Subgroups — D₁₉×#423 #14572187

Order 2432.

576 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₁₉	C₂	1	2	yes	maximal
2	C₂×C₄²×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926568	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926567	C₂	1	2	yes	maximal, complemented
5	#11926566	C₂	1	4	yes	maximal, complemented
6	C₄⋊C₈×D₁₉	C₂	1	4	yes	maximal, complemented
7	C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₁₉	C₄	1	2	yes	—
9	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉	C₄	1	2	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	2	yes	—
15	M₁₆×D₁₉	—	2	8	no	—
16	C₂×#64515	C₂²	1	4	yes	—
17	C₂×C₈×D₁₉	C₂²	1	4	yes	—
18	C₄²×D₁₉	C₄	1	1	yes	characteristic
19	C₄²×D₁₉	C₄	1	1	yes	characteristic
20	C₄²×D₁₉	C₄	1	1	yes	characteristic
21	C₄²×D₁₉	C₄	1	1	yes	characteristic
22	C₄²×D₁₉	C₂²	1	2	yes	—
23	C₄²×D₁₉	C₂²	1	2	yes	—
24	C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
25	Dic₁₉⋊C₈	C₂²	1	8	yes	complemented
26	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	complemented
27	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
31	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₁₉	—	2	8	no	—
33	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
39	C₂×C₄×D₁₉	D₄	1	4	yes	—
40	C₂×C₄×D₁₉	Q₈	1	4	yes	—
41	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
42	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
43	M₁₆×C₁₉	—	2	4	no	—
44	C₂×C₈×C₁₉	C₂³	1	4	yes	—
45	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂³	1	2	yes	—
48	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
50	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
51	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
53	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
54	C₄×Dic₁₉	C₂³	1	2	yes	—
55	#64520	—	2	4	no	—
56	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
57	#64515	—	2	8	no	—
58	C₈×D₁₉	—	2	8	no	—
59	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×D₁₉	—	2	4	no	—
61	C₂²×D₁₉	C₄⋊C₄	1	4	yes	—
62	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	4	no	—
65	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
66	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
70	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂×Dic₁₉	—	2	4	no	—
72	C₂×Dic₁₉	C₄⋊C₄	1	4	yes	—
73	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
74	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
77	C₄×D₁₉	—	2	4	no	—
78	C₄×D₁₉	—	2	4	no	—
79	C₄×D₁₉	—	2	4	no	—
80	C₄×D₁₉	C₄⋊C₄	1	4	yes	—
81	C₄×D₁₉	C₄⋊C₄	1	4	yes	—
82	C₄×D₁₉	M₁₆	1	8	yes	complemented
83	C₄×D₁₉	C₂×D₄	1	2	yes	—
84	C₄×D₁₉	C₂×D₄	1	2	yes	—
85	C₄×D₁₉	C₂×Q₈	1	2	yes	—
86	C₄×D₁₉	C₂×Q₈	1	2	yes	—
87	C₈×C₁₉	—	2	4	no	—
88	C₁₉⋊C₈	—	2	4	no	—
89	C₂×#423	—	19	1	no	maximal, Sylow
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
92	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
93	C₂×D₁₉	—	2	2	no	—
94	C₂×D₁₉	—	2	8	no	—
95	C₂×D₁₉	C₂×C₄⋊C₄	1	2	yes	—
96	C₂×D₁₉	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×D₁₉	C₂×M₁₆	1	4	yes	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
100	C₄×C₁₉	C₂×M₁₆	1	4	yes	complemented
101	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
102	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
103	Dic₁₉	—	2	2	no	—
104	Dic₁₉	C₂×C₄⋊C₄	1	2	yes	—
105	Dic₁₉	C₂×C₄⋊C₄	1	2	yes	—
106	Dic₁₉	C₂×M₁₆	1	4	yes	complemented
107	C₂²×M₁₆	—	19	2	no	—
108	C₂²×C₄²	—	19	1	no	—
109	#423	—	19	2	no	—
110	#423	—	19	1	no	—
111	#423	—	19	4	no	—
112	#423	D₁₉	1	1	yes	characteristic, direct product factor
113	C₂×C₄⋊C₈	—	19	4	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₁₉	C₂²×M₁₆	1	2	yes	—
117	D₁₉	—	2	2	no	—
118	D₁₉	#423	1	4	yes	direct product factor
119	C₂³×C₄	—	19	1	no	—
