Subgroups — C₁₉×#21681 #18027640

Order 4864.

1230 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#436	C₂	1	6	yes	maximal, complemented
2	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1954	C₂	1	6	yes	maximal, complemented
4	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
7	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
9	C₁₉×#436	—	2	24	no	—
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	6	yes	—
11	C₂×C₁₉×C₂²⋊C₈	C₂²	1	12	yes	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
14	C₁₉×#390	C₄	1	6	yes	—
15	C₁₉×#384	C₄	1	1	yes	characteristic
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₉	C₂×C₄	1	6	yes	—
18	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
19	C₂×M₁₆×C₁₉	—	2	24	no	—
20	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
21	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
22	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₁₉×#127	—	2	4	no	—
24	C₄×D₄×C₁₉	—	2	12	no	—
25	C₄×D₄×C₁₉	—	2	12	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
27	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	3	yes	—
29	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
31	C₁₉×C₄⋊C₈	—	2	12	no	—
32	C₁₉×C₂²⋊C₈	—	2	24	no	—
33	C₄×C₈×C₁₉	—	2	6	no	—
34	C₄×C₈×C₁₉	D₄	1	12	yes	complemented
35	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
36	C₂×D₄×C₁₉	—	2	12	no	—
37	C₂×D₄×C₁₉	—	2	12	no	—
38	C₂×D₄×C₁₉	—	2	12	no	—
39	C₂²×C₄×C₁₉	—	2	12	no	—
40	C₂²×C₄×C₁₉	—	2	12	no	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
43	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
44	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
45	M₁₆×C₁₉	—	4	16	no	—
46	C₂×C₈×C₁₉	—	2	6	no	—
47	C₂×C₈×C₁₉	—	2	12	no	—
48	C₂×C₈×C₁₉	C₂×D₄	1	6	yes	—
49	C₂×C₈×C₁₉	C₂×D₄	1	6	yes	—
50	C₄⋊C₄×C₁₉	—	2	12	no	—
51	C₂²⋊C₄×C₁₉	—	2	24	no	—
52	C₄²×C₁₉	—	2	6	no	—
53	C₄²×C₁₉	M₁₆	1	4	yes	complemented
54	C₄²×C₁₉	C₂×D₄	1	6	yes	—
55	C₄²×C₁₉	#41	1	6	yes	—
56	#21681	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂³×C₁₉	—	2	12	no	—
58	C₂³×C₁₉	—	2	4	no	—
59	C₂³×C₁₉	—	2	12	no	—
60	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
61	D₄×C₁₉	—	4	24	no	—
62	C₂×C₄×C₁₉	—	2	6	no	—
63	C₂×C₄×C₁₉	—	2	12	no	—
64	C₂×C₄×C₁₉	—	4	4	no	—
65	C₂×C₄×C₁₉	—	4	12	no	—
66	C₂×C₄×C₁₉	C₄×D₄	1	6	yes	—
67	C₂×C₄×C₁₉	C₄×D₄	1	6	yes	—
68	C₂×C₄×C₁₉	C₂×M₁₆	1	6	yes	—
69	C₂×C₄×C₁₉	#131	1	6	yes	—
70	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
71	C₂×C₄×C₁₉	C₂×#41	1	3	yes	—
72	C₈×C₁₉	—	2	6	no	—
73	C₈×C₁₉	—	4	4	no	—
74	C₈×C₁₉	#127	1	4	yes	complemented
75	C₂×#436	C₂×C₁₉	1	6	yes	complemented
76	C₄×#127	C₂×C₁₉	1	1	yes	characteristic
77	#1954	C₂×C₁₉	1	6	yes	complemented
78	#1842	C₂×C₁₉	1	1	yes	characteristic, complemented
79	C₄²×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
80	C₂²×C₁₉	—	4	4	no	—
81	C₂²×C₁₉	—	4	12	no	—
82	C₂²×C₁₉	—	4	12	no	—
83	C₂²×C₁₉	C₂×C₄×D₄	1	3	yes	—
84	C₂²×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×#131	1	3	yes	—
86	C₄×C₁₉	—	2	6	no	—
87	C₄×C₁₉	—	4	4	no	—
88	C₄×C₁₉	#436	1	12	yes	complemented
89	C₄×C₁₉	C₂×#127	1	1	yes	characteristic
90	C₄×C₁₉	#532	1	3	yes	—
91	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
92	C₂×#127	C₄×C₁₉	1	1	yes	characteristic
93	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
94	#436	—	2	24	no	—
95	C₂×C₄⋊C₈	C₂²×C₁₉	1	6	yes	—
96	C₂×C₂²⋊C₈	C₂²×C₁₉	1	12	yes	—
97	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
98	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
