Subgroups — C₂×C₁₉×#482 #14560944

Order 2432.

468 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#482	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄×C₁₉	—	2	1	no	—
10	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#121	—	2	2	no	—
15	C₁₉×#121	C₂²	1	4	yes	—
16	C₁₉×#117	—	2	2	no	—
17	C₁₉×#117	C₂²	1	4	yes	complemented
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	—	2	1	no	—
24	C₁₉×#107	C₂²	1	4	yes	complemented
25	C₁₉×#106	C₂²	1	4	yes	complemented
26	C₁₉×#102	C₂²	1	4	yes	complemented
27	C₁₉×#102	C₂²	1	4	yes	complemented
28	C₁₉×C₂²⋊C₈	C₂²	1	4	yes	complemented
29	C₂⁴×C₁₉	—	2	1	no	—
30	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
31	C₂×D₄×C₁₉	—	2	4	no	—
32	C₂×D₄×C₁₉	—	2	1	no	—
33	C₂×D₄×C₁₉	—	2	2	no	—
34	C₂×D₄×C₁₉	—	2	2	no	—
35	C₂×D₄×C₁₉	—	4	4	no	—
36	C₂×D₄×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	1	no	—
40	C₂²×C₄×C₁₉	—	2	1	no	—
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	D₄	1	2	yes	—
43	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂×C₈×C₁₉	C₂³	1	2	yes	—
50	C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂²⋊C₄×C₁₉	—	2	4	no	—
58	C₄²×C₁₉	—	2	4	no	—
59	C₂³×C₁₉	—	2	2	no	—
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	—	2	2	no	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	4	2	no	—
64	C₂³×C₁₉	—	4	2	no	—
65	C₂³×C₁₉	—	4	2	no	—
66	C₂³×C₁₉	C₂×D₄	1	2	yes	—
67	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
68	D₄×C₁₉	—	2	2	no	—
69	D₄×C₁₉	—	2	2	no	—
70	D₄×C₁₉	—	4	8	no	—
71	D₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	4	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#41	1	2	yes	—
85	C₂×C₄×C₁₉	#41	1	2	yes	—
86	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
87	C₈×C₁₉	—	2	2	no	—
88	C₈×C₁₉	—	2	2	no	—
89	C₂×#482	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	4	4	no	—
94	C₂²×C₁₉	—	4	2	no	—
95	C₂²×C₁₉	—	4	2	no	—
96	C₂²×C₁₉	—	4	2	no	—
97	C₂²×C₁₉	—	8	4	no	—
98	C₂²×C₁₉	#123	1	2	yes	—
99	C₂²×C₁₉	#135	1	2	yes	—
100	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
101	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	4	2	no	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	—	4	2	no	—
106	C₄×C₁₉	#123	1	2	yes	—
107	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
108	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
109	C₂×#121	C₂×C₁₉	1	1	yes	characteristic
110	C₂×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
111	#482	C₂×C₁₉	1	8	yes	direct product factor
112	C₂×#107	C₂×C₁₉	1	1	yes	characteristic, complemented
113	C₂×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
114	C₂×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
115	C₂×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
116	C₂×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
117	C₂×C₁₉	—	4	2	no	—
118	C₂×C₁₉	—	8	2	no	—
119	C₂×C₁₉	#482	1	4	yes	direct product factor
120	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
121	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
122	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
123	C₂²×D₄	—	2	1	no	—
124	C₂²×D₄	C₂²×C₁₉	1	1	yes	characteristic
125	C₂³×C₄	C₂²×C₁₉	1	1	yes	characteristic
126	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
127	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
128	#121	—	2	2	no	—
129	#121	C₂²×C₁₉	1	4	yes	—
130	#117	—	2	2	no	—
131	#117	C₂²×C₁₉	1	4	yes	complemented
132	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
133	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
134	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
135	C₂×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₄²	—	2	1	no	—
