Subgroups — C₁₉×#2344 #14560201

Order 2432.

604 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#117	C₂	1	2	yes	maximal
2	C₂²×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#389	C₂	1	2	yes	maximal, complemented
4	C₁₉×#387	C₂	1	4	yes	maximal, complemented
5	C₁₉×#381	C₂	1	2	yes	maximal
6	C₁₉×#380	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
8	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#117	—	2	8	no	—
12	C₂×C₄⋊C₄×C₁₉	C₄	1	8	yes	complemented
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂²	1	4	yes	—
23	C₁₉×#95	C₂²	1	2	yes	—
24	C₁₉×#95	C₂²	1	4	yes	—
25	C₁₉×#95	C₂²	1	2	yes	—
26	C₁₉×#95	C₂²	1	4	yes	—
27	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	—	2	4	no	—
29	C₂²×C₄×C₁₉	—	2	4	no	—
30	C₂²×C₄×C₁₉	—	2	4	no	—
31	C₂²×C₄×C₁₉	C₂×C₄	1	8	yes	—
32	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
34	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₄⋊C₄×C₁₉	—	2	8	no	—
41	C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
43	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
44	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
45	C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
48	C₄²×C₁₉	—	2	8	no	—
49	C₄²×C₁₉	—	2	4	no	—
50	C₂³×C₁₉	—	2	2	no	—
51	C₂³×C₁₉	—	2	2	no	—
52	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
53	C₂³×C₁₉	C₂×D₄	1	2	yes	—
54	C₂³×C₁₉	#41	1	2	yes	—
55	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
56	C₂×C₄×C₁₉	—	2	16	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	8	no	—
65	C₂×C₄×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	4	no	—
69	C₂×C₄×C₁₉	—	2	4	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
73	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
74	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
75	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
76	C₂×C₄×C₁₉	#41	1	4	yes	—
77	#2344	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₁₉	—	2	2	no	—
79	C₂²×C₁₉	—	2	2	no	—
80	C₂²×C₁₉	—	2	4	no	—
81	C₂²×C₁₉	—	2	4	no	—
82	C₂²×C₁₉	C₄×D₄	1	4	yes	—
83	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
84	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×#41	1	2	yes	—
86	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
87	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	2	4	no	—
90	C₄×C₁₉	—	2	4	no	—
91	C₄×C₁₉	—	2	4	no	—
92	C₄×C₁₉	—	4	4	no	—
93	C₄×C₁₉	—	4	2	no	—
94	C₄×C₁₉	#117	1	4	yes	complemented
95	C₂×#117	C₂×C₁₉	1	2	yes	—
96	C₂²×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
97	#389	C₂×C₁₉	1	2	yes	complemented
98	#387	C₂×C₁₉	1	4	yes	complemented
99	#381	C₂×C₁₉	1	2	yes	—
100	#380	C₂×C₁₉	1	1	yes	characteristic
101	C₄×C₄⋊C₄	C₂×C₁₉	1	2	yes	complemented
102	C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
103	C₂×C₁₉	—	2	4	no	—
104	C₂×C₁₉	C₂×#117	1	1	yes	characteristic
105	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
106	C₂×C₁₉	#519	1	1	yes	characteristic
107	C₂×C₁₉	#547	1	2	yes	—
108	C₂×C₁₉	#552	1	2	yes	—
109	C₂³×C₄	C₂²×C₁₉	1	2	yes	—
110	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
111	#117	—	2	8	no	—
112	C₂×C₄⋊C₄	C₄×C₁₉	1	8	yes	complemented
113	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
114	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
