Subgroups — C₁₉×#19668 #18025627

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3231	C₂	1	4	yes	maximal
2	C₁₉×#3170	C₂	1	2	yes	maximal
3	C₁₉×#1718	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1710	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1707	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#533	C₂²	1	4	yes	—
9	C₁₉×#500	C₂²	1	2	yes	—
10	C₁₉×#500	C₂²	1	4	yes	—
11	C₁₉×#498	C₂²	1	4	yes	—
12	C₁₉×#494	C₂²	1	2	yes	—
13	C₁₉×#487	C₂²	1	4	yes	—
14	C₁₉×#487	C₂²	1	4	yes	—
15	C₁₉×#487	C₂²	1	4	yes	—
16	C₁₉×#485	—	2	8	no	—
17	C₁₉×#479	—	2	8	no	—
18	C₁₉×#467	—	2	4	no	—
19	C₄×Q₁₆×C₁₉	—	2	4	no	—
20	C₁₉×#431	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#322	C₂²	1	2	yes	—
23	C₈²×C₁₉	C₂²	1	1	yes	characteristic
24	C₈²×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×Q₁₆×C₁₉	—	2	4	no	—
26	C₂²×C₈×C₁₉	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
28	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
29	C₁₉×#125	—	2	4	no	—
30	C₁₉×C₂²⋊Q₈	—	2	4	no	—
31	C₁₉×C₂²⋊Q₈	—	2	4	no	—
32	C₄×Q₈×C₁₉	—	2	4	no	—
33	C₄×Q₈×C₁₉	—	2	4	no	—
34	C₁₉×#117	—	2	4	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₁₉×#107	—	2	4	no	—
37	C₁₉×#107	—	2	8	no	—
38	C₁₉×#106	—	2	8	no	—
39	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
40	C₁₉×#103	—	2	8	no	—
41	C₁₉×#103	—	2	8	no	—
42	C₁₉×#103	—	2	8	no	—
43	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
44	C₄×C₈×C₁₉	D₄	1	2	yes	—
45	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₄×C₈×C₁₉	C₂³	1	2	yes	—
48	C₄×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂×Q₈×C₁₉	—	2	4	no	—
50	C₂×Q₈×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	Q₁₆×C₁₉	—	4	8	no	—
54	C₂×C₈×C₁₉	—	2	4	no	—
55	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
57	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
58	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
59	C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄⋊C₄×C₁₉	—	2	4	no	—
62	C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₄⋊C₄×C₁₉	—	4	4	no	—
64	C₄⋊C₄×C₁₉	—	4	4	no	—
65	C₂²⋊C₄×C₁₉	—	4	4	no	—
66	C₄²×C₁₉	—	4	4	no	—
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	C₂×D₄	1	2	yes	—
69	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
70	#19668	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂³×C₁₉	#127	1	1	yes	characteristic
72	Q₈×C₁₉	—	4	8	no	—
73	Q₈×C₁₉	—	4	8	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	#127	1	2	yes	—
79	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
82	C₈×C₁₉	—	2	2	no	—
83	C₈×C₁₉	—	2	4	no	—
84	C₈×C₁₉	—	2	4	no	—
85	C₈×C₁₉	#135	1	4	yes	—
86	#3231	C₂×C₁₉	1	4	yes	—
87	#3170	C₂×C₁₉	1	2	yes	—
88	#1718	C₂×C₁₉	1	4	yes	complemented
89	#1713	C₂×C₁₉	1	1	yes	characteristic, complemented
90	#1710	C₂×C₁₉	1	1	yes	characteristic, complemented
91	#1707	C₂×C₁₉	1	2	yes	complemented
92	#1450	C₂×C₁₉	1	1	yes	characteristic
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	8	4	no	—
99	C₄×C₁₉	—	8	4	no	—
100	C₄×C₁₉	C₂×#135	1	2	yes	—
101	C₄×C₁₉	#578	1	4	yes	—
102	#533	C₂²×C₁₉	1	4	yes	—
103	#500	C₂²×C₁₉	1	2	yes	—
104	#500	C₂²×C₁₉	1	4	yes	—
105	#498	C₂²×C₁₉	1	4	yes	—
106	#494	C₂²×C₁₉	1	2	yes	—
107	#487	C₂²×C₁₉	1	4	yes	—
108	#487	C₂²×C₁₉	1	4	yes	—
109	#487	C₂²×C₁₉	1	4	yes	—
110	#485	—	2	8	no	—