138	#107	C₂²×C₁₉	1	4	yes	complemented
139	#106	C₂²×C₁₉	1	4	yes	complemented
140	#102	C₂²×C₁₉	1	4	yes	complemented
141	#102	C₂²×C₁₉	1	4	yes	complemented
142	C₂²⋊C₈	C₂²×C₁₉	1	4	yes	complemented
143	C₁₉	C₂×#482	1	1	yes	characteristic, direct product factor, Sylow
144	C₂⁴	—	2	1	no	—
145	C₂⁴	D₄×C₁₉	1	1	yes	characteristic
146	C₂×D₄	—	2	4	no	—
147	C₂×D₄	—	2	1	no	—
148	C₂×D₄	—	2	2	no	—
149	C₂×D₄	—	2	2	no	—
150	C₂×D₄	—	4	4	no	—
151	C₂×D₄	C₂³×C₁₉	1	2	yes	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	1	no	—
155	C₂²×C₄	—	2	1	no	—
156	C₂²×C₄	—	2	1	no	—
157	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	D₄×C₁₉	1	2	yes	—
159	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
160	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	C₂³×C₁₉	1	2	yes	—
164	C₂×C₈	C₂³×C₁₉	1	2	yes	—
165	C₄⋊C₄	—	2	1	no	—
166	C₄⋊C₄	—	2	1	no	—
167	C₄⋊C₄	—	2	1	no	—
168	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
169	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
170	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
171	C₂²⋊C₄	—	2	4	no	—
172	C₂²⋊C₄	—	2	4	no	—
173	C₄²	—	2	4	no	—
174	C₂³	—	2	2	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	2	no	—
178	C₂³	—	4	2	no	—
179	C₂³	—	4	2	no	—
180	C₂³	—	4	2	no	—
181	C₂³	C₂×D₄×C₁₉	1	2	yes	—
182	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
183	D₄	—	2	2	no	—
184	D₄	—	2	2	no	—
185	D₄	—	4	8	no	—
186	D₄	—	4	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
198	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
199	C₂×C₄	#41×C₁₉	1	2	yes	—
200	C₂×C₄	#41×C₁₉	1	2	yes	—
201	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	2	2	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	2	2	no	—
206	C₂²	—	2	2	no	—
207	C₂²	—	4	4	no	—
208	C₂²	—	4	2	no	—
209	C₂²	—	4	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	8	4	no	—
212	C₂²	C₁₉×#123	1	2	yes	—
213	C₂²	C₁₉×#135	1	2	yes	—
214	C₂²	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
215	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	4	2	no	—
218	C₄	—	4	2	no	—
219	C₄	—	4	2	no	—
220	C₄	C₁₉×#123	1	2	yes	—
221	C₄	C₂×#41×C₁₉	1	1	yes	characteristic
222	C₄	C₂×#41×C₁₉	1	1	yes	characteristic
223	C₂	—	4	2	no	—
224	C₂	—	8	2	no	—
225	C₂	C₁₉×#482	1	4	yes	direct product factor
226	C₂	C₂×C₁₉×#123	1	1	yes	characteristic
227	C₂	C₂×C₁₉×#135	1	1	yes	characteristic
228	C₂	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#117	C₂	semidirect
3. C₁₉×#482	C₂	direct (N × H)
4. C₂×C₁₉×#107	C₂	semidirect
5. C₂×C₁₉×#106	C₂	semidirect
6. C₂×C₁₉×#102	C₂	semidirect
7. C₂×C₁₉×#102	C₂	semidirect
8. C₂×C₁₉×C₂²⋊C₈	C₂	semidirect
17. C₁₉×#117	C₂²	semidirect
24. C₁₉×#107	C₂²	semidirect
25. C₁₉×#106	C₂²	semidirect
26. C₁₉×#102	C₂²	semidirect
27. C₁₉×#102	C₂²	semidirect
28. C₁₉×C₂²⋊C₈	C₂²	semidirect
89. C₂×#482	C₁₉	direct (N × H)
110. C₂×#117	C₂×C₁₉	semidirect
111. #482	C₂×C₁₉	direct (N × H)
112. C₂×#107	C₂×C₁₉	semidirect
113. C₂×#106	C₂×C₁₉	semidirect
114. C₂×#102	C₂×C₁₉	semidirect
115. C₂×#102	C₂×C₁₉	semidirect
116. C₂×C₂²⋊C₈	C₂×C₁₉	semidirect
119. C₂×C₁₉	#482	direct (N × H)
131. #117	C₂²×C₁₉	semidirect
138. #107	C₂²×C₁₉	semidirect
139. #106	C₂²×C₁₉	semidirect
140. #102	C₂²×C₁₉	semidirect
141. #102	C₂²×C₁₉	semidirect
142. C₂²⋊C₈	C₂²×C₁₉	semidirect
143. C₁₉	C₂×#482	direct (N × H)
225. C₂	C₁₉×#482	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×C₁₉×#121	2
C₂×C₁₉×#117	2
C₁₉×#482	2
C₂×C₁₉×#107	2
C₂×C₁₉×#106	2
C₂×C₁₉×#102	2
C₂×C₁₉×C₂²⋊C₈	2
C₂×#482	19

Subgroups — C2×C19×#482 #14560944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#482 #14560944