Subgroups — C₁₉×#32856 #18038815

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2647	C₂	1	2	yes	maximal
2	C₁₉×#2101	C₂	1	4	yes	maximal
3	C₁₉×#2087	C₂	1	2	yes	maximal
4	C₁₉×#2086	C₂	1	2	yes	maximal
5	C₁₉×#2083	C₂	1	4	yes	maximal
6	C₁₉×#1832	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#107	C₂²	1	2	yes	—
8	C₂×C₁₉×#107	C₂²	1	2	yes	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₉×#400	—	2	4	no	—
12	C₁₉×#398	—	2	4	no	—
13	C₁₉×#389	C₂²	1	4	yes	—
14	C₁₉×#389	C₂²	1	4	yes	—
15	C₁₉×#384	C₂²	1	2	yes	—
16	C₁₉×#382	C₂²	1	2	yes	—
17	C₁₉×#376	C₂²	1	1	yes	characteristic
18	C₁₉×#340	C₂²	1	4	yes	—
19	C₁₉×#340	C₂²	1	4	yes	—
20	C₁₉×#340	C₂²	1	2	yes	—
21	C₁₉×#340	C₂²	1	2	yes	—
22	C₁₉×#336	C₂²	1	4	yes	—
23	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
29	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×#107	—	4	2	no	—
33	C₁₉×#107	—	4	2	no	—
34	C₁₉×C₄⋊C₈	—	4	1	no	—
35	C₁₉×C₄⋊C₈	—	4	1	no	—
36	C₁₉×#95	—	2	4	no	—
37	C₁₉×#95	—	2	4	no	—
38	C₁₉×#95	—	2	4	no	—
39	C₁₉×#95	D₄	1	2	yes	—
40	C₁₉×#95	D₄	1	2	yes	—
41	C₂²×C₄×C₁₉	—	2	4	no	—
42	C₂²×C₄×C₁₉	—	2	4	no	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	2	2	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₄⋊C₄×C₁₉	—	8	4	no	—
56	C₄⋊C₄×C₁₉	—	8	4	no	—
57	C₄⋊C₄×C₁₉	—	8	4	no	—
58	C₄²×C₁₉	—	2	1	no	—
59	C₄²×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	1	no	—
62	#32856	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	4	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	4	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	4	4	no	—
72	C₂×C₄×C₁₉	—	4	4	no	—
73	C₂×C₄×C₁₉	—	4	4	no	—
74	C₂×C₄×C₁₉	—	4	4	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
78	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
79	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
80	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
81	C₈×C₁₉	—	4	2	no	—
82	C₈×C₁₉	—	4	2	no	—
83	#2647	C₂×C₁₉	1	2	yes	—
84	#2101	C₂×C₁₉	1	4	yes	—
85	#2087	C₂×C₁₉	1	2	yes	—
86	#2086	C₂×C₁₉	1	2	yes	—
87	#2083	C₂×C₁₉	1	4	yes	—
88	#1832	C₂×C₁₉	1	1	yes	characteristic
89	C₂²×C₁₉	#536	1	2	yes	—
90	C₂²×C₁₉	#537	1	1	yes	characteristic
91	C₂²×C₁₉	#576	1	2	yes	—
92	C₂²×C₁₉	#578	1	2	yes	—
93	C₄×C₁₉	—	4	4	no	—
94	C₄×C₁₉	—	4	1	no	—
95	C₄×C₁₉	—	4	1	no	—
96	C₄×C₁₉	—	8	4	no	—
97	C₄×C₁₉	—	8	4	no	—
98	C₄×C₁₉	#563	1	1	yes	characteristic
99	C₄×C₁₉	#563	1	1	yes	characteristic
100	C₄×C₁₉	#564	1	2	yes	—
101	C₂×#107	C₂²×C₁₉	1	2	yes	—
102	C₂×#107	C₂²×C₁₉	1	2	yes	—
103	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
104	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
105	#400	—	2	4	no	—
106	#398	—	2	4	no	—
107	#389	C₂²×C₁₉	1	4	yes	—
108	#389	C₂²×C₁₉	1	4	yes	—
109	#384	C₂²×C₁₉	1	2	yes	—
110	#382	C₂²×C₁₉	1	2	yes	—
111	#376	C₂²×C₁₉	1	1	yes	characteristic
112	#340	C₂²×C₁₉	1	4	yes	—
113	#340	C₂²×C₁₉	1	4	yes	—
114	#340	C₂²×C₁₉	1	2	yes	—
115	#340	C₂²×C₁₉	1	2	yes	—
116	#336	C₂²×C₁₉	1	4	yes	—
117	C₂×C₁₉	#2822	1	1	yes	characteristic
118	C₂×C₁₉	#3243	1	4	yes	—
119	C₂×C₁₉	#3259	1	1	yes	characteristic
120	C₂×C₁₉	#3261	1	1	yes	characteristic
121	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
122	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
123	C₂×C₄⋊C₄	—	2	4	no	—
124	C₂×C₄⋊C₄	—	2	4	no	—
125	C₂×C₄⋊C₄	—	2	4	no	—
126	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
127	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
128	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
129	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
130	#107	—	4	2	no	—
131	#107	—	4	2	no	—
132	C₄⋊C₈	—	4	1	no	—
133	C₄⋊C₈	—	4	1	no	—
134	#95	—	2	4	no	—
135	#95	—	2	4	no	—
136	#95	—	2	4	no	—
137	#95	D₄×C₁₉	1	2	yes	—
138	#95	D₄×C₁₉	1	2	yes	—
139	C₁₉	#32856	1	1	yes	characteristic, direct product factor, Sylow
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
143	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
144	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
145	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	2	2	no	—
148	C₂×C₈	—	2	4	no	—
149	C₂×C₈	—	2	4	no	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	8	4	no	—
155	C₄⋊C₄	—	8	4	no	—
156	C₄⋊C₄	—	8	4	no	—
157	C₄²	—	2	1	no	—
158	C₄²	—	2	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	1	no	—
161	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
177	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
178	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
179	C₈	—	4	2	no	—
180	C₈	—	4	2	no	—
181	C₂²	C₁₉×#536	1	2	yes	—
182	C₂²	C₁₉×#537	1	1	yes	characteristic
183	C₂²	C₁₉×#576	1	2	yes	—
184	C₂²	C₁₉×#578	1	2	yes	—
185	C₄	—	4	4	no	—
186	C₄	—	4	1	no	—
187	C₄	—	4	1	no	—
188	C₄	—	8	4	no	—
189	C₄	—	8	4	no	—
190	C₄	C₁₉×#563	1	1	yes	characteristic
191	C₄	C₁₉×#563	1	1	yes	characteristic
192	C₄	C₁₉×#564	1	2	yes	—
193	C₂	C₁₉×#2822	1	1	yes	characteristic
194	C₂	C₁₉×#3243	1	4	yes	—
195	C₂	C₁₉×#3259	1	1	yes	characteristic
196	C₂	C₁₉×#3261	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
62. #32856	C₁₉	direct (N × H)
139. C₁₉	#32856	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×#2647	2
C₁₉×#2101	2
C₁₉×#2087	2
C₁₉×#2086	2
C₁₉×#2083	2
C₁₉×#1832	2
#32856	19

Subgroups — C19×#32856 #18038815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32856 #18038815