Subgroups — C₁₉⋊#7050 #18069151

Order 4864.

332 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563787	C₂	1	2	yes	maximal
2	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	4	yes	—
6	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
7	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
8	C₄³×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	D₄	1	2	yes	—
14	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	4	no	—
16	C₁₉×C₄⋊C₈	—	4	2	no	—
17	C₁₉×C₄⋊C₈	—	4	2	no	—
18	C₁₉×C₄⋊C₈	—	4	2	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
21	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
22	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
23	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
24	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
28	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	—	4	2	no	—
30	C₂×C₈×C₁₉	—	4	4	no	—
31	C₄²×C₁₉	—	2	2	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	4	1	no	—
36	C₄²×C₁₉	D₈	1	1	yes	characteristic
37	C₄²×C₁₉	D₈	1	2	yes	—
38	C₄²×C₁₉	SD₁₆	1	2	yes	—
39	C₄²×C₁₉	SD₁₆	1	2	yes	—
40	C₄²×C₁₉	SD₁₆	1	2	yes	—
41	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
42	C₄²×C₁₉	Q₁₆	1	2	yes	—
43	C₂×C₁₉⋊C₈	—	4	4	no	—
44	C₂×C₁₉⋊C₈	—	4	4	no	—
45	C₂×C₁₉⋊C₈	—	4	4	no	—
46	#7050	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	#95	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	#100	1	2	yes	—
55	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#101	1	2	yes	—
57	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#102	1	2	yes	—
59	C₂×C₄×C₁₉	#102	1	2	yes	—
60	C₂×C₄×C₁₉	#102	1	2	yes	—
61	C₂×C₄×C₁₉	#103	1	2	yes	—
62	C₂×C₄×C₁₉	#103	1	2	yes	—
63	C₂×C₄×C₁₉	#103	1	2	yes	—
64	C₂×C₄×C₁₉	#106	1	2	yes	—
65	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#107	1	2	yes	—
67	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
68	C₈×C₁₉	—	8	2	no	—
69	C₁₉⋊C₈	—	8	4	no	—
70	#1842	—	19	2	no	—
71	#1842	D₁₉	1	1	yes	characteristic
72	C₂²×C₁₉	#338	1	1	yes	characteristic
73	C₂²×C₁₉	#340	1	2	yes	—
74	C₂²×C₁₉	#340	1	1	yes	characteristic
75	C₂²×C₁₉	#343	1	2	yes	—
76	C₂²×C₁₉	#343	1	1	yes	characteristic
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	—	2	1	no	—
81	C₄×C₁₉	—	4	1	no	—
82	C₄×C₁₉	#331	1	2	yes	—
83	C₄×C₁₉	#331	1	1	yes	characteristic
84	C₄×C₁₉	#332	1	2	yes	—
85	C₄×C₁₉	#332	1	2	yes	—
86	C₄×C₁₉	#332	1	2	yes	—
87	C₄×C₁₉	#333	1	2	yes	—
88	C₄×C₁₉	#333	1	1	yes	characteristic
89	C₂×C₄⋊C₈	—	2	2	no	—
90	C₂×C₄⋊C₈	—	19	4	no	—
91	C₂×C₄⋊C₈	—	38	2	no	—
92	C₂×C₄⋊C₈	—	38	2	no	—
93	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
94	C₄³	C₂×D₁₉	1	1	yes	characteristic
95	C₂×C₁₉	#1292	1	2	yes	—
96	C₂×C₁₉	#1292	1	1	yes	characteristic
97	C₂×C₁₉	#1296	1	1	yes	characteristic
98	C₂×C₁₉	#1296	1	2	yes	—
99	C₂×C₁₉	#1309	1	1	yes	characteristic
100	C₂²×C₈	—	2	2	no	—
