Subgroups — C₁₉×#3567 #14561424

Order 2432.

950 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#562	C₂	1	3	yes	maximal, complemented
3	C₁₉×#553	C₂	1	6	yes	maximal, complemented
4	C₁₉×#552	C₂	1	6	yes	maximal, complemented
5	C₁₉×#540	C₂	1	6	yes	maximal, complemented
6	C₁₉×#539	C₂	1	6	yes	maximal, complemented
7	C₁₉×#529	C₂	1	3	yes	maximal, complemented
8	C₁₉×#127	C₂²	1	2	yes	—
9	C₁₉×#126	C₂²	1	6	yes	—
10	C₁₉×#126	C₂²	1	2	yes	—
11	C₁₉×#126	C₂²	1	6	yes	—
12	C₁₉×#125	C₂²	1	3	yes	—
13	C₁₉×#125	C₂²	1	6	yes	—
14	C₁₉×#125	C₂²	1	6	yes	—
15	C₁₉×#125	C₂²	1	6	yes	—
16	C₁₉×#124	C₂²	1	3	yes	—
17	C₁₉×#123	C₂²	1	6	yes	—
18	C₁₉×#123	C₂²	1	6	yes	—
19	C₁₉×#123	C₂²	1	6	yes	—
20	C₁₉×#123	C₂²	1	6	yes	—
21	C₁₉×#123	C₂²	1	6	yes	—
22	C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
23	C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
24	C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
25	C₁₉×#121	C₂²	1	3	yes	—
26	C₁₉×#121	C₂²	1	6	yes	—
27	C₁₉×#121	C₂²	1	6	yes	—
28	C₁₉×#121	C₂²	1	6	yes	—
29	C₁₉×#121	C₂²	1	6	yes	—
30	C₄×Q₈×C₁₉	C₂²	1	3	yes	—
31	C₄×D₄×C₁₉	C₂²	1	6	yes	—
32	C₄×D₄×C₁₉	C₂²	1	3	yes	—
33	C₄×D₄×C₁₉	C₂²	1	6	yes	—
34	C₄×D₄×C₁₉	C₂²	1	6	yes	—
35	C₁₉×#117	C₂²	1	6	yes	—
36	C₁₉×#117	C₂²	1	6	yes	—
37	C₂×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
38	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
40	C₂×D₄×C₁₉	C₂³	1	6	yes	—
41	C₂×D₄×C₁₉	C₂³	1	3	yes	—
42	C₂×D₄×C₁₉	C₂³	1	6	yes	—
43	C₂×D₄×C₁₉	C₂³	1	6	yes	—
44	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
45	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
46	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
47	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
48	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
49	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
50	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
51	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
52	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
53	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
54	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
55	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
56	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
57	C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
58	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
59	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
60	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
61	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
62	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
63	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
64	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
65	C₄²×C₁₉	C₂³	1	3	yes	—
66	C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₄²×C₁₉	C₂³	1	2	yes	—
68	C₄²×C₁₉	C₂³	1	6	yes	—
69	C₄²×C₁₉	C₂³	1	2	yes	—
70	C₂³×C₁₉	C₂⁴	1	6	yes	—
71	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
72	Q₈×C₁₉	—	4	3	no	—
73	D₄×C₁₉	—	4	6	no	—
74	D₄×C₁₉	—	4	6	no	—
75	D₄×C₁₉	—	4	6	no	—
76	D₄×C₁₉	—	4	3	no	—
77	C₂×C₄×C₁₉	—	4	6	no	—
78	C₂×C₄×C₁₉	—	4	3	no	—
79	C₂×C₄×C₁₉	—	4	6	no	—
80	C₂×C₄×C₁₉	—	4	6	no	—
81	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
82	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
83	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
84	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
85	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
86	#3567	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂²×C₁₉	—	2	6	no	—
88	C₂²×C₁₉	—	2	6	no	—
89	C₂²×C₁₉	—	2	3	no	—
90	C₂²×C₁₉	—	2	6	no	—
91	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
92	C₄×C₁₉	—	2	3	no	—
93	C₄×C₁₉	—	2	6	no	—
94	C₄×C₁₉	—	2	6	no	—
95	C₄×C₁₉	—	2	6	no	—
96	C₄×C₁₉	—	2	3	no	—
97	#564	C₂×C₁₉	1	1	yes	characteristic, complemented
98	#562	C₂×C₁₉	1	3	yes	complemented
99	#553	C₂×C₁₉	1	6	yes	complemented
100	#552	C₂×C₁₉	1	6	yes	complemented
101	#540	C₂×C₁₉	1	6	yes	complemented
102	#539	C₂×C₁₉	1	6	yes	complemented
103	#529	C₂×C₁₉	1	3	yes	complemented
