Subgroups — C₁₉×#13164 #18019123

Order 4864.

284 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2153	C₂	1	2	yes	maximal
2	C₂×C₁₉×#364	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1378	C₂	1	2	yes	maximal
6	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
7	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#108	C₄	1	1	yes	characteristic
10	C₁₉×#427	C₄	1	1	yes	characteristic
11	C₁₉×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#364	—	2	4	no	—
14	C₁₉×#364	—	2	1	no	—
15	C₁₉×#364	—	2	1	no	—
16	C₁₉×#346	—	2	1	no	—
17	C₄×C₁₆×C₁₉	—	2	1	no	—
18	C₁₉×#339	C₄	1	2	yes	—
19	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₁₉×#117	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₁₉×M₃₂	—	2	1	no	—
25	C₁₉×M₃₂	—	2	1	no	—
26	C₁₉×M₃₂	—	2	2	no	—
27	C₁₉×M₃₂	—	2	2	no	—
28	C₁₉×M₃₂	D₄	1	2	yes	—
29	C₁₉×M₃₂	Q₈	1	2	yes	—
30	C₂×C₁₆×C₁₉	—	2	1	no	—
31	C₂×C₁₆×C₁₉	—	2	1	no	—
32	C₂×C₁₆×C₁₉	—	2	2	no	—
33	C₁₉×#108	C₈	1	2	yes	—
34	C₁₉×#108	C₈	1	2	yes	—
35	C₁₉×#107	—	2	1	no	—
36	C₁₉×#106	—	2	1	no	—
37	C₁₉×#97	—	2	2	no	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
42	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	M₁₆×C₁₉	—	2	2	no	—
46	M₁₆×C₁₉	C₂×C₈	1	4	yes	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
52	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
53	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
54	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
59	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
66	C₁₆×C₁₉	—	2	2	no	—
67	C₁₆×C₁₉	—	2	2	no	—
68	C₁₆×C₁₉	—	4	2	no	—
69	#13164	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂³×C₁₉	#131	1	1	yes	characteristic
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
81	C₈×C₁₉	—	2	4	no	—
82	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
83	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
84	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
85	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
86	C₈×C₁₉	#121	1	1	yes	characteristic
87	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₈×C₁₉	#125	1	1	yes	characteristic
89	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
90	#2153	C₂×C₁₉	1	2	yes	—
91	C₂×#364	C₂×C₁₉	1	1	yes	characteristic
92	C₄×M₃₂	C₂×C₁₉	1	1	yes	characteristic
93	#1772	C₂×C₁₉	1	1	yes	characteristic
94	#1378	C₂×C₁₉	1	2	yes	—
95	C₂²×C₁₉	—	4	1	no	—
96	C₂²×C₁₉	#424	1	1	yes	characteristic
97	C₂²×C₁₉	#436	1	1	yes	characteristic
98	C₂²×C₁₉	C₈×Q₈	1	1	yes	characteristic
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	4	1	no	—
101	C₄×C₁₉	—	8	2	no	—
102	C₄×C₁₉	#389	1	1	yes	characteristic
103	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
104	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
105	C₄×C₁₉	#446	1	1	yes	characteristic
106	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
107	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
108	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
109	C₂×#108	C₄×C₁₉	1	1	yes	characteristic
110	#427	C₄×C₁₉	1	1	yes	characteristic
111	#405	C₂²×C₁₉	1	2	yes	—
112	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
113	#364	—	2	4	no	—
114	#364	—	2	1	no	—
115	#364	—	2	1	no	—
116	#346	—	2	1	no	—
117	C₄×C₁₆	—	2	1	no	—
118	#339	C₄×C₁₉	1	2	yes	—
119	C₂×C₁₉	—	2	1	no	—
120	C₂×C₁₉	—	2	1	no	—
121	C₂×C₁₉	—	2	1	no	—
122	C₂×C₁₉	#1939	1	1	yes	characteristic
123	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
124	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
125	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
126	#117	C₂×C₄×C₁₉	1	2	yes	—
127	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
128	M₃₂	—	2	1	no	—
129	M₃₂	—	2	1	no	—
130	M₃₂	—	2	2	no	—
131	M₃₂	—	2	2	no	—
132	M₃₂	D₄×C₁₉	1	2	yes	—
133	M₃₂	Q₈×C₁₉	1	2	yes	—
134	C₂×C₁₆	—	2	1	no	—
135	C₂×C₁₆	—	2	1	no	—
136	C₂×C₁₆	—	2	2	no	—
137	#108	C₈×C₁₉	1	2	yes	—
138	#108	C₈×C₁₉	1	2	yes	—
139	#107	—	2	1	no	—
140	#106	—	2	1	no	—
141	#97	—	2	2	no	—
142	C₄×C₈	—	2	2	no	—
143	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
144	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
145	C₄×C₈	Q₈×C₁₉	1	1	yes	characteristic
146	C₄×C₈	Q₈×C₁₉	1	1	yes	characteristic
147	C₁₉	#13164	1	1	yes	characteristic, direct product factor, Sylow
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
150	M₁₆	—	2	2	no	—
151	M₁₆	C₂×C₈×C₁₉	1	4	yes	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
154	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
155	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
156	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
157	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
158	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
159	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
160	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
161	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
162	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
163	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
164	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
165	C₄⋊C₄	—	2	2	no	—
166	C₂²⋊C₄	—	2	2	no	—
167	C₄²	—	2	1	no	—
168	C₄²	—	2	2	no	—
169	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
170	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
171	C₁₆	—	2	2	no	—
172	C₁₆	—	2	2	no	—
173	C₁₆	—	4	2	no	—
174	C₂³	C₁₉×#131	1	1	yes	characteristic
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
180	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
181	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
182	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
183	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
184	C₂×C₄	C₁₉×#131	1	1	yes	characteristic
185	C₈	—	2	4	no	—
186	C₈	C₁₉×C₄⋊C₈	1	1	yes	characteristic
187	C₈	C₁₉×C₄⋊C₈	1	1	yes	characteristic
188	C₈	C₁₉×C₄⋊C₈	1	1	yes	characteristic
189	C₈	C₁₉×C₄⋊C₈	1	1	yes	characteristic
190	C₈	C₁₉×#121	1	1	yes	characteristic
191	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
192	C₈	C₁₉×#125	1	1	yes	characteristic
193	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
194	C₂²	—	4	1	no	—
195	C₂²	C₁₉×#424	1	1	yes	characteristic
196	C₂²	C₁₉×#436	1	1	yes	characteristic
197	C₂²	C₈×Q₈×C₁₉	1	1	yes	characteristic
198	C₄	—	2	2	no	—
199	C₄	—	4	1	no	—
200	C₄	—	8	2	no	—
201	C₄	C₁₉×#389	1	1	yes	characteristic
202	C₄	C₂×C₁₉×C₄⋊C₈	1	1	yes	characteristic
203	C₄	C₈×D₄×C₁₉	1	1	yes	characteristic
204	C₄	C₁₉×#446	1	1	yes	characteristic
205	C₂	—	2	1	no	—
206	C₂	—	2	1	no	—
207	C₂	—	2	1	no	—
208	C₂	C₁₉×#1939	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₉	#121
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1939
prime radical	C₂³×C₁₉	#131
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
69. #13164	C₁₉	direct (N × H)
147. C₁₉	#13164	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×#2153	2
C₂×C₁₉×#364	2
C₄×C₁₉×M₃₂	2
C₁₉×#1772	2
C₁₉×#1378	2
#13164	19

Subgroups — C19×#13164 #18019123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13164 #18019123