116	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
117	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
118	C₂×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
119	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
120	C₂×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
121	C₂×C₄²	C₂²×C₁₉	1	4	yes	—
122	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
123	#95	C₂²×C₁₉	1	2	yes	—
124	#95	C₂²×C₁₉	1	4	yes	—
125	#95	C₂²×C₁₉	1	2	yes	—
126	#95	C₂²×C₁₉	1	4	yes	—
127	C₁₉	#2344	1	1	yes	characteristic, direct product factor, Sylow
128	C₂⁴	C₂³×C₁₉	1	1	yes	characteristic
129	C₂²×C₄	—	2	4	no	—
130	C₂²×C₄	—	2	4	no	—
131	C₂²×C₄	—	2	4	no	—
132	C₂²×C₄	C₂×C₄×C₁₉	1	8	yes	—
133	C₂²×C₄	C₂×C₄×C₁₉	1	4	yes	—
134	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
135	C₂²×C₄	C₂³×C₁₉	1	4	yes	—
136	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
137	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
138	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
139	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
140	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
141	C₄⋊C₄	—	2	8	no	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
144	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
145	C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
146	C₂²⋊C₄	—	2	4	no	—
147	C₂²⋊C₄	—	2	2	no	—
148	C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
149	C₄²	—	2	8	no	—
150	C₄²	—	2	4	no	—
151	C₂³	—	2	2	no	—
152	C₂³	—	2	2	no	—
153	C₂³	C₂²×C₄×C₁₉	1	2	yes	—
154	C₂³	C₂×D₄×C₁₉	1	2	yes	—
155	C₂³	#41×C₁₉	1	2	yes	—
156	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
157	C₂×C₄	—	2	16	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	8	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
173	C₂×C₄	C₂²×C₄×C₁₉	1	4	yes	—
174	C₂×C₄	C₂²×C₄×C₁₉	1	4	yes	—
175	C₂×C₄	C₂²×C₄×C₁₉	1	2	yes	—
176	C₂×C₄	C₂×D₄×C₁₉	1	4	yes	—
177	C₂×C₄	#41×C₁₉	1	4	yes	—
178	C₂²	—	2	2	no	—
179	C₂²	—	2	2	no	—
180	C₂²	—	2	4	no	—
181	C₂²	—	2	4	no	—
182	C₂²	C₄×D₄×C₁₉	1	4	yes	—
183	C₂²	C₂³×C₄×C₁₉	1	1	yes	characteristic
184	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
185	C₂²	C₂×#41×C₁₉	1	2	yes	—
186	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
187	C₂²	C₁₉×2₋¹⁺⁴	1	2	yes	—
188	C₄	—	2	2	no	—
189	C₄	—	2	4	no	—
190	C₄	—	2	4	no	—
191	C₄	—	2	4	no	—
192	C₄	—	4	4	no	—
193	C₄	—	4	2	no	—
194	C₄	C₁₉×#117	1	4	yes	complemented
195	C₂	—	2	4	no	—
196	C₂	C₂×C₁₉×#117	1	1	yes	characteristic
197	C₂	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
198	C₂	C₁₉×#519	1	1	yes	characteristic
199	C₂	C₁₉×#547	1	2	yes	—
200	C₂	C₁₉×#552	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#389	C₂	semidirect
4. C₁₉×#387	C₂	semidirect
7. C₄×C₄⋊C₄×C₁₉	C₂	semidirect
12. C₂×C₄⋊C₄×C₁₉	C₄	semidirect
77. #2344	C₁₉	direct (N × H)
94. C₄×C₁₉	#117	semidirect
97. #389	C₂×C₁₉	semidirect
98. #387	C₂×C₁₉	semidirect
101. C₄×C₄⋊C₄	C₂×C₁₉	semidirect
112. C₂×C₄⋊C₄	C₄×C₁₉	semidirect
127. C₁₉	#2344	direct (N × H)
194. C₄	C₁₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#117	2
C₂²×C₄⋊C₄×C₁₉	2
C₁₉×#389	2
C₁₉×#387	2
C₁₉×#381	2
C₁₉×#380	2
C₄×C₄⋊C₄×C₁₉	2
C₄×C₂²⋊C₄×C₁₉	2
#2344	19

Subgroups — C19×#2344 #14560201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2344 #14560201