Subgroups — C₁₉×#10318 #18016277

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#498	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₁₆×C₁₉	—	2	2	no	—
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₁₉×#498	—	2	2	no	—
13	C₁₉×#498	—	2	2	no	—
14	C₁₉×#494	—	2	2	no	—
15	C₁₉×#494	—	2	2	no	—
16	C₁₉×#487	—	2	2	no	—
17	C₁₉×#487	—	2	2	no	—
18	C₂×C₁₉×#106	—	2	2	no	—
19	C₂×C₁₉×#103	—	2	2	no	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₁₉×#340	—	2	2	no	—
25	C₁₉×#340	—	2	2	no	—
26	C₁₉×#340	—	2	2	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂×Q₁₆×C₁₉	—	2	8	no	—
31	C₂×Q₁₆×C₁₉	—	4	4	no	—
32	C₂×Q₁₆×C₁₉	—	4	4	no	—
33	C₂²×C₈×C₁₉	D₄	1	2	yes	—
34	C₂²×C₈×C₁₉	D₄	1	2	yes	—
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	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
47	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
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	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#106	—	2	8	no	—
59	C₁₉×#103	—	2	8	no	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	C₄×C₈×C₁₉	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₄×C₈×C₁₉	—	2	1	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	C₂×Q₈×C₁₉	—	2	2	no	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	2	no	—
73	C₂×Q₈×C₁₉	—	4	2	no	—
74	C₂×Q₈×C₁₉	—	4	2	no	—
75	C₂×Q₈×C₁₉	—	4	2	no	—
76	C₂×Q₈×C₁₉	—	4	2	no	—
77	C₂×Q₈×C₁₉	—	4	2	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	Q₁₆×C₁₉	—	4	16	no	—
86	C₂×C₈×C₁₉	—	2	2	no	—
87	C₂×C₈×C₁₉	—	2	2	no	—
88	C₂×C₈×C₁₉	—	2	2	no	—
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	SD₁₆	1	4	yes	—
94	C₂×C₈×C₁₉	Q₁₆	1	4	yes	complemented
95	C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₄⋊C₄×C₁₉	—	2	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	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	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	2	no	—
108	C₄⋊C₄×C₁₉	—	4	2	no	—
109	C₄⋊C₄×C₁₉	—	4	2	no	—
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	#10318	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	#127	1	1	yes	characteristic
116	Q₈×C₁₉	—	4	4	no	—
117	Q₈×C₁₉	—	4	4	no	—
118	Q₈×C₁₉	—	4	4	no	—
119	Q₈×C₁₉	—	8	2	no	—
120	Q₈×C₁₉	—	8	2	no	—
121	Q₈×C₁₉	—	8	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	8	1	no	—
126	C₂×C₄×C₁₉	—	8	1	no	—
127	C₂×C₄×C₁₉	—	8	1	no	—
128	C₂×C₄×C₁₉	—	8	1	no	—
129	C₂×C₄×C₁₉	—	8	1	no	—
130	C₂×C₄×C₁₉	—	8	1	no	—
131	C₂×C₄×C₁₉	—	8	1	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	—	8	1	no	—
134	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
141	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
142	C₂×C₄×C₁₉	#135	1	2	yes	—
143	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
144	C₂×C₄×C₁₉	#137	1	2	yes	—
145	C₂×C₄×C₁₉	#137	1	2	yes	—
146	C₈×C₁₉	—	2	4	no	—
147	C₈×C₁₉	—	2	4	no	—
148	C₈×C₁₉	—	4	2	no	—
149	C₂×#498	C₂×C₁₉	1	1	yes	characteristic
150	C₂×#494	C₂×C₁₉	1	1	yes	characteristic
151	C₂×#487	C₂×C₁₉	1	1	yes	characteristic
152	#1990	C₂×C₁₉	1	1	yes	characteristic
153	#1990	C₂×C₁₉	1	1	yes	characteristic
154	#1990	C₂×C₁₉	1	1	yes	characteristic
155	#1273	C₂×C₁₉	1	1	yes	characteristic
156	C₂²×C₁₉	#392	1	1	yes	characteristic
157	C₂²×C₁₉	#492	1	1	yes	characteristic
158	C₂²×C₁₉	#494	1	1	yes	characteristic
159	C₂²×C₁₉	#495	1	1	yes	characteristic
160	C₂²×C₁₉	#496	1	1	yes	characteristic
161	C₂²×C₁₉	#497	1	1	yes	characteristic
162	C₂²×C₁₉	#497	1	1	yes	characteristic
163	C₄×C₁₉	—	8	2	no	—
164	C₄×C₁₉	—	8	2	no	—
165	C₄×C₁₉	—	8	2	no	—
166	C₄×C₁₉	—	16	1	no	—
167	C₄×C₁₉	#450	1	2	yes	—
168	C₄×C₁₉	#451	1	2	yes	—
169	C₄×C₁₉	#452	1	2	yes	—
170	C₄×C₁₉	#460	1	2	yes	—
171	C₄×C₁₉	#462	1	2	yes	—
172	C₄×C₁₉	#464	1	2	yes	—
173	C₂²×Q₁₆	—	2	2	no	—
174	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
175	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
176	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
177	#498	—	2	2	no	—
178	#498	—	2	2	no	—
179	#494	—	2	2	no	—
180	#494	—	2	2	no	—
181	#487	—	2	2	no	—
182	#487	—	2	2	no	—
183	C₂×#106	—	2	2	no	—
184	C₂×#103	—	2	2	no	—
185	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
188	#384	C₂²×C₁₉	1	1	yes	characteristic
