Subgroups — C₁₉×#9417 #18015376

Order 4864.

442 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3184	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1291	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#532	C₂²	1	1	yes	characteristic
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₁₉×#498	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#493	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#486	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#486	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#469	—	2	2	no	—
15	C₁₉×#442	—	2	2	no	—
16	C₁₉×#435	—	2	2	no	—
17	C₁₉×#435	—	2	2	no	—
18	C₁₉×#432	C₂²	1	1	yes	characteristic
19	C₁₉×#432	C₂²	1	1	yes	characteristic
20	C₁₉×#432	C₂²	1	1	yes	characteristic
21	C₁₉×#408	—	2	2	no	—
22	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#383	C₂²	1	1	yes	characteristic
24	C₁₉×#329	—	2	2	no	—
25	C₁₉×#327	—	2	2	no	—
26	C₁₉×#327	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	1	no	—
28	C₂×#41×C₁₉	—	2	1	no	—
29	C₂×D₈×C₁₉	—	2	2	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₂²×C₈×C₁₉	—	2	2	no	—
33	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
34	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
35	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
36	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
37	C₁₉×#124	—	2	1	no	—
38	C₁₉×#124	—	2	1	no	—
39	C₁₉×#121	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	D₄	1	2	yes	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	D₄	1	2	yes	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₁₉×#106	—	2	2	no	—
49	C₁₉×C₄⋊C₈	—	2	1	no	—
50	C₁₉×C₄⋊C₈	—	2	1	no	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₁₉×#102	—	2	2	no	—
53	C₁₉×#102	—	2	2	no	—
54	C₁₉×C₂²⋊C₈	—	2	4	no	—
55	C₁₉×C₂²⋊C₈	—	2	1	no	—
56	C₁₉×C₂²⋊C₈	—	2	1	no	—
57	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
58	C₁₉×#97	—	2	1	no	—
59	C₁₉×#97	—	2	1	no	—
60	C₁₉×#97	—	2	1	no	—
61	C₁₉×#97	D₄	1	2	yes	—
62	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#95	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	1	no	—
67	#41×C₁₉	—	8	1	no	—
68	#41×C₁₉	—	8	1	no	—
69	#41×C₁₉	—	8	2	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	D₈×C₁₉	—	4	4	no	—
87	M₁₆×C₁₉	—	4	2	no	—
88	M₁₆×C₁₉	—	8	2	no	—
89	C₂×C₈×C₁₉	—	2	1	no	—
90	C₂×C₈×C₁₉	—	2	1	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	2	2	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	8	2	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
99	C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂²⋊C₄×C₁₉	—	4	1	no	—
102	C₂²⋊C₄×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	#9417	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₁₉	—	2	2	no	—
109	C₂³×C₁₉	—	4	1	no	—
110	C₂³×C₁₉	#121	1	1	yes	characteristic
111	Q₈×C₁₉	—	8	1	no	—
112	Q₈×C₁₉	—	8	1	no	—
113	D₄×C₁₉	—	4	2	no	—
114	D₄×C₁₉	—	4	2	no	—
115	D₄×C₁₉	—	8	1	no	—
116	D₄×C₁₉	—	8	1	no	—
117	D₄×C₁₉	—	8	1	no	—
118	D₄×C₁₉	—	8	1	no	—
119	D₄×C₁₉	—	8	2	no	—
120	D₄×C₁₉	—	8	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	1	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	8	2	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
138	C₈×C₁₉	—	2	2	no	—
139	C₈×C₁₉	—	4	2	no	—
140	C₈×C₁₉	—	4	2	no	—
