	#333	—	2	2	no	—
200	#332	—	2	2	no	—
201	C₂×C₁₉	#1684	1	2	yes	—
202	C₂×C₁₉	#1704	1	2	yes	—
203	C₂×C₁₉	#2001	1	1	yes	characteristic
204	C₂×C₁₉	#2015	1	1	yes	characteristic
205	C₂×C₁₉	#2019	1	1	yes	characteristic
206	C₂²×Q₈	—	2	1	no	—
207	C₂²×Q₈	—	2	1	no	—
208	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
209	C₂²×C₈	—	2	1	no	—
210	C₂²×C₈	—	2	1	no	—
211	C₂²×C₈	—	2	1	no	—
212	C₂²×C₈	D₄×C₁₉	1	2	yes	—
213	C₄⋊Q₈	—	2	1	no	—
214	C₄⋊Q₈	—	2	1	no	—
215	C₄⋊Q₈	—	2	1	no	—
216	C₄⋊Q₈	—	2	1	no	—
217	C₄⋊Q₈	—	2	1	no	—
218	C₄⋊Q₈	—	2	1	no	—
219	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
220	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
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	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
233	#107	—	2	4	no	—
234	#106	—	2	4	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	—	2	1	no	—
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
240	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
241	#103	—	2	4	no	—
242	#103	—	2	4	no	—
243	#103	—	2	8	no	—
244	C₄×C₈	—	2	1	no	—
245	C₄×C₈	—	2	1	no	—
246	C₁₉	#10277	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×Q₈	—	2	1	no	—
248	C₂×Q₈	—	2	1	no	—
249	C₂×Q₈	—	2	1	no	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	—	2	1	no	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	—	4	1	no	—
256	C₂×Q₈	—	4	2	no	—
257	C₂×Q₈	—	4	2	no	—
258	C₂×Q₈	—	8	2	no	—
259	C₂×Q₈	Q₁₆×C₁₉	1	2	yes	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
266	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	4	1	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	4	1	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	—	4	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄²	—	4	1	no	—
291	C₄²	—	4	1	no	—
292	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
294	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
295	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
296	C₂³	C₁₉×#121	1	1	yes	characteristic
297	Q₈	—	2	2	no	—
298	Q₈	—	2	2	no	—
299	Q₈	—	4	1	no	—
300	Q₈	—	4	1	no	—
301	Q₈	—	4	4	no	—
302	Q₈	—	8	2	no	—
303	Q₈	—	8	2	no	—
304	Q₈	—	8	1	no	—
305	Q₈	—	8	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
317	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
318	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
319	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
320	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
321	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
322	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
323	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
324	C₂×C₄	C₁₉×#135	1	2	yes	—
325	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
326	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
327	C₂×C₄	C₁₉×#137	1	2	yes	—
328	C₈	—	4	2	no	—
329	C₈	—	4	2	no	—
330	C₈	—	4	2	no	—
331	C₈	—	8	1	no	—
332	C₂²	C₁₉×#392	1	1	yes	characteristic
333	C₂²	C₁₉×#464	1	2	yes	—
334	C₂²	C₁₉×#467	1	1	yes	characteristic
335	C₂²	C₁₉×#470	1	1	yes	characteristic
336	C₂²	C₁₉×#471	1	2	yes	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	4	2	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	1	no	—
342	C₄	—	8	2	no	—
343	C₄	C₁₉×#451	1	1	yes	characteristic
344	C₄	C₁₉×#451	1	1	yes	characteristic
345	C₄	C₁₉×#452	1	1	yes	characteristic
346	C₄	C₁₉×#452	1	1	yes	characteristic
347	C₄	C₁₉×#452	1	2	yes	—
348	C₄	C₁₉×#495	1	1	yes	characteristic
349	C₄	C₁₉×#497	1	1	yes	characteristic
350	C₂	C₁₉×#1684	1	2	yes	—
351	C₂	C₁₉×#1704	1	2	yes	—
352	C₂	C₁₉×#2001	1	1	yes	characteristic
353	C₂	C₁₉×#2015	1	1	yes	characteristic
354	C₂	C₁₉×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#121
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
118. #10277	C₁₉	direct (N × H)
246. C₁₉	#10277	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×#477	2
C₂×C₁₉×#475	2
C₁₉×#1984	2
C₂×C₁₉×#333	2
C₂×C₁₉×#332	2
C₁₉×#1277	2
#10277	19

Subgroups — C19×#10277 #18016236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10277 #18016236