99	#390	C₄×C₁₉	1	6	yes	—
100	#384	C₄×C₁₉	1	1	yes	characteristic
101	C₄³	C₂²×C₁₉	1	1	yes	characteristic
102	C₂×C₁₉	—	8	4	no	—
103	C₂×C₁₉	C₄×#127	1	1	yes	characteristic
104	C₂×C₁₉	C₂×#436	1	3	yes	—
105	C₂×C₁₉	#2931	1	3	yes	—
106	C₂²×D₄	C₂×C₄×C₁₉	1	6	yes	—
107	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
108	C₂×M₁₆	—	2	24	no	—
109	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
110	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
111	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
112	#127	—	2	4	no	—
113	C₄×D₄	—	2	12	no	—
114	C₄×D₄	—	2	12	no	—
115	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
116	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
117	C₂×C₄²	C₂×C₄×C₁₉	1	3	yes	—
118	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
120	C₄⋊C₈	—	2	12	no	—
121	C₂²⋊C₈	—	2	24	no	—
122	C₄×C₈	—	2	6	no	—
123	C₄×C₈	D₄×C₁₉	1	12	yes	complemented
124	C₁₉	#21681	1	1	yes	characteristic, direct product factor, Sylow
125	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
126	C₂×D₄	—	2	12	no	—
127	C₂×D₄	—	2	12	no	—
128	C₂×D₄	—	2	12	no	—
129	C₂²×C₄	—	2	12	no	—
130	C₂²×C₄	—	2	12	no	—
131	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
132	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
133	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
134	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
135	M₁₆	—	4	16	no	—
136	C₂×C₈	—	2	6	no	—
137	C₂×C₈	—	2	12	no	—
138	C₂×C₈	C₂×D₄×C₁₉	1	6	yes	—
139	C₂×C₈	C₂×D₄×C₁₉	1	6	yes	—
140	C₄⋊C₄	—	2	12	no	—
141	C₂²⋊C₄	—	2	24	no	—
142	C₄²	—	2	6	no	—
143	C₄²	M₁₆×C₁₉	1	4	yes	complemented
144	C₄²	C₂×D₄×C₁₉	1	6	yes	—
145	C₄²	#41×C₁₉	1	6	yes	—
146	C₂³	—	2	12	no	—
147	C₂³	—	2	4	no	—
148	C₂³	—	2	12	no	—
149	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
150	D₄	—	4	24	no	—
151	C₂×C₄	—	2	6	no	—
152	C₂×C₄	—	2	12	no	—
153	C₂×C₄	—	4	4	no	—
154	C₂×C₄	—	4	12	no	—
155	C₂×C₄	C₄×D₄×C₁₉	1	6	yes	—
156	C₂×C₄	C₄×D₄×C₁₉	1	6	yes	—
157	C₂×C₄	C₂×M₁₆×C₁₉	1	6	yes	—
158	C₂×C₄	C₁₉×#131	1	6	yes	—
159	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
160	C₂×C₄	C₂×#41×C₁₉	1	3	yes	—
161	C₈	—	2	6	no	—
162	C₈	—	4	4	no	—
163	C₈	C₁₉×#127	1	4	yes	complemented
164	C₂²	—	4	12	no	—
165	C₂²	—	4	12	no	—
166	C₂²	—	4	4	no	—
167	C₂²	C₂×C₄×D₄×C₁₉	1	3	yes	—
168	C₂²	C₂²×M₁₆×C₁₉	1	1	yes	characteristic
169	C₂²	C₂×C₁₉×#131	1	3	yes	—
170	C₄	—	2	6	no	—
171	C₄	—	4	4	no	—
172	C₄	C₁₉×#436	1	12	yes	complemented
173	C₄	C₂×C₁₉×#127	1	1	yes	characteristic
174	C₄	C₁₉×#532	1	3	yes	—
175	C₂	—	8	4	no	—
176	C₂	C₄×C₁₉×#127	1	1	yes	characteristic
177	C₂	C₂×C₁₉×#436	1	3	yes	—
178	C₂	C₁₉×#2931	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂×C₁₉×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#436	C₂	semidirect
3. C₁₉×#1954	C₂	semidirect
4. C₁₉×#1842	C₂	semidirect
5. C₄²×C₈×C₁₉	C₂	semidirect
34. C₄×C₈×C₁₉	D₄	semidirect
53. C₄²×C₁₉	M₁₆	semidirect
56. #21681	C₁₉	direct (N × H)
74. C₈×C₁₉	#127	semidirect
75. C₂×#436	C₂×C₁₉	semidirect
77. #1954	C₂×C₁₉	semidirect
78. #1842	C₂×C₁₉	semidirect
79. C₄²×C₈	C₂×C₁₉	semidirect
88. C₄×C₁₉	#436	semidirect
123. C₄×C₈	D₄×C₁₉	semidirect
124. C₁₉	#21681	direct (N × H)
143. C₄²	M₁₆×C₁₉	semidirect
163. C₈	C₁₉×#127	semidirect
172. C₄	C₁₉×#436	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#436	2
C₄×C₁₉×#127	2
C₁₉×#1954	2
C₁₉×#1842	2
C₄²×C₈×C₁₉	2
#21681	19

Subgroups — C19×#21681 #18027640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21681 #18027640