Subgroups — C₁₉×#13271 #18019230

Order 4864.

332 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#364	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1389	C₂	1	2	yes	maximal
5	C₁₉×#1384	C₂	1	2	yes	maximal
6	C₁₉×#533	—	2	1	no	—
7	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
8	C₁₉×#500	—	2	1	no	—
9	C₁₉×#499	—	2	1	no	—
10	C₁₉×#499	C₄	1	2	yes	complemented
11	C₁₉×#498	C₄	1	2	yes	complemented
12	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
13	C₁₉×#427	—	2	1	no	—
14	C₁₉×#427	C₂²	1	2	yes	—
15	C₁₉×#427	C₂²	1	1	yes	characteristic
16	C₁₉×#405	—	2	1	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#364	—	2	1	no	—
19	C₁₉×#364	—	2	1	no	—
20	C₁₉×#339	—	2	1	no	—
21	C₂×M₁₆×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×#125	—	2	2	no	—
26	C₁₉×C₂²⋊Q₈	—	4	2	no	—
27	C₄×Q₈×C₁₉	—	4	2	no	—
28	C₁₉×#117	—	2	1	no	—
29	C₁₉×#117	—	2	2	no	—
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₁₉×M₃₂	—	2	2	no	—
32	C₁₉×M₃₂	—	2	2	no	—
33	C₂×C₁₆×C₁₉	—	2	2	no	—
34	C₁₉×#108	—	2	1	no	—
35	C₁₉×#108	Q₈	1	2	yes	complemented
36	C₁₉×#107	—	2	2	no	—
37	C₁₉×#107	—	2	2	no	—
38	C₁₉×#107	—	2	1	no	—
39	C₁₉×#106	—	2	2	no	—
40	C₁₉×#106	C₂×C₄	1	4	yes	—
41	C₁₉×#106	Q₈	1	2	yes	complemented
42	C₁₉×#97	—	4	1	no	—
43	C₄×C₈×C₁₉	—	4	1	no	—
44	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	M₁₆×C₁₉	—	2	2	no	—
52	M₁₆×C₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	4	1	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
57	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
58	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
59	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
60	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
65	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	4	4	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₂²⋊C₄×C₁₉	—	4	1	no	—
71	C₂²⋊C₄×C₁₉	—	4	2	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₁₆×C₁₉	—	4	2	no	—
78	#13271	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
80	Q₈×C₁₉	—	8	4	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	4	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₈×C₁₉	—	4	2	no	—
93	C₈×C₁₉	#103	1	1	yes	characteristic
94	C₈×C₁₉	#103	1	1	yes	characteristic
95	C₈×C₁₉	#103	1	1	yes	characteristic
96	C₈×C₁₉	#103	1	1	yes	characteristic
97	C₈×C₁₉	C₄×Q₈	1	1	yes	characteristic
98	C₈×C₁₉	C₄×Q₈	1	1	yes	characteristic
99	C₈×C₁₉	#124	1	1	yes	characteristic
100	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
101	#3160	C₂×C₁₉	1	1	yes	characteristic
102	C₂×#364	C₂×C₁₉	1	1	yes	characteristic
103	#1772	C₂×C₁₉	1	1	yes	characteristic
104	#1389	C₂×C₁₉	1	2	yes	—
105	#1384	C₂×C₁₉	1	2	yes	—
106	C₂²×C₁₉	—	4	1	no	—
107	C₂²×C₁₉	#418	1	1	yes	characteristic
108	C₂²×C₁₉	#476	1	1	yes	characteristic
109	C₂²×C₁₉	#477	1	1	yes	characteristic
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	4	1	no	—
112	C₄×C₁₉	—	8	2	no	—
113	C₄×C₁₉	—	8	4	no	—
114	C₄×C₁₉	#391	1	1	yes	characteristic
115	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
116	C₄×C₁₉	#476	1	1	yes	characteristic
117	C₄×C₁₉	#477	1	1	yes	characteristic
118	#533	—	2	1	no	—
119	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
120	#500	—	2	1	no	—
121	#499	—	2	1	no	—
122	#499	C₄×C₁₉	1	2	yes	complemented
123	#498	C₄×C₁₉	1	2	yes	complemented
124	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
125	#427	—	2	1	no	—
126	#427	C₂²×C₁₉	1	2	yes	—
127	#427	C₂²×C₁₉	1	1	yes	characteristic
128	#405	—	2	1	no	—
129	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
130	#364	—	2	1	no	—
131	#364	—	2	1	no	—
132	#339	—	2	1	no	—
133	C₂×C₁₉	—	2	1	no	—
134	C₂×C₁₉	—	2	1	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	#1987	1	1	yes	characteristic
137	C₂×M₁₆	—	2	1	no	—
138	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