141	C₈×C₁₉	—	4	1	no	—
142	C₈×C₁₉	—	8	1	no	—
143	#3184	C₂×C₁₉	1	1	yes	characteristic
144	#2980	C₂×C₁₉	1	1	yes	characteristic, complemented
145	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
146	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
147	#1514	C₂×C₁₉	1	1	yes	characteristic, complemented
148	#1291	C₂×C₁₉	1	1	yes	characteristic, complemented
149	#1288	C₂×C₁₉	1	1	yes	characteristic, complemented
150	C₂²×C₁₉	—	2	1	no	—
151	C₂²×C₁₉	—	2	1	no	—
152	C₂²×C₁₉	—	2	1	no	—
153	C₂²×C₁₉	—	4	2	no	—
154	C₂²×C₁₉	—	4	2	no	—
155	C₂²×C₁₉	—	4	2	no	—
156	C₂²×C₁₉	—	8	1	no	—
157	C₂²×C₁₉	—	8	1	no	—
158	C₂²×C₁₉	—	8	1	no	—
159	C₂²×C₁₉	#386	1	1	yes	characteristic
160	C₄×C₁₉	—	2	1	no	—
161	C₄×C₁₉	—	2	1	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	2	1	no	—
164	C₄×C₁₉	—	2	1	no	—
165	C₄×C₁₉	—	2	1	no	—
166	C₄×C₁₉	—	4	2	no	—
167	C₄×C₁₉	—	8	1	no	—
168	C₄×C₁₉	—	16	1	no	—
169	#532	C₂²×C₁₉	1	1	yes	characteristic
170	#532	C₂²×C₁₉	1	1	yes	characteristic
171	#498	C₄×C₁₉	1	1	yes	characteristic, complemented
172	#493	C₄×C₁₉	1	1	yes	characteristic, complemented
173	#486	C₄×C₁₉	1	1	yes	characteristic, complemented
174	#486	C₄×C₁₉	1	1	yes	characteristic, complemented
175	#469	—	2	2	no	—
176	#442	—	2	2	no	—
177	#435	—	2	2	no	—
178	#435	—	2	2	no	—
179	#432	C₂²×C₁₉	1	1	yes	characteristic
180	#432	C₂²×C₁₉	1	1	yes	characteristic
181	#432	C₂²×C₁₉	1	1	yes	characteristic
182	#408	—	2	2	no	—
183	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
184	#383	C₂²×C₁₉	1	1	yes	characteristic
185	#329	—	2	2	no	—
186	#327	—	2	2	no	—
187	#327	—	2	2	no	—
188	C₂×C₁₉	—	4	1	no	—
189	C₂×C₁₉	—	8	2	no	—
190	C₂×C₁₉	—	16	1	no	—
191	C₂×C₁₉	#1884	1	1	yes	characteristic
192	C₂×C₁₉	#1903	1	1	yes	characteristic
193	C₂×C₁₉	#1904	1	1	yes	characteristic
194	C₂×#41	—	2	1	no	—
195	C₂×#41	—	2	1	no	—
196	C₂×D₈	—	2	2	no	—
197	C₂×M₁₆	—	2	1	no	—
198	C₂×M₁₆	—	2	2	no	—
199	C₂²×C₈	—	2	2	no	—
200	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
201	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
202	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
203	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
204	#124	—	2	1	no	—
205	#124	—	2	1	no	—
206	#121	—	2	1	no	—
207	#121	—	2	1	no	—
208	#121	—	2	1	no	—
209	#121	D₄×C₁₉	1	2	yes	—
210	C₄×D₄	—	2	1	no	—
211	C₄×D₄	—	2	1	no	—
212	C₄×D₄	—	2	1	no	—
213	C₄×D₄	D₄×C₁₉	1	2	yes	—
214	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
215	#106	—	2	2	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	—	2	1	no	—
218	C₄⋊C₈	—	2	1	no	—
219	#102	—	2	2	no	—
220	#102	—	2	2	no	—
221	C₂²⋊C₈	—	2	4	no	—
222	C₂²⋊C₈	—	2	1	no	—
223	C₂²⋊C₈	—	2	1	no	—
224	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
225	#97	—	2	1	no	—
226	#97	—	2	1	no	—
227	#97	—	2	1	no	—
228	#97	D₄×C₁₉	1	2	yes	—
229	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
230	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
231	#95	—	2	1	no	—
232	#95	—	2	1	no	—
233	#95	—	2	1	no	—
234	C₁₉	#9417	1	1	yes	characteristic, direct product factor, Sylow
235	#41	—	8	1	no	—
236	#41	—	8	1	no	—
237	#41	—	8	2	no	—
238	C₂×Q₈	—	2	1	no	—
239	C₂×Q₈	—	2	1	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	—	2	1	no	—
243	C₂×D₄	—	2	1	no	—
244	C₂×D₄	—	2	1	no	—
245	C₂×D₄	—	2	1	no	—
