Subgroups — C₁₉×#13015 #18018974

Order 4864.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1969	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
11	C₂×C₁₉×Q₃₂	—	2	2	no	—
12	C₂×C₁₉×Q₃₂	—	2	2	no	—
13	C₂×C₁₉×Q₃₂	C₄	1	4	yes	complemented
14	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₁₉	—	2	2	no	—
17	C₄×Q₁₆×C₁₉	—	2	2	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	—	2	1	no	—
21	C₂×C₁₉×#103	—	2	1	no	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#358	—	2	2	no	—
25	C₁₉×#358	—	2	2	no	—
26	C₂²×Q₈×C₁₉	—	2	1	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₁₆×C₁₉	—	2	1	no	—
29	C₂×Q₁₆×C₁₉	—	2	1	no	—
30	C₂×Q₁₆×C₁₉	—	2	1	no	—
31	C₂×Q₁₆×C₁₉	—	2	1	no	—
32	C₂×Q₁₆×C₁₉	—	2	1	no	—
33	C₂×Q₁₆×C₁₉	—	2	1	no	—
34	C₂×Q₁₆×C₁₉	—	2	1	no	—
35	C₂×Q₁₆×C₁₉	—	2	1	no	—
36	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
39	C₂×Q₁₆×C₁₉	D₄	1	2	yes	—
40	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
42	C₄×Q₈×C₁₉	—	2	4	no	—
43	C₄×Q₈×C₁₉	—	4	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
47	C₂×C₄²×C₁₉	—	4	1	no	—
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₁₉×Q₃₂	—	2	8	no	—
50	C₂×C₁₆×C₁₉	—	2	1	no	—
51	C₂×C₁₆×C₁₉	—	2	1	no	—
52	C₂×C₁₆×C₁₉	—	2	1	no	—
53	C₂×C₁₆×C₁₉	—	2	1	no	—
54	C₂×C₁₆×C₁₉	—	2	1	no	—
55	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	—
56	C₁₉×#107	—	2	1	no	—
57	C₁₉×#107	—	2	1	no	—
58	C₁₉×#107	—	2	1	no	—
59	C₁₉×#107	D₄	1	2	yes	—
60	C₁₉×#103	—	2	4	no	—
61	C₁₉×#103	—	4	2	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	1	no	—
64	C₁₉×#95	—	4	1	no	—
65	C₁₉×#95	—	4	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	—	2	2	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	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	D₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	Q₁₆×C₁₉	—	2	2	no	—
86	Q₁₆×C₁₉	—	2	2	no	—
87	Q₁₆×C₁₉	—	2	2	no	—
88	Q₁₆×C₁₉	—	2	2	no	—
89	Q₁₆×C₁₉	—	2	2	no	—
90	Q₁₆×C₁₉	—	4	1	no	—
91	Q₁₆×C₁₉	—	4	1	no	—
92	Q₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	2	1	no	—
95	C₂×C₈×C₁₉	—	2	1	no	—
96	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
101	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	4	4	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	—	2	1	no	—
108	C₄²×C₁₉	—	2	1	no	—
109	C₄²×C₁₉	—	4	4	no	—
110	C₁₆×C₁₉	—	2	2	no	—
111	C₁₆×C₁₉	—	4	1	no	—
112	#13015	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
114	Q₈×C₁₉	—	2	4	no	—
115	Q₈×C₁₉	—	4	2	no	—
116	Q₈×C₁₉	—	4	2	no	—
117	Q₈×C₁₉	—	4	2	no	—
118	Q₈×C₁₉	—	4	2	no	—
119	Q₈×C₁₉	—	4	2	no	—
120	Q₈×C₁₉	—	8	1	no	—
121	Q₈×C₁₉	—	8	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	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	—	8	1	no	—
134	C₂×C₄×C₁₉	—	8	1	no	—
135	C₂×C₄×C₁₉	—	8	1	no	—
136	C₂×C₄×C₁₉	—	8	1	no	—
137	C₂×C₄×C₁₉	—	8	1	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	Q₃₂	1	2	yes	complemented
140	C₂×C₄×C₁₉	C₄×D₄	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	#135	1	1	yes	characteristic
144	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₈×C₁₉	—	4	1	no	—
147	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₈×C₁₉	#121	1	1	yes	characteristic
150	C₈×C₁₉	#123	1	1	yes	characteristic