101	C₂²×C₈	—	38	4	no	—
102	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
103	C₂×C₄²	C₄×D₁₉	1	2	yes	—
104	C₂×C₄²	D₇₆	1	1	yes	characteristic
105	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
106	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
107	C₄⋊C₈	—	4	2	no	—
108	C₄⋊C₈	—	4	2	no	—
109	C₄⋊C₈	—	4	2	no	—
110	C₄⋊C₈	—	76	4	no	—
111	C₄⋊C₈	—	76	2	no	—
112	C₄⋊C₈	—	76	2	no	—
113	C₄⋊C₈	—	76	2	no	—
114	C₄⋊C₈	—	76	2	no	—
115	C₁₉	#7050	1	1	yes	characteristic, complemented, Sylow
116	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
117	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
118	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
119	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
120	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
121	C₂×C₈	—	4	4	no	—
122	C₂×C₈	—	4	2	no	—
123	C₂×C₈	—	76	4	no	—
124	C₂×C₈	—	76	4	no	—
125	C₂×C₈	—	76	4	no	—
126	C₄²	—	2	2	no	—
127	C₄²	—	2	2	no	—
128	C₄²	—	2	1	no	—
129	C₄²	—	2	1	no	—
130	C₄²	—	4	1	no	—
131	C₄²	#64516	1	2	yes	—
132	C₄²	D₁₅₂	1	1	yes	characteristic
133	C₄²	Dic₇₆	1	1	yes	characteristic
134	C₄²	#64525	1	2	yes	—
135	C₄²	#64526	1	2	yes	—
136	C₄²	#64527	1	2	yes	—
137	C₄²	#64528	1	2	yes	—
138	C₂³	C₁₉⋊#95	1	1	yes	characteristic
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	#10597264	1	2	yes	—
146	C₂×C₄	#10597265	1	2	yes	—
147	C₂×C₄	#10597266	1	2	yes	—
148	C₂×C₄	#10597267	1	2	yes	—
149	C₂×C₄	#10597273	1	2	yes	—
150	C₂×C₄	#10597274	1	1	yes	characteristic
151	C₂×C₄	#10597275	1	1	yes	characteristic
152	C₂×C₄	#10597278	1	2	yes	—
153	C₂×C₄	#10597280	1	2	yes	—
154	C₂×C₄	#10597281	1	2	yes	—
155	C₂×C₄	#10597289	1	2	yes	—
156	C₂×C₄	#10597290	1	1	yes	characteristic
157	C₂×C₄	#10597292	1	2	yes	—
158	C₂×C₄	#10597293	1	1	yes	characteristic
159	C₈	—	8	2	no	—
160	C₈	—	152	4	no	—
161	C₂²	C₁₉⋊#338	1	1	yes	characteristic
162	C₂²	#11926306	1	2	yes	—
163	C₂²	#11926307	1	1	yes	characteristic
164	C₂²	#11926312	1	2	yes	—
165	C₂²	#11926313	1	1	yes	characteristic
166	C₄	—	2	2	no	—
167	C₄	—	2	2	no	—
168	C₄	—	2	1	no	—
169	C₄	—	2	1	no	—
170	C₄	—	4	1	no	—
171	C₄	#11926287	1	2	yes	—
172	C₄	#11926288	1	1	yes	characteristic
173	C₄	#11926289	1	2	yes	—
174	C₄	#11926290	1	2	yes	—
175	C₄	#11926291	1	2	yes	—
176	C₄	#11926292	1	2	yes	—
177	C₄	#11926293	1	1	yes	characteristic
178	C₂	#14561509	1	2	yes	—
179	C₂	#14561510	1	1	yes	characteristic
180	C₂	#14561518	1	1	yes	characteristic
181	C₂	#14561519	1	2	yes	—
182	C₂	C₁₉⋊#1309	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1842	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#7050
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
115. C₁₉	#7050	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
C₁₉×#1842	2
#7050	19

Subgroups — C19⋊#7050 #18069151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#7050 #18069151