189	#340	—	2	2	no	—
190	#340	—	2	2	no	—
191	#340	—	2	2	no	—
192	C₂×C₁₉	#1707	1	1	yes	characteristic
193	C₂×C₁₉	#1716	1	1	yes	characteristic
194	C₂×C₁₉	#1720	1	1	yes	characteristic
195	C₂×C₁₉	#1723	1	1	yes	characteristic
196	C₂×C₁₉	#2014	1	1	yes	characteristic
197	C₂×C₁₉	#2015	1	1	yes	characteristic
198	C₂×C₁₉	#2016	1	1	yes	characteristic
199	C₂²×Q₈	—	2	1	no	—
200	C₂²×Q₈	—	2	1	no	—
201	C₂²×Q₈	—	2	1	no	—
202	C₂×Q₁₆	—	2	8	no	—
203	C₂×Q₁₆	—	4	4	no	—
204	C₂×Q₁₆	—	4	4	no	—
205	C₂²×C₈	D₄×C₁₉	1	2	yes	—
206	C₂²×C₈	D₄×C₁₉	1	2	yes	—
207	C₂²×C₈	D₄×C₁₉	1	2	yes	—
208	C₄⋊Q₈	—	2	1	no	—
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	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	D₄×C₁₉	1	2	yes	—
218	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
219	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	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×C₄²	C₂³×C₁₉	1	1	yes	characteristic
230	#106	—	2	8	no	—
231	#103	—	2	8	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	C₄×C₈	—	2	1	no	—
237	C₄×C₈	—	2	1	no	—
238	C₁₉	#10318	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	2	2	no	—
242	C₂×Q₈	—	4	1	no	—
243	C₂×Q₈	—	4	1	no	—
244	C₂×Q₈	—	4	1	no	—
245	C₂×Q₈	—	4	2	no	—
246	C₂×Q₈	—	4	2	no	—
247	C₂×Q₈	—	4	2	no	—
248	C₂×Q₈	—	4	2	no	—
249	C₂×Q₈	—	4	2	no	—
250	C₂×Q₈	—	4	2	no	—
251	C₂²×C₄	—	4	1	no	—
252	C₂²×C₄	—	4	1	no	—
253	C₂²×C₄	—	4	1	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
258	Q₁₆	—	4	16	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	SD₁₆×C₁₉	1	4	yes	—
267	C₂×C₈	Q₁₆×C₁₉	1	4	yes	complemented
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	4	1	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	—	4	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
285	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₄²	#41×C₁₉	1	1	yes	characteristic
287	C₂³	C₁₉×#127	1	1	yes	characteristic
288	Q₈	—	4	4	no	—
289	Q₈	—	4	4	no	—
290	Q₈	—	4	4	no	—
291	Q₈	—	8	2	no	—
292	Q₈	—	8	2	no	—
293	Q₈	—	8	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	8	1	no	—
298	C₂×C₄	—	8	1	no	—
299	C₂×C₄	—	8	1	no	—
300	C₂×C₄	—	8	1	no	—
301	C₂×C₄	—	8	1	no	—
302	C₂×C₄	—	8	1	no	—
303	C₂×C₄	—	8	1	no	—
304	C₂×C₄	—	8	1	no	—
305	C₂×C₄	—	8	1	no	—
306	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
307	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
308	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
309	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
310	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
311	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
312	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
313	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
314	C₂×C₄	C₁₉×#135	1	2	yes	—
315	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
316	C₂×C₄	C₁₉×#137	1	2	yes	—
317	C₂×C₄	C₁₉×#137	1	2	yes	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	4	2	no	—
321	C₂²	C₁₉×#392	1	1	yes	characteristic
322	C₂²	C₁₉×#492	1	1	yes	characteristic
323	C₂²	C₁₉×#494	1	1	yes	characteristic
324	C₂²	C₁₉×#495	1	1	yes	characteristic
325	C₂²	C₁₉×#496	1	1	yes	characteristic
326	C₂²	C₁₉×#497	1	1	yes	characteristic
327	C₂²	C₁₉×#497	1	1	yes	characteristic
328	C₄	—	8	2	no	—
329	C₄	—	8	2	no	—
330	C₄	—	8	2	no	—
331	C₄	—	16	1	no	—
332	C₄	C₁₉×#450	1	2	yes	—
333	C₄	C₁₉×#451	1	2	yes	—
334	C₄	C₁₉×#452	1	2	yes	—
335	C₄	C₁₉×#460	1	2	yes	—
336	C₄	C₁₉×#462	1	2	yes	—
337	C₄	C₁₉×#464	1	2	yes	—
338	C₂	C₁₉×#1707	1	1	yes	characteristic
339	C₂	C₁₉×#1716	1	1	yes	characteristic
340	C₂	C₁₉×#1720	1	1	yes	characteristic
341	C₂	C₁₉×#1723	1	1	yes	characteristic
342	C₂	C₁₉×#2014	1	1	yes	characteristic
343	C₂	C₁₉×#2015	1	1	yes	characteristic
344	C₂	C₁₉×#2016	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#127
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
94. C₂×C₈×C₁₉	Q₁₆	semidirect
114. #10318	C₁₉	direct (N × H)
238. C₁₉	#10318	direct (N × H)
267. C₂×C₈	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#498	2
C₂×C₁₉×#494	2
C₂×C₁₉×#487	2
C₁₉×#1990	2
C₁₉×#1273	2
#10318	19

Subgroups — C19×#10318 #18016277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10318 #18016277