111	#479	—	2	8	no	—
112	#467	—	2	4	no	—
113	C₄×Q₁₆	—	2	4	no	—
114	#431	C₂²×C₁₉	1	2	yes	—
115	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
116	#322	C₂²×C₁₉	1	2	yes	—
117	C₈²	C₂²×C₁₉	1	1	yes	characteristic
118	C₈²	C₂²×C₁₉	1	1	yes	characteristic
119	C₂×C₁₉	—	4	1	no	—
120	C₂×C₁₉	#3147	1	1	yes	characteristic
121	C₂×C₁₉	#3156	1	2	yes	—
122	C₂×Q₁₆	—	2	4	no	—
123	C₂²×C₈	D₄×C₁₉	1	2	yes	—
124	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
125	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
126	#125	—	2	4	no	—
127	C₂²⋊Q₈	—	2	4	no	—
128	C₂²⋊Q₈	—	2	4	no	—
129	C₄×Q₈	—	2	4	no	—
130	C₄×Q₈	—	2	4	no	—
131	#117	—	2	4	no	—
132	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
133	#107	—	2	4	no	—
134	#107	—	2	8	no	—
135	#106	—	2	8	no	—
136	C₄⋊C₈	D₄×C₁₉	1	4	yes	—
137	#103	—	2	8	no	—
138	#103	—	2	8	no	—
139	#103	—	2	8	no	—
140	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
141	C₄×C₈	D₄×C₁₉	1	2	yes	—
142	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
143	C₄×C₈	C₂³×C₁₉	1	2	yes	—
144	C₄×C₈	C₂³×C₁₉	1	2	yes	—
145	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
146	C₁₉	#19668	1	1	yes	characteristic, direct product factor, Sylow
147	C₂×Q₈	—	2	4	no	—
148	C₂×Q₈	—	2	4	no	—
149	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
150	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
151	Q₁₆	—	4	8	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
154	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
155	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
156	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
157	C₄⋊C₄	—	2	4	no	—
158	C₄⋊C₄	—	2	4	no	—
159	C₄⋊C₄	—	2	4	no	—
160	C₄⋊C₄	—	2	4	no	—
161	C₄⋊C₄	—	4	4	no	—
162	C₄⋊C₄	—	4	4	no	—
163	C₂²⋊C₄	—	4	4	no	—
164	C₄²	—	4	4	no	—
165	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
166	C₄²	C₂×D₄×C₁₉	1	2	yes	—
167	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
168	C₂³	C₁₉×#127	1	1	yes	characteristic
169	Q₈	—	4	8	no	—
170	Q₈	—	4	8	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	C₁₉×#127	1	2	yes	—
176	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
177	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
178	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
179	C₈	—	2	2	no	—
180	C₈	—	2	4	no	—
181	C₈	—	2	4	no	—
182	C₈	C₁₉×#135	1	4	yes	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	2	no	—
185	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
186	C₄	—	2	1	no	—
187	C₄	—	2	2	no	—
188	C₄	—	8	4	no	—
189	C₄	—	8	4	no	—
190	C₄	C₂×C₁₉×#135	1	2	yes	—
191	C₄	C₁₉×#578	1	4	yes	—
192	C₂	—	4	1	no	—
193	C₂	C₁₉×#3147	1	1	yes	characteristic
194	C₂	C₁₉×#3156	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#127
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1718	C₂	semidirect
4. C₁₉×#1713	C₂	semidirect
5. C₁₉×#1710	C₂	semidirect
6. C₁₉×#1707	C₂	semidirect
70. #19668	C₁₉	direct (N × H)
88. #1718	C₂×C₁₉	semidirect
89. #1713	C₂×C₁₉	semidirect
90. #1710	C₂×C₁₉	semidirect
91. #1707	C₂×C₁₉	semidirect
146. C₁₉	#19668	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×#3231	2
C₁₉×#3170	2
C₁₉×#1718	2
C₁₉×#1713	2
C₁₉×#1710	2
C₁₉×#1707	2
C₁₉×#1450	2
#19668	19

Subgroups — C19×#19668 #18025627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19668 #18025627