Subgroups — C₁₉×#13253 #18019212

Order 4864.

494 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#358	C₂	1	4	yes	maximal
4	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₁₆×C₁₉	—	2	1	no	—
6	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
8	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#494	—	2	2	no	—
10	C₁₉×#494	C₄	1	4	yes	complemented
11	C₂×C₁₉×#107	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₁₉×C₄⋊C₁₆	—	2	2	no	—
15	C₁₉×#358	—	2	8	no	—
16	C₁₉×#340	—	2	1	no	—
17	C₂²×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₁₆×C₁₉	—	2	4	no	—
19	C₂×Q₁₆×C₁₉	—	2	4	no	—
20	C₂×Q₁₆×C₁₉	—	2	2	no	—
21	C₂×Q₁₆×C₁₉	—	2	4	no	—
22	C₂×Q₁₆×C₁₉	—	4	4	no	—
23	C₂×Q₁₆×C₁₉	C₂×C₄	1	4	yes	—
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
26	C₁₉×C₄⋊Q₈	—	2	4	no	—
27	C₁₉×C₄⋊Q₈	—	4	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₂×C₄²×C₁₉	—	4	1	no	—
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₁₆×C₁₉	—	2	4	no	—
34	C₂×C₁₆×C₁₉	—	2	2	no	—
35	C₁₉×#107	—	2	2	no	—
36	C₁₉×#107	D₄	1	4	yes	—
37	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₁₉×#95	—	4	1	no	—
40	C₂×Q₈×C₁₉	—	2	4	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	4	no	—
43	C₂×Q₈×C₁₉	—	4	4	no	—
44	C₂²×C₄×C₁₉	—	4	2	no	—
45	C₂²×C₄×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	Q₁₆×C₁₉	—	2	8	no	—
50	Q₁₆×C₁₉	—	4	8	no	—
51	Q₁₆×C₁₉	—	4	2	no	—
52	Q₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₉	#41	1	2	yes	—
59	C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₄⋊C₄×C₁₉	—	4	4	no	—
61	C₄⋊C₄×C₁₉	—	4	4	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	—	8	2	no	—
64	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₉	SD₁₆	1	2	yes	—
66	C₁₆×C₁₉	—	4	2	no	—
67	#13253	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
69	Q₈×C₁₉	—	4	4	no	—
70	Q₈×C₁₉	—	4	4	no	—
71	Q₈×C₁₉	—	8	4	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	4	4	no	—
74	C₂×C₄×C₁₉	—	4	4	no	—
75	C₂×C₄×C₁₉	—	8	4	no	—
76	C₂×C₄×C₁₉	—	8	2	no	—
77	C₂×C₄×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	#102	1	2	yes	—
79	C₂×C₄×C₁₉	#102	1	2	yes	—
80	C₂×C₄×C₁₉	SD₃₂	1	2	yes	—
81	C₂×C₄×C₁₉	Q₃₂	1	2	yes	—
82	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#121	1	2	yes	—
84	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
86	C₈×C₁₉	—	2	2	no	—
87	C₈×C₁₉	C₄×D₄	1	2	yes	—
88	C₈×C₁₉	#124	1	1	yes	characteristic
89	C₈×C₁₉	#127	1	1	yes	characteristic
90	C₂×#494	C₂×C₁₉	1	1	yes	characteristic
91	C₂×C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
92	C₂×#358	C₂×C₁₉	1	4	yes	—
93	C₄×#107	C₂×C₁₉	1	1	yes	characteristic
94	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
95	C₂²×C₁₉	#459	1	2	yes	—
96	C₂²×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
97	C₂²×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
98	C₂²×C₁₉	#510	1	2	yes	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	8	4	no	—
101	C₄×C₁₉	—	8	4	no	—
102	C₄×C₁₉	#358	1	4	yes	complemented
103	C₄×C₁₉	#390	1	1	yes	characteristic
104	C₄×C₁₉	#418	1	1	yes	characteristic
105	C₄×C₁₉	#460	1	2	yes	—
106	C₂²×Q₁₆	—	2	1	no	—
107	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
108	C₂×C₄⋊Q₈	—	2	1	no	—
109	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
110	#494	—	2	2	no	—
111	#494	C₄×C₁₉	1	4	yes	complemented
112	C₂×#107	C₂²×C₁₉	1	2	yes	—
113	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
114	C₄×C₄⋊C₄	—	2	1	no	—
115	C₄⋊C₁₆	—	2	2	no	—
116	#358	—	2	8	no	—