120	C₂³×C₄	—	19	2	no	—
121	C₂×M₁₆	—	19	2	no	—
122	C₂×M₁₆	—	19	4	no	—
123	C₂×M₁₆	—	38	8	no	—
124	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
125	C₂²×C₈	—	19	4	no	—
126	C₂×C₄²	—	19	2	no	—
127	C₂×C₄²	—	19	1	no	—
128	C₂×C₄²	—	19	1	no	—
129	C₂×C₄²	—	19	1	no	—
130	C₂×C₄²	—	19	1	no	—
131	C₂×C₄²	—	19	1	no	—
132	C₂×C₄²	—	19	2	no	—
133	C₂×C₄²	—	19	2	no	—
134	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
135	C₄⋊C₈	—	19	8	no	—
136	C₄⋊C₈	—	19	4	no	—
137	C₄⋊C₈	C₂×D₁₉	1	4	yes	complemented
138	C₁₉	C₂×#423	1	1	yes	characteristic, complemented, Sylow
139	C₂⁴	—	19	1	no	—
140	C₂²×C₄	—	19	1	no	—
141	C₂²×C₄	—	19	1	no	—
142	C₂²×C₄	—	19	1	no	—
143	C₂²×C₄	—	19	2	no	—
144	C₂²×C₄	—	19	4	no	—
145	C₂²×C₄	—	19	4	no	—
146	C₂²×C₄	—	19	1	no	—
147	C₂²×C₄	—	19	1	no	—
148	C₂²×C₄	—	19	2	no	—
149	C₂²×C₄	—	19	2	no	—
150	C₂²×C₄	—	19	2	no	—
151	C₂²×C₄	—	19	2	no	—
152	C₂²×C₄	—	38	8	no	—
153	C₂²×C₄	C₄×D₁₉	1	2	yes	—
154	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
155	M₁₆	—	2	4	no	—
156	M₁₆	—	38	8	no	—
157	M₁₆	—	38	4	no	—
158	C₂×C₈	—	19	4	no	—
159	C₂×C₈	—	38	8	no	—
160	C₂×C₈	C₂²×D₁₉	1	4	yes	—
161	C₄²	—	19	2	no	—
162	C₄²	—	19	1	no	—
163	C₄²	—	19	2	no	—
164	C₄²	—	19	2	no	—
165	C₄²	—	19	2	no	—
166	C₄²	—	19	1	no	—
167	C₄²	—	19	2	no	—
168	C₄²	C₄×D₁₉	1	1	yes	characteristic
169	C₄²	C₄×D₁₉	1	1	yes	characteristic
170	C₄²	C₂²×D₁₉	1	2	yes	—
171	C₂³	—	19	1	no	—
172	C₂³	—	19	1	no	—
173	C₂³	—	19	4	no	—
174	C₂³	—	38	4	no	—
175	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	19	2	no	—
178	C₂×C₄	—	19	1	no	—
179	C₂×C₄	—	19	1	no	—
180	C₂×C₄	—	19	4	no	—
181	C₂×C₄	—	19	2	no	—
182	C₂×C₄	—	19	2	no	—
183	C₂×C₄	—	19	2	no	—
184	C₂×C₄	—	19	2	no	—
185	C₂×C₄	—	19	4	no	—
186	C₂×C₄	—	19	4	no	—
187	C₂×C₄	—	19	8	no	—
188	C₂×C₄	—	19	2	no	—
189	C₂×C₄	—	38	4	no	—
190	C₂×C₄	—	38	4	no	—
191	C₂×C₄	—	38	4	no	—
192	C₂×C₄	—	38	4	no	—
193	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
194	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
195	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
196	C₂×C₄	D₄×D₁₉	1	2	yes	—
197	C₂×C₄	Q₈×D₁₉	1	2	yes	—
198	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
199	C₈	—	2	4	no	—
200	C₈	—	38	4	no	—
201	C₂²	—	2	2	no	—
202	C₂²	—	19	4	no	—
203	C₂²	—	19	2	no	—
204	C₂²	—	19	2	no	—
205	C₂²	—	38	8	no	—
206	C₂²	—	38	2	no	—
207	C₂²	C₄⋊C₄×D₁₉	1	2	yes	—
208	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	—	19	4	no	—
211	C₄	—	19	2	no	—
212	C₄	—	19	2	no	—
213	C₄	—	38	2	no	—
214	C₄	C₄⋊C₄×D₁₉	1	2	yes	—
215	C₄	M₁₆×D₁₉	1	4	yes	complemented
216	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
217	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
218	C₂	—	2	2	no	—
219	C₂	—	19	4	no	—
220	C₂	—	38	2	no	—
221	C₂	C₂×C₄⋊C₄×D₁₉	1	1	yes	characteristic
222	C₂	C₂×M₁₆×D₁₉	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#423	C₂
prime radical	C₂³×D₁₉	C₂×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#423	D₁₉
hypocenter	C₁₉	C₂×#423
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
3. #11926568	C₂	semidirect
4. #11926567	C₂	semidirect
5. #11926566	C₂	semidirect
6. C₄⋊C₈×D₁₉	C₂	semidirect
7. C₁₉×#423	C₂	semidirect
24. C₁₉×C₄⋊C₈	C₂²	semidirect
25. Dic₁₉⋊C₈	C₂²	semidirect
26. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
82. C₄×D₁₉	M₁₆	semidirect
100. C₄×C₁₉	C₂×M₁₆	semidirect
106. Dic₁₉	C₂×M₁₆	semidirect
112. #423	D₁₉	direct (N × H)
118. D₁₉	#423	direct (N × H)
137. C₄⋊C₈	C₂×D₁₉	semidirect
138. C₁₉	C₂×#423	semidirect
215. C₄	M₁₆×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₁₉	2
C₂×C₄²×D₁₉	2
#11926568	2
#11926567	2
#11926566	2
C₄⋊C₈×D₁₉	2
C₁₉×#423	2
C₂×#423	19

Subgroups — D19×#423 #14572187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×#423 #14572187