Subgroups — C₁₉×#11647 #18017606

Order 4864.

310 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1332	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1331	C₂	1	2	yes	maximal, complemented
6	C₁₉×#529	—	2	1	no	—
7	C₁₉×#499	C₄	1	1	yes	characteristic
8	C₁₉×#495	C₄	1	1	yes	characteristic
9	C₁₉×#488	—	2	1	no	—
10	C₁₉×#467	C₄	1	1	yes	characteristic
11	C₁₉×#466	C₄	1	1	yes	characteristic
12	C₁₉×#465	—	2	1	no	—
13	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₄×SD₁₆×C₁₉	—	2	1	no	—
15	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#431	—	2	1	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×C₄⋊C₁₆	—	2	1	no	—
19	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
20	C₄×C₁₆×C₁₉	C₂²	1	2	yes	—
21	C₁₉×#335	C₂²	1	2	yes	—
22	C₁₉×#334	—	2	1	no	—
23	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×SD₁₆×C₁₉	—	2	1	no	—
25	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₁₉×#126	—	4	1	no	—
29	C₁₉×#125	—	2	1	no	—
30	C₁₉×#124	—	2	1	no	—
31	C₁₉×#123	—	4	1	no	—
32	C₁₉×C₂²⋊Q₈	—	2	1	no	—
33	C₁₉×#121	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₄×D₄×C₁₉	—	4	1	no	—
37	C₁₉×#117	—	4	1	no	—
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₁₆×C₁₉	—	2	2	no	—
40	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
41	C₁₉×#107	C₂×C₄	1	1	yes	characteristic
42	C₁₉×#106	—	2	1	no	—
43	C₁₉×C₄⋊C₈	—	2	2	no	—
44	C₁₉×#103	—	2	1	no	—
45	C₁₉×#103	—	2	1	no	—
46	C₁₉×#102	—	2	1	no	—
47	C₁₉×#102	—	2	1	no	—
48	C₁₉×C₂²⋊C₈	—	4	1	no	—
49	C₄×C₈×C₁₉	—	4	1	no	—
50	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
53	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×Q₈×C₁₉	—	2	1	no	—
55	C₂×D₄×C₁₉	—	2	1	no	—
56	C₂×D₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
61	Q₁₆×C₁₉	—	2	2	no	—
62	SD₁₆×C₁₉	—	4	2	no	—
63	D₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	—	4	1	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₂²⋊C₄×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	C₄²×C₁₉	—	4	1	no	—
83	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₄²×C₁₉	D₈	1	1	yes	characteristic
85	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
86	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₁₆×C₁₉	—	4	2	no	—
88	#11647	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂³×C₁₉	—	4	1	no	—
90	C₂³×C₁₉	#102	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	1	no	—
92	Q₈×C₁₉	—	4	1	no	—
93	D₄×C₁₉	—	4	1	no	—
94	D₄×C₁₉	—	4	1	no	—
95	D₄×C₁₉	—	8	2	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	8	2	no	—
104	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	2	1	no	—
113	C₈×C₁₉	—	8	2	no	—
114	C₈×C₁₉	#131	1	2	yes	—
115	#3168	C₂×C₁₉	1	1	yes	characteristic
116	#2162	C₂×C₁₉	1	1	yes	characteristic, complemented
117	#1564	C₂×C₁₉	1	1	yes	characteristic, complemented
118	#1332	C₂×C₁₉	1	2	yes	complemented
119	#1331	C₂×C₁₉	1	2	yes	complemented
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	8	1	no	—
124	C₂²×C₁₉	—	8	1	no	—
125	C₂²×C₁₉	—	8	1	no	—
126	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	8	1	no	—
132	C₄×C₁₉	—	8	1	no	—
133	C₄×C₁₉	—	8	1	no	—
134	C₄×C₁₉	#408	1	1	yes	characteristic
135	C₄×C₁₉	#421	1	1	yes	characteristic
136	C₄×C₁₉	#508	1	2	yes	—
137	#529	—	2	1	no	—
138	#499	C₄×C₁₉	1	1	yes	characteristic
139	#495	C₄×C₁₉	1	1	yes	characteristic
140	#488	—	2	1	no	—
141	#467	C₄×C₁₉	1	1	yes	characteristic
142	#466	C₄×C₁₉	1	1	yes	characteristic
143	#465	—	2	1	no	—
144	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
145	C₄×SD₁₆	—	2	1	no	—
146	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
147	#431	—	2	1	no	—
148	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
149	C₄⋊C₁₆	—	2	1	no	—
150	C₂²⋊C₁₆	—	2	1	no	—
151	C₄×C₁₆	C₂²×C₁₉	1	2	yes	—
152	#335	C₂²×C₁₉	1	2	yes	—
153	#334	—	2	1	no	—
154	C₂×C₁₉	—	4	1	no	—
155	C₂×C₁₉	—	16	1	no	—
156	C₂×C₁₉	#1480	1	1	yes	characteristic
157	C₂×C₁₉	#2138	1	1	yes	characteristic
158	C₂×C₁₉	#2143	1	1	yes	characteristic
159	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
