Subgroups — C₄×C₁₉⋊#338 #18087706

Order 4864.

858 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64520	C₂	1	2	yes	maximal
2	C₂×C₁₉⋊#338	C₂	1	4	yes	maximal
3	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₂²	1	4	yes	—
5	C₄×#64520	—	2	4	no	—
6	C₄×#64520	—	2	4	no	—
7	C₂×#10597260	C₄	1	4	yes	—
8	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	—
9	C₁₉⋊#338	C₄	1	16	yes	direct product factor
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×M₁₆×C₁₉	—	2	4	no	—
13	C₂×C₁₉×#97	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
15	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
16	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	—	2	4	no	—
18	C₂×M₁₆×C₁₉	—	2	4	no	—
19	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	D₄	1	4	yes	—
27	C₂×#64520	—	2	4	no	—
28	C₂×#64520	—	2	4	no	—
29	C₂×#64520	—	2	8	no	—
30	C₂×#64520	C₂×C₄	1	16	yes	—
31	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
32	C₁₉×#97	—	2	4	no	—
33	C₄×C₈×C₁₉	—	2	4	no	—
34	#10597260	—	2	8	no	—
35	C₄×C₁₉⋊C₈	—	2	8	no	—
36	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	—	4	4	no	—
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
39	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂²×C₄×C₁₉	#41	1	4	yes	—
48	M₁₆×C₁₉	—	2	16	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	C₄²	1	8	yes	—
52	C₄²×C₁₉	C₄²	1	2	yes	—
53	C₄²×C₁₉	C₄²	1	1	yes	characteristic
54	C₄²×C₁₉	C₄²	1	1	yes	characteristic
55	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
57	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
59	#64520	—	2	16	no	—
60	#64520	—	2	16	no	—
61	C₂×C₁₉⋊C₈	—	2	8	no	—
62	C₂×C₁₉⋊C₈	—	2	8	no	—
63	C₂×C₁₉⋊C₈	C₄²	1	16	yes	—
64	C₄×#338	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	—	4	2	no	—
66	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
67	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
69	C₂×C₄×C₁₉	—	2	8	no	—
70	C₂×C₄×C₁₉	—	2	4	no	—
71	C₂×C₄×C₁₉	—	4	4	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	#95	1	4	yes	—
74	C₂×C₄×C₁₉	#95	1	2	yes	—
75	C₂×C₄×C₁₉	#95	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
77	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
79	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
81	C₂×C₄×C₁₉	#117	1	4	yes	—
82	C₂×C₄×C₁₉	#117	1	2	yes	—
83	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
84	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
85	C₈×C₁₉	—	2	8	no	—
86	C₁₉⋊C₈	—	2	16	no	—
87	C₂×C₄×M₁₆	—	19	2	no	—
88	C₂×C₄×M₁₆	D₁₉	1	1	yes	characteristic
89	C₂×#338	—	19	4	no	—
90	C₂²×C₁₉	—	2	4	no	—
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	—	4	4	no	—
93	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
94	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
95	C₂²×C₁₉	C₄×C₄⋊C₄	1	4	yes	—
96	C₄×C₁₉	—	2	4	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	#338	1	4	yes	complemented
99	C₄×C₁₉	C₄³	1	1	yes	characteristic
100	C₄×C₁₉	#376	1	1	yes	characteristic
101	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
102	C₄×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
103	C₂²×M₁₆	—	19	4	no	—
104	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
105	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
106	C₄×M₁₆	—	2	4	no	—
107	C₄×M₁₆	—	38	4	no	—
108	C₄×M₁₆	—	38	4	no	—
109	C₂×#97	—	19	4	no	—
110	C₂×#97	Dic₁₉	1	2	yes	—
111	C₂×C₄×C₈	—	19	4	no	—
112	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
113	#338	—	19	16	no	—
114	C₂×C₁₉	—	2	2	no	—
115	C₂×C₁₉	—	2	4	no	—
116	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
117	C₂×C₁₉	C₂×#338	1	2	yes	—