139	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
140	C₄⋊Q₈	—	2	2	no	—
141	#125	—	2	2	no	—
142	C₂²⋊Q₈	—	4	2	no	—
143	C₄×Q₈	—	4	2	no	—
144	#117	—	2	2	no	—
145	#117	—	2	1	no	—
146	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
147	M₃₂	—	2	2	no	—
148	M₃₂	—	2	2	no	—
149	C₂×C₁₆	—	2	2	no	—
150	#108	—	2	1	no	—
151	#108	Q₈×C₁₉	1	2	yes	complemented
152	#107	—	2	2	no	—
153	#107	—	2	2	no	—
154	#107	—	2	1	no	—
155	#106	—	2	2	no	—
156	#106	C₂×C₄×C₁₉	1	4	yes	—
157	#106	Q₈×C₁₉	1	2	yes	complemented
158	#97	—	4	1	no	—
159	C₄×C₈	—	4	1	no	—
160	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
161	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
162	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
163	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
164	C₁₉	#13271	1	1	yes	characteristic, direct product factor, Sylow
165	C₂×Q₈	—	4	2	no	—
166	C₂²×C₄	—	2	1	no	—
167	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
168	M₁₆	—	2	2	no	—
169	M₁₆	—	4	1	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
172	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
173	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
174	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
175	C₂×C₈	Q₁₆×C₁₉	1	1	yes	characteristic
176	C₂×C₈	Q₁₆×C₁₉	1	1	yes	characteristic
177	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
178	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
179	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
180	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
181	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
182	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	4	4	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₂²⋊C₄	—	4	1	no	—
188	C₂²⋊C₄	—	4	2	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	4	1	no	—
191	C₄²	—	4	2	no	—
192	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
193	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
194	C₁₆	—	4	2	no	—
195	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
196	Q₈	—	8	4	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
203	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
206	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
207	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₈	—	4	2	no	—
209	C₈	C₁₉×#103	1	1	yes	characteristic
210	C₈	C₁₉×#103	1	1	yes	characteristic
211	C₈	C₁₉×#103	1	1	yes	characteristic
212	C₈	C₁₉×#103	1	1	yes	characteristic
213	C₈	C₄×Q₈×C₁₉	1	1	yes	characteristic
214	C₈	C₄×Q₈×C₁₉	1	1	yes	characteristic
215	C₈	C₁₉×#124	1	1	yes	characteristic
216	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
217	C₂²	—	4	1	no	—
218	C₂²	C₁₉×#418	1	1	yes	characteristic
219	C₂²	C₁₉×#476	1	1	yes	characteristic
220	C₂²	C₁₉×#477	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	4	1	no	—
223	C₄	—	8	4	no	—
224	C₄	—	8	2	no	—
225	C₄	C₁₉×#391	1	1	yes	characteristic
226	C₄	C₂×C₁₉×#103	1	1	yes	characteristic
227	C₄	C₁₉×#476	1	1	yes	characteristic
228	C₄	C₁₉×#477	1	1	yes	characteristic
229	C₂	—	2	1	no	—
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	C₁₉×#1987	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#476
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1987
prime radical	C₂³×C₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₁₉×#499	C₄	semidirect
11. C₁₉×#498	C₄	semidirect
35. C₁₉×#108	Q₈	semidirect
41. C₁₉×#106	Q₈	semidirect
78. #13271	C₁₉	direct (N × H)
122. #499	C₄×C₁₉	semidirect
123. #498	C₄×C₁₉	semidirect
151. #108	Q₈×C₁₉	semidirect
157. #106	Q₈×C₁₉	semidirect
164. C₁₉	#13271	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×#3160	2
C₂×C₁₉×#364	2
C₁₉×#1772	2
C₁₉×#1389	2
C₁₉×#1384	2
#13271	19

Subgroups — C19×#13271 #18019230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13271 #18019230