Subgroups — C₁₉×#7296 #18013255

Order 4864.

242 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2162	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#107	—	2	1	no	—
5	C₁₉×#423	—	2	1	no	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₁₉×C₄⋊C₁₆	C₄	1	2	yes	complemented
9	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
10	C₄×C₁₆×C₁₉	—	2	1	no	—
11	C₁₉×#340	C₄	1	2	yes	—
12	C₁₉×#335	—	2	1	no	—
13	C₁₉×#335	C₄	1	2	yes	complemented
14	C₂×M₁₆×C₁₉	—	4	1	no	—
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	—	4	1	no	—
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₉	—	2	2	no	—
21	C₁₉×#107	—	2	4	no	—
22	C₁₉×C₄⋊C₈	—	2	2	no	—
23	C₁₉×C₄⋊C₈	—	4	1	no	—
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
28	C₁₉×#95	—	4	1	no	—
29	C₂²×C₄×C₁₉	—	4	2	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
33	M₁₆×C₁₉	—	8	1	no	—
34	M₁₆×C₁₉	—	8	1	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₂×C₈×C₁₉	—	4	2	no	—
38	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₄⋊C₄×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	—	8	1	no	—
45	C₄²×C₁₉	—	8	1	no	—
46	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
48	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
49	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
50	C₁₆×C₁₉	—	4	2	no	—
51	#7296	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂³×C₁₉	#102	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	4	no	—
57	C₂×C₄×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	—	8	2	no	—
59	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
65	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
66	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
67	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
68	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
69	C₈×C₁₉	—	2	1	no	—
70	C₈×C₁₉	—	2	1	no	—
71	C₈×C₁₉	—	2	1	no	—
72	C₈×C₁₉	—	8	2	no	—
73	C₈×C₁₉	#104	1	2	yes	—
74	#2162	C₂×C₁₉	1	1	yes	characteristic
75	C₄×#107	C₂×C₁₉	1	1	yes	characteristic
76	#1567	C₂×C₁₉	1	1	yes	characteristic
77	C₂²×C₁₉	—	2	1	no	—
78	C₂²×C₁₉	—	2	1	no	—
79	C₂²×C₁₉	#340	1	1	yes	characteristic
80	C₂²×C₁₉	#357	1	1	yes	characteristic
81	C₂²×C₁₉	#358	1	1	yes	characteristic
82	C₄×C₁₉	—	2	1	no	—
83	C₄×C₁₉	—	2	1	no	—
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	8	4	no	—
86	C₄×C₁₉	#339	1	1	yes	characteristic
87	C₄×C₁₉	#344	1	1	yes	characteristic
88	C₄×C₁₉	#357	1	1	yes	characteristic
89	C₄×C₁₉	#358	1	1	yes	characteristic
90	C₄×C₁₉	#366	1	1	yes	characteristic
91	C₄×C₁₉	#367	1	1	yes	characteristic
92	C₂×#107	—	2	1	no	—
93	#423	—	2	1	no	—
94	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
95	C₄×C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₁₆	C₄×C₁₉	1	2	yes	complemented
97	C₂²⋊C₁₆	—	2	1	no	—
98	C₄×C₁₆	—	2	1	no	—
99	#340	C₄×C₁₉	1	2	yes	—
100	#335	—	2	1	no	—
101	#335	C₄×C₁₉	1	2	yes	complemented
102	C₂×C₁₉	—	2	1	no	—
103	C₂×C₁₉	—	2	1	no	—
104	C₂×C₁₉	#1303	1	1	yes	characteristic
105	C₂×C₁₉	#1380	1	1	yes	characteristic
106	C₂×C₁₉	#1389	1	1	yes	characteristic
107	C₂×M₁₆	—	4	1	no	—
108	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
109	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
110	C₂×C₄⋊C₄	—	2	2	no	—
111	C₂×C₄²	—	4	1	no	—
112	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
113	C₂×C₁₆	—	2	2	no	—
114	#107	—	2	4	no	—
115	C₄⋊C₈	—	2	2	no	—
116	C₄⋊C₈	—	4	1	no	—
117	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
118	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
119	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
120	C₄×C₈	Q₈×C₁₉	1	1	yes	characteristic
121	#95	—	4	1	no	—
122	C₁₉	#7296	1	1	yes	characteristic, direct product factor, Sylow
123	C₂²×C₄	—	4	2	no	—
124	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
125	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
126	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
127	M₁₆	—	8	1	no	—
128	M₁₆	—	8	1	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	4	1	no	—
131	C₂×C₈	—	4	2	no	—
132	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
133	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
134	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
135	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	—	4	2	no	—
138	C₄²	—	8	1	no	—
139	C₄²	—	8	1	no	—
140	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
141	C₄²	C₄⋊C₄×C₁₉	1	1	yes	characteristic
142	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
143	C₄²	Q₁₆×C₁₉	1	1	yes	characteristic
144	C₁₆	—	4	2	no	—
145	C₂³	C₁₉×#102	1	1	yes	characteristic
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	4	1	no	—
149	C₂×C₄	—	4	4	no	—
150	C₂×C₄	—	8	2	no	—
151	C₂×C₄	—	8	2	no	—
152	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
153	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
154	C₂×C₄	C₁₉×#103	1	1	yes	characteristic
155	C₂×C₄	C₁₉×#103	1	1	yes	characteristic
156	C₂×C₄	C₁₉×#106	1	1	yes	characteristic
157	C₂×C₄	C₁₉×#107	1	1	yes	characteristic
158	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
159	C₂×C₄	C₁₉×SD₃₂	1	1	yes	characteristic
160	C₂×C₄	C₁₉×SD₃₂	1	1	yes	characteristic
161	C₂×C₄	C₁₉×Q₃₂	1	1	yes	characteristic
162	C₈	—	2	1	no	—
163	C₈	—	2	1	no	—
164	C₈	—	2	1	no	—
165	C₈	—	8	2	no	—
166	C₈	C₁₉×#104	1	2	yes	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	C₁₉×#340	1	1	yes	characteristic
170	C₂²	C₁₉×#357	1	1	yes	characteristic
171	C₂²	C₁₉×#358	1	1	yes	characteristic
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	8	4	no	—
176	C₄	C₁₉×#339	1	1	yes	characteristic
177	C₄	C₁₉×#344	1	1	yes	characteristic
178	C₄	C₁₉×#357	1	1	yes	characteristic
179	C₄	C₁₉×#358	1	1	yes	characteristic
180	C₄	C₁₉×#366	1	1	yes	characteristic
181	C₄	C₁₉×#367	1	1	yes	characteristic
182	C₂	—	2	1	no	—
183	C₂	—	2	1	no	—
184	C₂	C₁₉×#1303	1	1	yes	characteristic
185	C₂	C₁₉×#1380	1	1	yes	characteristic
186	C₂	C₁₉×#1389	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#102
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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
8. C₁₉×C₄⋊C₁₆	C₄	semidirect
13. C₁₉×#335	C₄	semidirect
51. #7296	C₁₉	direct (N × H)
96. C₄⋊C₁₆	C₄×C₁₉	semidirect
101. #335	C₄×C₁₉	semidirect
122. C₁₉	#7296	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×#2162	2
C₄×C₁₉×#107	2
C₁₉×#1567	2
#7296	19

Subgroups — C19×#7296 #18013255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7296 #18013255