117	#340	—	2	1	no	—
118	C₂×C₁₉	#1982	1	1	yes	characteristic
119	C₂×C₁₉	C₂×#358	1	1	yes	characteristic
120	C₂×C₁₉	#2141	1	1	yes	characteristic
121	C₂×C₁₉	#2208	1	2	yes	—
122	C₂×C₁₉	#2209	1	2	yes	—
123	C₂²×Q₈	—	2	2	no	—
124	C₂×Q₁₆	—	2	4	no	—
125	C₂×Q₁₆	—	2	4	no	—
126	C₂×Q₁₆	—	2	2	no	—
127	C₂×Q₁₆	—	2	4	no	—
128	C₂×Q₁₆	—	4	4	no	—
129	C₂×Q₁₆	C₂×C₄×C₁₉	1	4	yes	—
130	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
132	C₄⋊Q₈	—	2	4	no	—
133	C₄⋊Q₈	—	4	2	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	4	1	no	—
136	C₂×C₄⋊C₄	—	4	1	no	—
137	C₂×C₄²	—	4	1	no	—
138	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
139	C₂×C₁₆	—	2	4	no	—
140	C₂×C₁₆	—	2	2	no	—
141	#107	—	2	2	no	—
142	#107	D₄×C₁₉	1	4	yes	—
143	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
144	C₄×C₈	D₄×C₁₉	1	2	yes	—
145	#95	—	4	1	no	—
146	C₁₉	#13253	1	1	yes	characteristic, direct product factor, Sylow
147	C₂×Q₈	—	2	4	no	—
148	C₂×Q₈	—	4	2	no	—
149	C₂×Q₈	—	4	4	no	—
150	C₂×Q₈	—	4	4	no	—
151	C₂²×C₄	—	4	2	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
154	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
156	Q₁₆	—	2	8	no	—
157	Q₁₆	—	4	8	no	—
158	Q₁₆	—	4	2	no	—
159	Q₁₆	—	4	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
162	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
163	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
164	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
165	C₂×C₈	#41×C₁₉	1	2	yes	—
166	C₄⋊C₄	—	2	4	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	4	no	—
169	C₄⋊C₄	—	4	4	no	—
170	C₄²	—	8	2	no	—
171	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
172	C₄²	SD₁₆×C₁₉	1	2	yes	—
173	C₁₆	—	4	2	no	—
174	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
175	Q₈	—	4	4	no	—
176	Q₈	—	4	4	no	—
177	Q₈	—	8	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	8	4	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	8	2	no	—
184	C₂×C₄	C₁₉×#102	1	2	yes	—
185	C₂×C₄	C₁₉×#102	1	2	yes	—
186	C₂×C₄	C₁₉×SD₃₂	1	2	yes	—
187	C₂×C₄	C₁₉×Q₃₂	1	2	yes	—
188	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
189	C₂×C₄	C₁₉×#121	1	2	yes	—
190	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
191	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
192	C₈	—	2	2	no	—
193	C₈	C₄×D₄×C₁₉	1	2	yes	—
194	C₈	C₁₉×#124	1	1	yes	characteristic
195	C₈	C₁₉×#127	1	1	yes	characteristic
196	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
197	C₂²	C₁₉×#459	1	2	yes	—
198	C₂²	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
199	C₂²	C₂×C₁₉×Q₃₂	1	1	yes	characteristic
200	C₂²	C₁₉×#510	1	2	yes	—
201	C₄	—	2	2	no	—
202	C₄	—	8	4	no	—
203	C₄	—	8	4	no	—
204	C₄	C₁₉×#358	1	4	yes	complemented
205	C₄	C₁₉×#390	1	1	yes	characteristic
206	C₄	C₁₉×#418	1	1	yes	characteristic
207	C₄	C₁₉×#460	1	2	yes	—
208	C₂	C₁₉×#1982	1	1	yes	characteristic
209	C₂	C₂×C₁₉×#358	1	1	yes	characteristic
210	C₂	C₁₉×#2141	1	1	yes	characteristic
211	C₂	C₁₉×#2208	1	2	yes	—
212	C₂	C₁₉×#2209	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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
10. C₁₉×#494	C₄	semidirect
67. #13253	C₁₉	direct (N × H)
102. C₄×C₁₉	#358	semidirect
111. #494	C₄×C₁₉	semidirect
146. C₁₉	#13253	direct (N × H)
204. C₄	C₁₉×#358	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#494	2
C₂×C₁₉×C₄⋊C₁₆	2
C₂×C₁₉×#358	2
C₄×C₁₉×#107	2
#13253	19

Subgroups — C19×#13253 #18019212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13253 #18019212