Subgroups — C₁₉×#9492 #18015451

Order 4864.

600 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2873	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2598	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1490	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1464	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1288	C₂	1	2	yes	maximal, complemented
6	C₂²×M₁₆×C₁₉	—	2	1	no	—
7	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
9	C₁₉×#432	C₂²	1	2	yes	—
10	C₁₉×#405	—	2	4	no	—
11	C₄×M₁₆×C₁₉	—	2	1	no	—
12	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#400	C₄	1	1	yes	characteristic
14	C₁₉×#399	C₄	1	1	yes	characteristic
15	C₁₉×#394	C₄	1	1	yes	characteristic
16	C₁₉×#392	C₄	1	1	yes	characteristic
17	C₁₉×#388	—	2	1	no	—
18	C₁₉×#386	—	2	1	no	—
19	C₁₉×#386	—	2	1	no	—
20	C₁₉×#385	—	2	1	no	—
21	C₁₉×#383	C₂²	1	1	yes	characteristic
22	C₁₉×D₄⋊C₈	—	2	4	no	—
23	C₁₉×#324	—	2	1	no	—
24	C₁₉×#323	—	2	1	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×M₁₆×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	2	4	no	—
31	C₂×M₁₆×C₁₉	—	2	4	no	—
32	C₂×M₁₆×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₁₉×#117	—	2	2	no	—
37	C₁₉×#117	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×C₄⋊C₈	—	2	2	no	—
52	C₁₉×C₂²⋊C₈	—	2	2	no	—
53	C₁₉×#97	—	2	2	no	—
54	C₁₉×#97	—	2	2	no	—
55	C₁₉×#97	—	2	2	no	—
56	C₄×C₈×C₁₉	—	2	2	no	—
57	C₄×C₈×C₁₉	D₄	1	4	yes	complemented
58	C₁₉×#95	—	2	1	no	—
59	C₁₉×#95	—	2	1	no	—
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
63	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
64	C₂⁴×C₁₉	—	2	1	no	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×C₁₉	—	4	2	no	—
68	C₂×D₄×C₁₉	—	4	2	no	—
69	C₂×D₄×C₁₉	—	4	2	no	—
70	C₂×D₄×C₁₉	—	8	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	—	8	1	no	—
80	C₂²×C₄×C₁₉	—	8	1	no	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	M₁₆×C₁₉	—	2	8	no	—
88	M₁₆×C₁₉	—	2	4	no	—
89	M₁₆×C₁₉	—	2	4	no	—
90	C₂×C₈×C₁₉	—	2	8	no	—
91	C₂×C₈×C₁₉	—	2	4	no	—
92	C₂×C₈×C₁₉	—	4	2	no	—
93	C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	8	1	no	—
97	C₂²⋊C₄×C₁₉	—	2	2	no	—
98	C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂²⋊C₄×C₁₉	—	4	2	no	—
100	C₂²⋊C₄×C₁₉	—	4	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	1	no	—
102	C₂²⋊C₄×C₁₉	—	4	1	no	—
103	C₂²⋊C₄×C₁₉	—	8	1	no	—
104	C₂²⋊C₄×C₁₉	—	8	1	no	—
105	C₄²×C₁₉	—	2	1	no	—
106	C₄²×C₁₉	—	2	1	no	—
107	C₄²×C₁₉	C₂×D₄	1	2	yes	—
108	C₄²×C₁₉	#41	1	2	yes	—
109	#9492	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	—	4	1	no	—
114	C₂³×C₁₉	—	4	1	no	—
115	C₂³×C₁₉	—	4	1	no	—
116	C₂³×C₁₉	—	4	1	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	—	4	1	no	—
119	C₂³×C₁₉	—	4	1	no	—
120	C₂³×C₁₉	—	4	1	no	—
121	C₂³×C₁₉	#104	1	2	yes	—
122	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	D₄×C₁₉	—	2	4	no	—
124	D₄×C₁₉	—	4	2	no	—
125	D₄×C₁₉	—	8	4	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	8	4	no	—
149	C₂×C₄×C₁₉	#104	1	2	yes	—
150	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#121	1	2	yes	—
153	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
154	C₈×C₁₉	—	2	8	no	—
155	C₈×C₁₉	—	8	2	no	—
156	#2873	C₂×C₁₉	1	1	yes	characteristic, complemented
157	#2598	C₂×C₁₉	1	1	yes	characteristic
158	#1490	C₂×C₁₉	1	2	yes	complemented
159	#1464	C₂×C₁₉	1	1	yes	characteristic, complemented
160	#1288	C₂×C₁₉	1	2	yes	complemented
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	2	no	—
164	C₂²×C₁₉	—	4	2	no	—
165	C₂²×C₁₉	—	4	2	no	—
166	C₂²×C₁₉	—	4	2	no	—
167	C₂²×C₁₉	—	4	1	no	—
168	C₂²×C₁₉	—	4	1	no	—
169	C₂²×C₁₉	—	4	2	no	—
170	C₂²×C₁₉	—	8	1	no	—
171	C₂²×C₁₉	—	8	1	no	—
172	C₂²×C₁₉	—	8	1	no	—
173	C₂²×C₁₉	—	8	1	no	—
174	C₂²×C₁₉	—	8	1	no	—
175	C₂²×C₁₉	#386	1	1	yes	characteristic
176	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	—	8	1	no	—