246	C₂×D₄	—	4	1	no	—
247	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	4	1	no	—
250	C₂²×C₄	—	4	1	no	—
251	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
253	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
254	D₈	—	4	4	no	—
255	M₁₆	—	4	2	no	—
256	M₁₆	—	8	2	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	4	1	no	—
262	C₂×C₈	—	8	2	no	—
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	—	2	1	no	—
265	C₄⋊C₄	—	2	1	no	—
266	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
267	C₂²⋊C₄	—	2	2	no	—
268	C₂²⋊C₄	—	2	2	no	—
269	C₂²⋊C₄	—	4	1	no	—
270	C₂²⋊C₄	—	4	1	no	—
271	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
272	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
273	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
274	C₄²	#41×C₁₉	1	1	yes	characteristic
275	C₂³	—	2	2	no	—
276	C₂³	—	4	1	no	—
277	C₂³	C₁₉×#121	1	1	yes	characteristic
278	Q₈	—	8	1	no	—
279	Q₈	—	8	1	no	—
280	D₄	—	4	2	no	—
281	D₄	—	4	2	no	—
282	D₄	—	8	1	no	—
283	D₄	—	8	1	no	—
284	D₄	—	8	1	no	—
285	D₄	—	8	1	no	—
286	D₄	—	8	2	no	—
287	D₄	—	8	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	4	1	no	—
290	C₂×C₄	—	4	1	no	—
291	C₂×C₄	—	4	1	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	1	no	—
295	C₂×C₄	—	8	2	no	—
296	C₂×C₄	—	8	1	no	—
297	C₂×C₄	—	8	1	no	—
298	C₂×C₄	—	8	1	no	—
299	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
301	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
302	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
303	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
304	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
305	C₈	—	2	2	no	—
306	C₈	—	4	2	no	—
307	C₈	—	4	2	no	—
308	C₈	—	4	1	no	—
309	C₈	—	8	1	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	4	2	no	—
314	C₂²	—	4	2	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	8	1	no	—
317	C₂²	—	8	1	no	—
318	C₂²	—	8	1	no	—
319	C₂²	C₁₉×#386	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	1	no	—
322	C₄	—	2	1	no	—
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	4	2	no	—
327	C₄	—	8	1	no	—
328	C₄	—	16	1	no	—
329	C₂	—	4	1	no	—
330	C₂	—	8	2	no	—
331	C₂	—	16	1	no	—
332	C₂	C₁₉×#1884	1	1	yes	characteristic
333	C₂	C₁₉×#1903	1	1	yes	characteristic
334	C₂	C₁₉×#1904	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3184	C₂
LCS	G ▷ C₄² ▷ 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
2. C₁₉×#2980	C₂	semidirect
3. C₁₉×#1536	C₂	semidirect
4. C₁₉×#1514	C₂	semidirect
5. C₁₉×#1514	C₂	semidirect
6. C₁₉×#1291	C₂	semidirect
7. C₁₉×#1288	C₂	semidirect
10. C₁₉×#498	C₄	semidirect
11. C₁₉×#493	C₄	semidirect
12. C₁₉×#486	C₄	semidirect
13. C₁₉×#486	C₄	semidirect
107. #9417	C₁₉	direct (N × H)
144. #2980	C₂×C₁₉	semidirect
145. #1536	C₂×C₁₉	semidirect
146. #1514	C₂×C₁₉	semidirect
147. #1514	C₂×C₁₉	semidirect
148. #1291	C₂×C₁₉	semidirect
149. #1288	C₂×C₁₉	semidirect
171. #498	C₄×C₁₉	semidirect
172. #493	C₄×C₁₉	semidirect
173. #486	C₄×C₁₉	semidirect
174. #486	C₄×C₁₉	semidirect
234. C₁₉	#9417	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×#3184	2
C₁₉×#2980	2
C₁₉×#1536	2
C₁₉×#1514	2
C₁₉×#1291	2
C₁₉×#1288	2
#9417	19

Subgroups — C19×#9417 #18015376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9417 #18015376