Subgroups — C₁₉×#8297 #18014256

Order 4864.

342 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic
4	C₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1278	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1278	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#431	C₂²	1	1	yes	characteristic
9	C₁₉×#431	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#108	C₄	1	2	yes	—
11	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#341	C₄	1	2	yes	—
17	C₁₉×#335	C₄	1	2	yes	—
18	C₁₉×#334	C₄	1	2	yes	—
19	C₁₉×#322	—	2	1	no	—
20	C₁₉×#322	—	2	1	no	—
21	C₁₉×#322	—	2	1	no	—
22	C₁₉×#322	C₄	1	2	yes	—
23	C₁₉×#322	C₄	1	2	yes	—
24	C₈²×C₁₉	—	2	1	no	—
25	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₉	—	2	1	no	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×#108	—	2	4	no	—
33	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
34	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
35	C₁₉×C₂²⋊C₈	—	2	1	no	—
36	C₁₉×C₂²⋊C₈	—	2	1	no	—
37	C₁₉×#97	—	2	1	no	—
38	C₁₉×#97	—	2	1	no	—
39	C₄×C₈×C₁₉	—	2	1	no	—
40	C₄×C₈×C₁₉	—	2	1	no	—
41	C₄×C₈×C₁₉	—	2	1	no	—
42	C₄×C₈×C₁₉	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	M₁₆×C₁₉	—	2	2	no	—
56	M₁₆×C₁₉	—	2	2	no	—
57	M₁₆×C₁₉	—	2	2	no	—
58	M₁₆×C₁₉	M₁₆	1	4	yes	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	4	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
73	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
74	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	#41	1	1	yes	characteristic
78	#8297	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
89	C₂×C₄×C₁₉	#131	1	2	yes	—
90	C₈×C₁₉	—	2	1	no	—
91	C₈×C₁₉	—	2	1	no	—
92	C₈×C₁₉	—	2	1	no	—
93	C₈×C₁₉	—	2	1	no	—
94	C₈×C₁₉	—	2	2	no	—
95	C₈×C₁₉	—	2	4	no	—
96	C₈×C₁₉	—	4	2	no	—
97	C₈×C₁₉	—	4	2	no	—
98	C₈×C₁₉	—	4	2	no	—
99	C₈×C₁₉	—	4	2	no	—
100	C₈×C₁₉	#108	1	4	yes	complemented
101	C₄×#108	C₂×C₁₉	1	1	yes	characteristic
102	#1564	C₂×C₁₉	1	1	yes	characteristic
103	#1451	C₂×C₁₉	1	1	yes	characteristic
104	C₈×M₁₆	C₂×C₁₉	1	1	yes	characteristic
105	C₂×#322	C₂×C₁₉	1	1	yes	characteristic
106	#1278	C₂×C₁₉	1	1	yes	characteristic
107	#1278	C₂×C₁₉	1	1	yes	characteristic
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₁₉	#446	1	2	yes	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
115	C₄×C₁₉	#405	1	1	yes	characteristic
116	C₄×C₁₉	C₂×#108	1	2	yes	—
117	C₄×C₁₉	#435	1	2	yes	—
118	C₄×C₁₉	#444	1	2	yes	—
119	#431	C₂²×C₁₉	1	1	yes	characteristic
120	#431	C₂²×C₁₉	1	1	yes	characteristic
121	C₂×#108	C₄×C₁₉	1	2	yes	—
122	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
123	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
127	#341	C₄×C₁₉	1	2	yes	—
128	#335	C₄×C₁₉	1	2	yes	—
129	#334	C₄×C₁₉	1	2	yes	—
130	#322	—	2	1	no	—
131	#322	—	2	1	no	—
132	#322	—	2	1	no	—
133	#322	C₄×C₁₉	1	2	yes	—
134	#322	C₄×C₁₉	1	2	yes	—
135	C₈²	—	2	1	no	—
136	C₂×C₁₉	—	2	2	no	—
137	C₂×C₁₉	#1771	1	1	yes	characteristic
138	C₂×C₁₉	#1773	1	1	yes	characteristic
139	C₂×C₁₉	C₄×#108	1	1	yes	characteristic
140	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
141	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
142	C₂²×C₈	—	2	1	no	—
143	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
144	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
145	C₂²×C₈	Q₈×C₁₉	1	2	yes	—
146	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
147	#108	—	2	4	no	—
148	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
149	C₄⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
150	C₂²⋊C₈	—	2	1	no	—
151	C₂²⋊C₈	—	2	1	no	—
152	#97	—	2	1	no	—
153	#97	—	2	1	no	—
154	C₄×C₈	—	2	1	no	—
155	C₄×C₈	—	2	1	no	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	—	2	1	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
160	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
161	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
162	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
163	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
164	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
165	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
166	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
167	C₁₉	#8297	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
169	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
170	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
171	M₁₆	—	2	2	no	—
172	M₁₆	—	2	2	no	—
173	M₁₆	—	2	2	no	—
174	M₁₆	M₁₆×C₁₉	1	4	yes	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
185	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
186	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
187	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
188	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
189	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
190	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
191	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
192	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
193	C₄²	#41×C₁₉	1	1	yes	characteristic
194	C₂³	C₄×Q₈×C₁₉	1	1	yes	characteristic
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	C₂×C₄²×C₁₉	1	1	yes	characteristic
198	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
199	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
200	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
201	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
202	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
203	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
204	C₂×C₄	C₁₉×#131	1	2	yes	—
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	—	2	1	no	—
208	C₈	—	2	1	no	—
209	C₈	—	2	2	no	—
210	C₈	—	2	4	no	—
211	C₈	—	4	2	no	—
212	C₈	—	4	2	no	—
213	C₈	—	4	2	no	—
214	C₈	—	4	2	no	—
215	C₈	C₁₉×#108	1	4	yes	complemented
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	C₄×C₄⋊C₄×C₁₉	1	1	yes	characteristic
219	C₂²	C₁₉×#446	1	2	yes	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	C₄×M₁₆×C₁₉	1	1	yes	characteristic
223	C₄	C₁₉×#405	1	1	yes	characteristic
224	C₄	C₂×C₁₉×#108	1	2	yes	—
225	C₄	C₁₉×#435	1	2	yes	—
226	C₄	C₁₉×#444	1	2	yes	—
227	C₂	—	2	2	no	—
228	C₂	C₁₉×#1771	1	1	yes	characteristic
229	C₂	C₁₉×#1773	1	1	yes	characteristic
230	C₂	C₄×C₁₉×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×C₄⋊C₄
prime radical	C₂³×C₁₉	C₄×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
78. #8297	C₁₉	direct (N × H)
100. C₈×C₁₉	#108	semidirect
167. C₁₉	#8297	direct (N × H)
215. C₈	C₁₉×#108	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×#108	2
C₁₉×#1564	2
C₁₉×#1451	2
C₈×M₁₆×C₁₉	2
C₂×C₁₉×#322	2
C₁₉×#1278	2
#8297	19

Subgroups — C19×#8297 #18014256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8297 #18014256