Subgroups — C₁₉×#8165 #18014124

Order 4864.

430 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1451	C₂	1	2	yes	maximal
5	C₁₉×#1283	C₂	1	2	yes	maximal
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₈×Q₈×C₁₉	—	2	2	no	—
8	C₈×Q₈×C₁₉	—	2	2	no	—
9	C₁₉×#431	C₂²	1	2	yes	—
10	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#101	C₄	1	2	yes	—
13	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#343	C₄	1	2	yes	—
17	C₁₉×#324	C₄	1	4	yes	—
18	C₁₉×#322	—	2	2	no	—
19	C₁₉×#322	—	2	2	no	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₁₉×C₄⋊C₈	—	2	4	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×#101	—	2	4	no	—
35	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
36	C₁₉×#97	—	2	2	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	C₄×C₈×C₁₉	D₄	1	2	yes	—
42	C₄×C₈×C₁₉	D₄	1	2	yes	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
46	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
47	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	M₁₆×C₁₉	—	2	4	no	—
52	M₁₆×C₁₉	—	2	4	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	4	no	—
56	C₂×C₈×C₁₉	—	2	4	no	—
57	C₂×C₈×C₁₉	—	4	1	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	2	no	—
66	C₄²×C₁₉	C₂×D₄	1	2	yes	—
67	C₄²×C₁₉	#41	1	2	yes	—
68	#8165	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	Q₈×C₁₉	—	2	8	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	#97	1	4	yes	—
79	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
84	C₂×C₄×C₁₉	#131	1	2	yes	—
85	C₈×C₁₉	—	2	1	no	—
86	C₈×C₁₉	—	2	2	no	—
87	C₈×C₁₉	—	4	4	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	4	4	no	—
90	C₈×C₁₉	#101	1	2	yes	complemented
91	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic
92	C₄×#101	C₂×C₁₉	1	1	yes	characteristic
93	#1461	C₂×C₁₉	1	1	yes	characteristic
94	#1451	C₂×C₁₉	1	2	yes	—
95	#1283	C₂×C₁₉	1	2	yes	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
100	C₂²×C₁₉	#405	1	1	yes	characteristic
101	C₄×C₁₉	—	2	4	no	—
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
106	C₄×C₁₉	#413	1	1	yes	characteristic
107	C₄×C₁₉	#435	1	4	yes	—
108	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
109	C₈×Q₈	—	2	2	no	—
110	C₈×Q₈	—	2	2	no	—
111	#431	C₂²×C₁₉	1	2	yes	—
112	C₂×C₄⋊C₈	C₄×C₁₉	1	2	yes	—
113	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
114	C₂×#101	C₄×C₁₉	1	2	yes	—
115	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
116	C₂×C₄×C₈	C₄×C₁₉	1	2	yes	—
117	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
118	#343	C₄×C₁₉	1	2	yes	—
119	#324	C₄×C₁₉	1	4	yes	—
120	#322	—	2	2	no	—
121	#322	—	2	2	no	—
122	C₂×C₁₉	—	2	1	no	—
123	C₂×C₁₉	—	2	1	no	—
124	C₂×C₁₉	#1752	1	1	yes	characteristic
125	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
126	C₂×C₁₉	#1757	1	1	yes	characteristic
127	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
128	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
129	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
130	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
131	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
132	C₄×Q₈	—	2	2	no	—
133	C₄×Q₈	—	2	2	no	—
134	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
135	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
136	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
137	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
138	C₄⋊C₈	—	2	4	no	—
139	C₄⋊C₈	—	2	2	no	—
140	C₄⋊C₈	—	2	2	no	—
141	#101	—	2	4	no	—
142	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
143	#97	—	2	2	no	—
144	C₄×C₈	—	2	2	no	—
145	C₄×C₈	—	2	2	no	—
146	C₄×C₈	—	2	2	no	—
147	C₄×C₈	—	2	2	no	—
148	C₄×C₈	D₄×C₁₉	1	2	yes	—
149	C₄×C₈	D₄×C₁₉	1	2	yes	—
150	C₁₉	#8165	1	1	yes	characteristic, direct product factor, Sylow
151	C₂×Q₈	—	2	2	no	—
152	C₂×Q₈	—	2	2	no	—
153	C₂×Q₈	M₁₆×C₁₉	1	4	yes	—
154	C₂²×C₄	C₄²×C₁₉	1	2	yes	—
155	C₂²×C₄	C₄²×C₁₉	1	2	yes	—
156	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
159	M₁₆	—	2	4	no	—
160	M₁₆	—	2	4	no	—
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	2	4	no	—
164	C₂×C₈	—	2	4	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
168	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
169	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	2	2	no	—
174	C₄²	C₂×D₄×C₁₉	1	2	yes	—
175	C₄²	#41×C₁₉	1	2	yes	—
176	C₂³	C₂×C₄²×C₁₉	1	1	yes	characteristic
177	Q₈	—	2	8	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	4	1	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	C₁₉×#97	1	4	yes	—
186	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
187	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
188	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
189	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
190	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
191	C₂×C₄	C₁₉×#131	1	2	yes	—
192	C₈	—	2	1	no	—
193	C₈	—	2	2	no	—
194	C₈	—	4	4	no	—
195	C₈	—	4	2	no	—
196	C₈	—	4	4	no	—
197	C₈	C₁₉×#101	1	2	yes	complemented
198	C₂²	—	2	1	no	—
199	C₂²	—	2	1	no	—
200	C₂²	C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
201	C₂²	C₂×C₁₉×#97	1	1	yes	characteristic
202	C₂²	C₁₉×#405	1	1	yes	characteristic
203	C₄	—	2	4	no	—
204	C₄	—	2	1	no	—
205	C₄	—	2	2	no	—
206	C₄	—	4	2	no	—
207	C₄	C₂×C₁₉×#101	1	1	yes	characteristic
208	C₄	C₁₉×#413	1	1	yes	characteristic
209	C₄	C₁₉×#435	1	4	yes	—
210	C₂	—	2	1	no	—
211	C₂	—	2	1	no	—
212	C₂	C₁₉×#1752	1	1	yes	characteristic
213	C₂	C₄×C₁₉×#101	1	1	yes	characteristic
214	C₂	C₁₉×#1757	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
68. #8165	C₁₉	direct (N × H)
90. C₈×C₁₉	#101	semidirect
150. C₁₉	#8165	direct (N × H)
197. C₈	C₁₉×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₁₉	2
C₄×C₁₉×#101	2
C₁₉×#1461	2
C₁₉×#1451	2
C₁₉×#1283	2
#8165	19

Subgroups — C19×#8165 #18014124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8165 #18014124