Subgroups — C₁₉×#32848 #18038807

Order 4864.

604 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2859	C₂	1	2	yes	maximal
2	C₁₉×#2099	C₂	1	4	yes	maximal
3	C₁₉×#2086	C₂	1	4	yes	maximal
4	C₁₉×#2083	C₂	1	4	yes	maximal
5	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#125	—	2	2	no	—
7	C₂×C₁₉×#107	C₂²	1	4	yes	—
8	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
9	C₁₉×#389	—	2	2	no	—
10	C₁₉×#389	—	2	2	no	—
11	C₁₉×#389	C₂²	1	4	yes	—
12	C₁₉×#389	C₂²	1	4	yes	—
13	C₁₉×#384	C₂²	1	2	yes	—
14	C₁₉×#384	C₂²	1	2	yes	—
15	C₁₉×#382	—	2	2	no	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#340	C₂²	1	8	yes	—
18	C₁₉×#340	C₂²	1	4	yes	—
19	C₁₉×#336	C₂²	1	4	yes	—
20	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
21	C₁₉×#125	—	4	8	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	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	D₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₁₉×#107	—	4	4	no	—
36	C₁₉×C₄⋊C₈	—	4	2	no	—
37	C₁₉×#95	—	2	4	no	—
38	C₁₉×#95	—	2	4	no	—
39	C₂²×C₄×C₁₉	—	2	4	no	—
40	C₂²×C₄×C₁₉	—	2	4	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	—	2	8	no	—
48	C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₄⋊C₄×C₁₉	—	2	8	no	—
50	C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₄⋊C₄×C₁₉	—	4	4	no	—
53	C₄⋊C₄×C₁₉	—	4	4	no	—
54	C₄⋊C₄×C₁₉	—	4	8	no	—
55	C₄⋊C₄×C₁₉	—	4	8	no	—
56	C₄⋊C₄×C₁₉	—	4	4	no	—
57	C₄²×C₁₉	—	2	4	no	—
58	C₄²×C₁₉	—	2	1	no	—
59	C₄²×C₁₉	—	2	4	no	—
60	C₄²×C₁₉	—	2	1	no	—
61	C₄²×C₁₉	—	4	1	no	—
62	C₄²×C₁₉	D₈	1	4	yes	—
63	#32848	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	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	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	C₂×D₈	1	4	yes	—
80	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
81	C₂×C₄×C₁₉	#137	1	4	yes	—
82	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
83	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
84	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
85	C₈×C₁₉	—	4	4	no	—
86	#2859	C₂×C₁₉	1	2	yes	—
87	#2099	C₂×C₁₉	1	4	yes	—
88	#2086	C₂×C₁₉	1	4	yes	—
89	#2083	C₂×C₁₉	1	4	yes	—
90	#1831	C₂×C₁₉	1	1	yes	characteristic
91	C₂²×C₁₉	#536	1	2	yes	—
92	C₂²×C₁₉	#537	1	1	yes	characteristic
93	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
94	C₂²×C₁₉	C₂×#137	1	2	yes	—
95	C₂²×C₁₉	#575	1	1	yes	characteristic
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	4	1	no	—
100	C₄×C₁₉	—	8	4	no	—
101	C₄×C₁₉	—	8	4	no	—
102	C₄×C₁₉	#563	1	2	yes	—
103	C₄×C₁₉	#564	1	2	yes	—
104	C₂×#125	—	2	2	no	—
105	C₂×#107	C₂²×C₁₉	1	4	yes	—
106	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
107	#389	—	2	2	no	—
108	#389	—	2	2	no	—
109	#389	C₂²×C₁₉	1	4	yes	—
110	#389	C₂²×C₁₉	1	4	yes	—
111	#384	C₂²×C₁₉	1	2	yes	—
112	#384	C₂²×C₁₉	1	2	yes	—
113	#382	—	2	2	no	—
114	C₄³	C₂²×C₁₉	1	1	yes	characteristic
115	#340	C₂²×C₁₉	1	8	yes	—
116	#340	C₂²×C₁₉	1	4	yes	—
117	#336	C₂²×C₁₉	1	4	yes	—
118	C₂×C₁₉	#2822	1	1	yes	characteristic
119	C₂×C₁₉	#3226	1	2	yes	—
120	C₂×C₁₉	#3236	1	2	yes	—
121	C₂×C₁₉	#3245	1	1	yes	characteristic
122	C₂×C₁₉	#3255	1	1	yes	characteristic
123	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
124	#125	—	4	8	no	—
125	C₂×C₄⋊C₄	—	2	2	no	—
126	C₂×C₄⋊C₄	—	2	2	no	—
127	C₂×C₄⋊C₄	—	2	4	no	—
128	C₂×C₄⋊C₄	—	2	4	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
132	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
133	C₂×C₄²	D₄×C₁₉	1	2	yes	—
134	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
135	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
136	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
137	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
138	#107	—	4	4	no	—
139	C₄⋊C₈	—	4	2	no	—
140	#95	—	2	4	no	—
141	#95	—	2	4	no	—
142	C₁₉	#32848	1	1	yes	characteristic, direct product factor, Sylow
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	—	2	4	no	—
145	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
147	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
148	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
149	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	2	8	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	2	8	no	—
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	—	4	4	no	—
156	C₄⋊C₄	—	4	4	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₄⋊C₄	—	4	8	no	—
159	C₄⋊C₄	—	4	8	no	—
160	C₄⋊C₄	—	4	4	no	—
161	C₄²	—	2	4	no	—
162	C₄²	—	2	1	no	—
163	C₄²	—	2	4	no	—
164	C₄²	—	2	1	no	—
165	C₄²	—	4	1	no	—
166	C₄²	D₈×C₁₉	1	4	yes	—
167	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	C₂×D₈×C₁₉	1	4	yes	—
183	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
184	C₂×C₄	C₁₉×#137	1	4	yes	—
185	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
187	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
188	C₈	—	4	4	no	—
189	C₂²	C₁₉×#536	1	2	yes	—
190	C₂²	C₁₉×#537	1	1	yes	characteristic
191	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
192	C₂²	C₂×C₁₉×#137	1	2	yes	—
193	C₂²	C₁₉×#575	1	1	yes	characteristic
194	C₄	—	2	4	no	—
195	C₄	—	2	4	no	—
196	C₄	—	2	2	no	—
197	C₄	—	4	1	no	—
198	C₄	—	8	4	no	—
199	C₄	—	8	4	no	—
200	C₄	C₁₉×#563	1	2	yes	—
201	C₄	C₁₉×#564	1	2	yes	—
202	C₂	C₁₉×#2822	1	1	yes	characteristic
203	C₂	C₁₉×#3226	1	2	yes	—
204	C₂	C₁₉×#3236	1	2	yes	—
205	C₂	C₁₉×#3245	1	1	yes	characteristic
206	C₂	C₁₉×#3255	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 ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
63. #32848	C₁₉	direct (N × H)
142. C₁₉	#32848	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×#2859	2
C₁₉×#2099	2
C₁₉×#2086	2
C₁₉×#2083	2
C₁₉×#1831	2
#32848	19

Subgroups — C19×#32848 #18038807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32848 #18038807