118	C₂³×C₄	Dic₃₈	1	2	yes	—
119	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₂×M₁₆	—	2	4	no	—
121	C₂×M₁₆	—	2	4	no	—
122	C₂×M₁₆	—	19	16	no	—
123	C₂×M₁₆	—	38	4	no	—
124	C₂×M₁₆	—	38	8	no	—
125	C₂×M₁₆	—	38	4	no	—
126	C₂×M₁₆	C₄×D₁₉	1	8	yes	—
127	C₂²×C₈	—	19	8	no	—
128	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
129	C₂×C₄²	C₄×D₁₉	1	2	yes	—
130	C₂×C₄²	C₄×D₁₉	1	2	yes	—
131	C₂×C₄²	D₇₆	1	2	yes	—
132	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
135	#97	—	2	4	no	—
136	#97	—	38	8	no	—
137	C₄×C₈	—	2	4	no	—
138	C₄×C₈	—	38	8	no	—
139	C₁₉	C₄×#338	1	1	yes	characteristic, complemented, Sylow
140	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
141	C₂²×C₄	—	4	4	no	—
142	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
143	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
144	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
145	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
146	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
147	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
148	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
149	C₂²×C₄	#64541	1	4	yes	—
150	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
152	M₁₆	—	2	16	no	—
153	M₁₆	—	38	16	no	—
154	M₁₆	—	38	16	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	19	16	no	—
158	C₂×C₈	—	38	8	no	—
159	C₂×C₈	—	38	8	no	—
160	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
161	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
162	C₄²	C₄×Dic₁₉	1	2	yes	—
163	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
164	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
165	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
166	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
167	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
168	C₂³	—	4	2	no	—
169	C₂³	C₄×Dic₃₈	1	4	yes	—
170	C₂³	C₂×Dic₁₉⋊C₄	1	2	yes	—
171	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
172	C₂×C₄	—	2	8	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	C₁₉⋊#95	1	4	yes	—
177	C₂×C₄	C₁₉⋊#95	1	2	yes	—
178	C₂×C₄	C₁₉⋊#95	1	2	yes	—
179	C₂×C₄	C₄²×D₁₉	1	4	yes	—
180	C₂×C₄	#10597318	1	4	yes	—
181	C₂×C₄	C₄×D₇₆	1	4	yes	—
182	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
184	C₂×C₄	#10597372	1	2	yes	—
185	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
186	C₂×C₄	C₄×C₂²⋊D₁₉	1	8	yes	—
187	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
188	C₈	—	2	8	no	—
189	C₈	—	38	16	no	—
190	C₂²	—	2	4	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	4	4	no	—
193	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
194	C₂²	C₄×C₄⋊Dic₁₉	1	2	yes	—
195	C₂²	C₄×Dic₁₉⋊C₄	1	4	yes	—
196	C₄	—	2	4	no	—
197	C₄	—	2	2	no	—
198	C₄	C₁₉⋊#338	1	4	yes	direct product factor
199	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
200	C₄	#11926390	1	1	yes	characteristic
201	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
202	C₄	C₄×(C₂×D₁₉)⋊C₄	1	4	yes	—
203	C₂	—	2	2	no	—
204	C₂	—	2	4	no	—
205	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
206	C₂	C₂×C₁₉⋊#338	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₁₉
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₉
hypocenter	C₁₉	C₄×#338
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
9. C₁₉⋊#338	C₄	direct (N × H)
98. C₄×C₁₉	#338	semidirect
139. C₁₉	C₄×#338	semidirect
198. C₄	C₁₉⋊#338	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#64520	2
C₂×C₁₉⋊#338	2
C₂×C₄×M₁₆×C₁₉	2
C₄×#338	19

Subgroups — C4×C19⋊#338 #18087706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉⋊#338 #18087706