151	C₂²×Q₃₂	C₂×C₁₉	1	1	yes	characteristic
152	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
153	C₂×#358	C₂×C₁₉	1	1	yes	characteristic
154	C₂×#358	C₂×C₁₉	1	1	yes	characteristic
155	#1969	C₂×C₁₉	1	1	yes	characteristic
156	#1380	C₂×C₁₉	1	1	yes	characteristic
157	#1374	C₂×C₁₉	1	1	yes	characteristic
158	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
159	C₂²×C₁₉	#447	1	1	yes	characteristic
160	C₂²×C₁₉	#459	1	1	yes	characteristic
161	C₂²×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
162	C₂²×C₁₉	#508	1	1	yes	characteristic
163	C₂²×C₁₉	#510	1	1	yes	characteristic
164	C₂²×C₁₉	#510	1	1	yes	characteristic
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	4	4	no	—
167	C₄×C₁₉	—	4	1	no	—
168	C₄×C₁₉	—	8	2	no	—
169	C₄×C₁₉	—	8	2	no	—
170	C₄×C₁₉	—	16	1	no	—
171	C₄×C₁₉	#386	1	1	yes	characteristic
172	C₄×C₁₉	#442	1	1	yes	characteristic
173	C₄×C₁₉	#449	1	1	yes	characteristic
174	C₄×C₁₉	#463	1	1	yes	characteristic
175	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
176	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
177	C₂×C₄×Q₈	—	2	1	no	—
178	C₂×Q₃₂	—	2	2	no	—
179	C₂×Q₃₂	—	2	2	no	—
180	C₂×Q₃₂	C₄×C₁₉	1	4	yes	complemented
181	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
182	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
183	C₄×Q₁₆	—	2	2	no	—
184	C₄×Q₁₆	—	2	2	no	—
185	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
186	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
187	C₂×#103	—	2	1	no	—
188	C₂×#103	—	2	1	no	—
189	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
190	#391	—	2	1	no	—
191	#358	—	2	2	no	—
192	#358	—	2	2	no	—
193	C₂×C₁₉	#1879	1	1	yes	characteristic
194	C₂×C₁₉	C₄×Q₃₂	1	1	yes	characteristic
195	C₂×C₁₉	#2176	1	1	yes	characteristic
196	C₂×C₁₉	#2188	1	1	yes	characteristic
197	C₂×C₁₉	#2189	1	1	yes	characteristic
198	C₂×C₁₉	#2209	1	1	yes	characteristic
199	C₂×C₁₉	#2211	1	1	yes	characteristic
200	C₂²×Q₈	—	2	1	no	—
201	C₂²×Q₈	—	2	1	no	—
202	C₂×Q₁₆	—	2	1	no	—
203	C₂×Q₁₆	—	2	1	no	—
204	C₂×Q₁₆	—	2	1	no	—
205	C₂×Q₁₆	—	2	1	no	—
206	C₂×Q₁₆	—	2	1	no	—
207	C₂×Q₁₆	—	2	1	no	—
208	C₂×Q₁₆	—	2	1	no	—
209	C₂×Q₁₆	—	2	1	no	—
210	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
211	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
212	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
213	C₂×Q₁₆	D₄×C₁₉	1	2	yes	—
214	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
216	C₄×Q₈	—	2	4	no	—
217	C₄×Q₈	—	4	2	no	—
218	C₂×C₄⋊C₄	—	2	1	no	—
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄⋊C₄	—	4	1	no	—
221	C₂×C₄²	—	4	1	no	—
222	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
223	Q₃₂	—	2	8	no	—
224	C₂×C₁₆	—	2	1	no	—
225	C₂×C₁₆	—	2	1	no	—
226	C₂×C₁₆	—	2	1	no	—
227	C₂×C₁₆	—	2	1	no	—
228	C₂×C₁₆	—	2	1	no	—
229	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	—
230	#107	—	2	1	no	—
231	#107	—	2	1	no	—
232	#107	—	2	1	no	—
233	#107	D₄×C₁₉	1	2	yes	—
234	#103	—	2	4	no	—
235	#103	—	4	2	no	—
236	C₄×C₈	—	2	1	no	—
237	C₄×C₈	—	2	1	no	—
238	#95	—	4	1	no	—
239	#95	—	4	1	no	—
240	C₁₉	#13015	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×Q₈	—	2	2	no	—