160	C₂×SD₁₆	—	2	1	no	—
161	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
162	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
163	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
164	#126	—	4	1	no	—
165	#125	—	2	1	no	—
166	#124	—	2	1	no	—
167	#123	—	4	1	no	—
168	C₂²⋊Q₈	—	2	1	no	—
169	#121	—	2	1	no	—
170	C₄×Q₈	—	2	1	no	—
171	C₄×D₄	—	2	1	no	—
172	C₄×D₄	—	4	1	no	—
173	#117	—	4	1	no	—
174	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
175	C₂×C₁₆	—	2	2	no	—
176	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
177	#107	C₂×C₄×C₁₉	1	1	yes	characteristic
178	#106	—	2	1	no	—
179	C₄⋊C₈	—	2	2	no	—
180	#103	—	2	1	no	—
181	#103	—	2	1	no	—
182	#102	—	2	1	no	—
183	#102	—	2	1	no	—
184	C₂²⋊C₈	—	4	1	no	—
185	C₄×C₈	—	4	1	no	—
186	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
187	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
188	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
189	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
190	C₁₉	#11647	1	1	yes	characteristic, direct product factor, Sylow
191	C₂×Q₈	—	2	1	no	—
192	C₂×D₄	—	2	1	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
196	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
197	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
198	Q₁₆	—	2	2	no	—
199	SD₁₆	—	4	2	no	—
200	D₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	4	1	no	—
203	C₂×C₈	—	4	2	no	—
204	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
205	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
206	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
207	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
208	C₄⋊C₄	—	2	1	no	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	—	4	1	no	—
211	C₄⋊C₄	—	4	1	no	—
212	C₄⋊C₄	—	4	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₂²⋊C₄	—	4	1	no	—
215	C₂²⋊C₄	—	4	1	no	—
216	C₂²⋊C₄	—	4	1	no	—
217	C₂²⋊C₄	—	4	1	no	—
218	C₂²⋊C₄	—	4	1	no	—
219	C₄²	—	4	1	no	—
220	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
221	C₄²	D₈×C₁₉	1	1	yes	characteristic
222	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
223	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
224	C₁₆	—	4	2	no	—
225	C₂³	—	4	1	no	—
226	C₂³	C₁₉×#102	1	1	yes	characteristic
227	Q₈	—	4	1	no	—
228	Q₈	—	4	1	no	—
229	D₄	—	4	1	no	—
230	D₄	—	4	1	no	—
231	D₄	—	8	2	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
241	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
242	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
243	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
244	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
245	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
246	C₈	—	2	1	no	—
247	C₈	—	2	1	no	—
248	C₈	—	2	1	no	—
249	C₈	—	8	2	no	—
250	C₈	C₁₉×#131	1	2	yes	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	8	1	no	—
255	C₂²	—	8	1	no	—
256	C₂²	—	8	1	no	—
257	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	8	1	no	—
263	C₄	—	8	1	no	—
264	C₄	—	8	1	no	—
265	C₄	C₁₉×#408	1	1	yes	characteristic
266	C₄	C₁₉×#421	1	1	yes	characteristic
267	C₄	C₁₉×#508	1	2	yes	—
268	C₂	—	4	1	no	—
269	C₂	—	16	1	no	—
270	C₂	C₁₉×#1480	1	1	yes	characteristic
271	C₂	C₁₉×#2138	1	1	yes	characteristic
272	C₂	C₁₉×#2143	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#102
prime radical	C₁₉×#466	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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
2. C₁₉×#2162	C₂	semidirect
3. C₁₉×#1564	C₂	semidirect
4. C₁₉×#1332	C₂	semidirect
5. C₁₉×#1331	C₂	semidirect
88. #11647	C₁₉	direct (N × H)
116. #2162	C₂×C₁₉	semidirect
117. #1564	C₂×C₁₉	semidirect
118. #1332	C₂×C₁₉	semidirect
119. #1331	C₂×C₁₉	semidirect
190. C₁₉	#11647	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×#3168	2
C₁₉×#2162	2
C₁₉×#1564	2
C₁₉×#1332	2
C₁₉×#1331	2
#11647	19

Subgroups — C19×#11647 #18017606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11647 #18017606