104	C₂×C₁₉	—	4	6	no	—
105	C₂×C₁₉	—	4	1	no	—
106	C₂×C₁₉	#585	1	3	yes	—
107	#127	C₂²×C₁₉	1	2	yes	—
108	#126	C₂²×C₁₉	1	6	yes	—
109	#126	C₂²×C₁₉	1	2	yes	—
110	#126	C₂²×C₁₉	1	6	yes	—
111	#125	C₂²×C₁₉	1	3	yes	—
112	#125	C₂²×C₁₉	1	6	yes	—
113	#125	C₂²×C₁₉	1	6	yes	—
114	#125	C₂²×C₁₉	1	6	yes	—
115	#124	C₂²×C₁₉	1	3	yes	—
116	#123	C₂²×C₁₉	1	6	yes	—
117	#123	C₂²×C₁₉	1	6	yes	—
118	#123	C₂²×C₁₉	1	6	yes	—
119	#123	C₂²×C₁₉	1	6	yes	—
120	#123	C₂²×C₁₉	1	6	yes	—
121	C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
122	C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
123	C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
124	#121	C₂²×C₁₉	1	3	yes	—
125	#121	C₂²×C₁₉	1	6	yes	—
126	#121	C₂²×C₁₉	1	6	yes	—
127	#121	C₂²×C₁₉	1	6	yes	—
128	#121	C₂²×C₁₉	1	6	yes	—
129	C₄×Q₈	C₂²×C₁₉	1	3	yes	—
130	C₄×D₄	C₂²×C₁₉	1	6	yes	—
131	C₄×D₄	C₂²×C₁₉	1	3	yes	—
132	C₄×D₄	C₂²×C₁₉	1	6	yes	—
133	C₄×D₄	C₂²×C₁₉	1	6	yes	—
134	#117	C₂²×C₁₉	1	6	yes	—
135	#117	C₂²×C₁₉	1	6	yes	—
136	C₂×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
137	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
138	C₁₉	#3567	1	1	yes	characteristic, direct product factor, Sylow
139	C₂×Q₈	C₂³×C₁₉	1	3	yes	—
140	C₂×D₄	C₂³×C₁₉	1	6	yes	—
141	C₂×D₄	C₂³×C₁₉	1	3	yes	—
142	C₂×D₄	C₂³×C₁₉	1	6	yes	—
143	C₂×D₄	C₂³×C₁₉	1	6	yes	—
144	C₂²×C₄	C₂³×C₁₉	1	3	yes	—
145	C₂²×C₄	C₂³×C₁₉	1	6	yes	—
146	C₂²×C₄	C₂³×C₁₉	1	6	yes	—
147	C₂²×C₄	C₂³×C₁₉	1	6	yes	—
148	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
149	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
150	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
151	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
152	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
153	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
154	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
155	C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
156	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
157	C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
158	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
159	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
160	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
161	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
162	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
163	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
164	C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
165	C₄²	C₂³×C₁₉	1	3	yes	—
166	C₄²	C₂³×C₁₉	1	1	yes	characteristic
167	C₄²	C₂³×C₁₉	1	2	yes	—
168	C₄²	C₂³×C₁₉	1	6	yes	—
169	C₄²	C₂³×C₁₉	1	2	yes	—
170	C₂³	C₂⁴×C₁₉	1	6	yes	—
171	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
172	Q₈	—	4	3	no	—
173	D₄	—	4	6	no	—
174	D₄	—	4	6	no	—
175	D₄	—	4	6	no	—
176	D₄	—	4	3	no	—
177	C₂×C₄	—	4	6	no	—
178	C₂×C₄	—	4	3	no	—
179	C₂×C₄	—	4	6	no	—
180	C₂×C₄	—	4	6	no	—
181	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
182	C₂×C₄	C₂⁴×C₁₉	1	3	yes	—
183	C₂×C₄	C₂⁴×C₁₉	1	6	yes	—
184	C₂×C₄	C₂⁴×C₁₉	1	6	yes	—
185	C₂×C₄	C₂⁴×C₁₉	1	6	yes	—
186	C₂²	—	2	6	no	—
187	C₂²	—	2	6	no	—
188	C₂²	—	2	3	no	—
189	C₂²	—	2	6	no	—
190	C₂²	C₂⁵×C₁₉	1	1	yes	characteristic
191	C₄	—	2	3	no	—
192	C₄	—	2	6	no	—
193	C₄	—	2	6	no	—
194	C₄	—	2	6	no	—
195	C₄	—	2	3	no	—
196	C₂	—	4	6	no	—
197	C₂	—	4	1	no	—
198	C₂	C₁₉×#585	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#564	C₂	semidirect
2. C₁₉×#562	C₂	semidirect
3. C₁₉×#553	C₂	semidirect
4. C₁₉×#552	C₂	semidirect
5. C₁₉×#540	C₂	semidirect
6. C₁₉×#539	C₂	semidirect
7. C₁₉×#529	C₂	semidirect
86. #3567	C₁₉	direct (N × H)
97. #564	C₂×C₁₉	semidirect
98. #562	C₂×C₁₉	semidirect
99. #553	C₂×C₁₉	semidirect
100. #552	C₂×C₁₉	semidirect
101. #540	C₂×C₁₉	semidirect
102. #539	C₂×C₁₉	semidirect
103. #529	C₂×C₁₉	semidirect
138. C₁₉	#3567	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×#564	2
C₁₉×#562	2
C₁₉×#553	2
C₁₉×#552	2
C₁₉×#540	2
C₁₉×#539	2
C₁₉×#529	2
#3567	19

Subgroups — C19×#3567 #14561424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3567 #14561424