186	C₄×C₁₉	—	8	1	no	—
187	C₄×C₁₉	—	8	1	no	—
188	C₂²×M₁₆	—	2	1	no	—
189	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
190	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
191	#432	C₂²×C₁₉	1	2	yes	—
192	#405	—	2	4	no	—
193	C₄×M₁₆	—	2	1	no	—
194	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
195	#400	C₄×C₁₉	1	1	yes	characteristic
196	#399	C₄×C₁₉	1	1	yes	characteristic
197	#394	C₄×C₁₉	1	1	yes	characteristic
198	#392	C₄×C₁₉	1	1	yes	characteristic
199	#388	—	2	1	no	—
200	#386	—	2	1	no	—
201	#386	—	2	1	no	—
202	#385	—	2	1	no	—
203	#383	C₂²×C₁₉	1	1	yes	characteristic
204	D₄⋊C₈	—	2	4	no	—
205	#324	—	2	1	no	—
206	#323	—	2	1	no	—
207	C₂×C₁₉	—	2	1	no	—
208	C₂×C₁₉	—	2	1	no	—
209	C₂×C₁₉	—	4	2	no	—
210	C₂×C₁₉	—	8	2	no	—
211	C₂×C₁₉	#1891	1	1	yes	characteristic
212	C₂×C₁₉	#1896	1	1	yes	characteristic
213	C₂×C₁₉	#1910	1	1	yes	characteristic
214	C₂²×D₄	—	2	1	no	—
215	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
216	C₂³×C₄	—	2	1	no	—
217	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
218	C₂×M₁₆	—	2	4	no	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	#117	—	2	2	no	—
226	#117	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	#97	—	2	2	no	—
243	#97	—	2	2	no	—
244	#97	—	2	2	no	—
245	C₄×C₈	—	2	2	no	—
246	C₄×C₈	D₄×C₁₉	1	4	yes	complemented
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
252	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
253	C₁₉	#9492	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	—	2	1	no	—
255	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	4	2	no	—
258	C₂×D₄	—	4	2	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂×D₄	—	8	1	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	8	1	no	—
270	C₂²×C₄	—	8	1	no	—
271	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
277	M₁₆	—	2	8	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	2	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	8	1	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	4	2	no	—
290	C₂²⋊C₄	—	4	1	no	—
291	C₂²⋊C₄	—	4	1	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₂²⋊C₄	—	8	1	no	—
294	C₂²⋊C₄	—	8	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	C₂×D₄×C₁₉	1	2	yes	—
298	C₄²	#41×C₁₉	1	2	yes	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	4	1	no	—
303	C₂³	—	4	1	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	C₁₉×#104	1	2	yes	—
311	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
312	D₄	—	2	4	no	—
313	D₄	—	4	2	no	—
314	D₄	—	8	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	C₁₉×#104	1	2	yes	—
339	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
340	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
341	C₂×C₄	C₁₉×#121	1	2	yes	—
342	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
343	C₈	—	2	8	no	—
344	C₈	—	8	2	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	C₁₉×#386	1	1	yes	characteristic
360	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
361	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	2	1	no	—
374	C₂	—	4	2	no	—
375	C₂	—	8	2	no	—
376	C₂	C₁₉×#1891	1	1	yes	characteristic
377	C₂	C₁₉×#1896	1	1	yes	characteristic
378	C₂	C₁₉×#1910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#392	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2873	C₂	semidirect
3. C₁₉×#1490	C₂	semidirect
4. C₁₉×#1464	C₂	semidirect
5. C₁₉×#1288	C₂	semidirect
57. C₄×C₈×C₁₉	D₄	semidirect
109. #9492	C₁₉	direct (N × H)
156. #2873	C₂×C₁₉	semidirect
158. #1490	C₂×C₁₉	semidirect
159. #1464	C₂×C₁₉	semidirect
160. #1288	C₂×C₁₉	semidirect
246. C₄×C₈	D₄×C₁₉	semidirect
253. C₁₉	#9492	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×#2873	2
C₁₉×#2598	2
C₁₉×#1490	2
C₁₉×#1464	2
C₁₉×#1288	2
#9492	19

Subgroups — C19×#9492 #18015451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9492 #18015451