242	C₂×Q₈	—	2	2	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	2	2	no	—
245	C₂×Q₈	—	4	1	no	—
246	C₂×Q₈	—	4	1	no	—
247	C₂×Q₈	—	4	1	no	—
248	C₂×Q₈	—	4	1	no	—
249	C₂×Q₈	—	4	1	no	—
250	C₂×Q₈	—	4	1	no	—
251	C₂×Q₈	—	4	1	no	—
252	C₂×Q₈	—	4	1	no	—
253	C₂²×C₄	—	4	1	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
258	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
260	Q₁₆	—	2	2	no	—
261	Q₁₆	—	2	2	no	—
262	Q₁₆	—	2	2	no	—
263	Q₁₆	—	2	2	no	—
264	Q₁₆	—	2	2	no	—
265	Q₁₆	—	4	1	no	—
266	Q₁₆	—	4	1	no	—
267	Q₁₆	C₂²⋊C₄×C₁₉	1	4	yes	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
273	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
275	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
276	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₄⋊C₄	—	4	1	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	4	4	no	—
285	C₁₆	—	2	2	no	—
286	C₁₆	—	4	1	no	—
287	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
288	Q₈	—	2	4	no	—
289	Q₈	—	4	2	no	—
290	Q₈	—	4	2	no	—
291	Q₈	—	4	2	no	—
292	Q₈	—	4	2	no	—
293	Q₈	—	4	2	no	—
294	Q₈	—	8	1	no	—
295	Q₈	—	8	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	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	8	1	no	—
307	C₂×C₄	—	8	1	no	—
308	C₂×C₄	—	8	1	no	—
309	C₂×C₄	—	8	1	no	—
310	C₂×C₄	—	8	1	no	—
311	C₂×C₄	—	8	1	no	—
312	C₂×C₄	—	8	1	no	—
313	C₂×C₄	C₁₉×Q₃₂	1	2	yes	complemented
314	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
315	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
316	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
317	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
318	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₈	—	4	1	no	—
321	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
322	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
323	C₈	C₁₉×#121	1	1	yes	characteristic
324	C₈	C₁₉×#123	1	1	yes	characteristic
325	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
326	C₂²	C₁₉×#447	1	1	yes	characteristic
327	C₂²	C₁₉×#459	1	1	yes	characteristic
328	C₂²	C₂×C₁₉×Q₃₂	1	1	yes	characteristic
329	C₂²	C₁₉×#508	1	1	yes	characteristic
330	C₂²	C₁₉×#510	1	1	yes	characteristic
331	C₂²	C₁₉×#510	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	4	1	no	—
334	C₄	—	4	4	no	—
335	C₄	—	8	2	no	—
336	C₄	—	8	2	no	—
337	C₄	—	16	1	no	—
338	C₄	C₁₉×#386	1	1	yes	characteristic
339	C₄	C₁₉×#442	1	1	yes	characteristic
340	C₄	C₁₉×#449	1	1	yes	characteristic
341	C₄	C₁₉×#463	1	1	yes	characteristic
342	C₂	C₁₉×#1879	1	1	yes	characteristic
343	C₂	C₄×C₁₉×Q₃₂	1	1	yes	characteristic
344	C₂	C₁₉×#2176	1	1	yes	characteristic
345	C₂	C₁₉×#2188	1	1	yes	characteristic
346	C₂	C₁₉×#2189	1	1	yes	characteristic
347	C₂	C₁₉×#2209	1	1	yes	characteristic
348	C₂	C₁₉×#2211	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₉×Q₃₂	C₄	semidirect
112. #13015	C₁₉	direct (N × H)
139. C₂×C₄×C₁₉	Q₃₂	semidirect
180. C₂×Q₃₂	C₄×C₁₉	semidirect
240. C₁₉	#13015	direct (N × H)
313. C₂×C₄	C₁₉×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×Q₃₂	2
C₂×C₄×Q₁₆×C₁₉	2
C₂×C₁₉×#358	2
C₁₉×#1969	2
C₁₉×#1380	2
C₁₉×#1374	2
#13015	19

Subgroups — C19×#13015 #18018974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13015 #18018974