Subgroups — C₁₉×#9850 #18015809

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1994	C₂	1	2	yes	maximal
3	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1566	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1493	C₂	1	2	yes	maximal
6	C₁₉×#533	C₂²	1	2	yes	—
7	C₁₉×#500	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#494	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#487	C₄	1	2	yes	complemented
10	C₁₉×#467	—	2	2	no	—
11	C₄×Q₁₆×C₁₉	—	2	2	no	—
12	C₁₉×#423	C₂²	1	2	yes	—
13	C₂×C₁₉×#97	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#339	—	2	4	no	—
18	C₁₉×#334	—	2	2	no	—
19	C₁₉×Q₈⋊C₈	—	2	4	no	—
20	C₂×Q₁₆×C₁₉	—	2	2	no	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	D₄	1	2	yes	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
26	C₁₉×#125	—	2	2	no	—
27	C₁₉×C₂²⋊Q₈	—	2	2	no	—
28	C₁₉×C₂²⋊Q₈	—	2	2	no	—
29	C₄×Q₈×C₁₉	—	2	2	no	—
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₁₉×#117	—	2	2	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₁₉×#107	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×#103	—	2	4	no	—
40	C₁₉×#97	—	2	8	no	—
41	C₄×C₈×C₁₉	—	2	1	no	—
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	2	yes	—
45	C₄×C₈×C₁₉	D₄	1	2	yes	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
52	Q₁₆×C₁₉	—	4	4	no	—
53	M₁₆×C₁₉	—	4	4	no	—
54	C₂×C₈×C₁₉	—	2	4	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	4	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	2	4	no	—
68	C₄²×C₁₉	—	2	4	no	—
69	C₄²×C₁₉	—	4	2	no	—
70	C₄²×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	#9850	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂³×C₁₉	#121	1	1	yes	characteristic
77	Q₈×C₁₉	—	4	4	no	—
78	Q₈×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	4	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#137	1	4	yes	—
93	C₈×C₁₉	—	2	4	no	—
94	C₈×C₁₉	—	2	2	no	—
95	C₈×C₁₉	—	8	2	no	—
96	C₈×C₁₉	#104	1	4	yes	—
97	#3170	C₂×C₁₉	1	1	yes	characteristic
98	#1994	C₂×C₁₉	1	2	yes	—
99	C₄×#97	C₂×C₁₉	1	1	yes	characteristic
100	#1566	C₂×C₁₉	1	1	yes	characteristic
101	#1493	C₂×C₁₉	1	2	yes	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	#390	1	1	yes	characteristic
105	C₂²×C₁₉	#470	1	2	yes	—
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	4	4	no	—
109	C₄×C₁₉	—	8	2	no	—
110	C₄×C₁₉	—	8	2	no	—
111	C₄×C₁₉	C₂×#104	1	2	yes	—
112	C₄×C₁₉	#441	1	2	yes	—
113	C₄×C₁₉	#444	1	2	yes	—
114	C₄×C₁₉	#497	1	2	yes	—
115	#533	C₂²×C₁₉	1	2	yes	—
116	#500	C₄×C₁₉	1	1	yes	characteristic, complemented
117	#494	C₄×C₁₉	1	1	yes	characteristic, complemented
118	#487	C₄×C₁₉	1	2	yes	complemented
119	#467	—	2	2	no	—
120	C₄×Q₁₆	—	2	2	no	—
121	#423	C₂²×C₁₉	1	2	yes	—
122	C₂×#97	—	2	2	no	—
123	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
125	C₄³	C₂²×C₁₉	1	1	yes	characteristic
126	#339	—	2	4	no	—
127	#334	—	2	2	no	—
128	Q₈⋊C₈	—	2	4	no	—
129	C₂×C₁₉	—	2	2	no	—
130	C₂×C₁₉	#1962	1	1	yes	characteristic
131	C₂×C₁₉	#1971	1	1	yes	characteristic
132	C₂×C₁₉	#1975	1	1	yes	characteristic
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	D₄×C₁₉	1	2	yes	—
137	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
138	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
139	#125	—	2	2	no	—
140	C₂²⋊Q₈	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	#117	—	2	2	no	—
145	C₂×C₄²	—	2	1	no	—
146	C₂×C₄²	—	2	1	no	—
147	C₂×C₄²	D₄×C₁₉	1	2	yes	—
148	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
149	#107	—	2	2	no	—
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	#103	—	2	4	no	—
153	#97	—	2	8	no	—
154	C₄×C₈	—	2	1	no	—
155	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
156	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
157	C₄×C₈	D₄×C₁₉	1	2	yes	—
158	C₄×C₈	D₄×C₁₉	1	2	yes	—
159	C₁₉	#9850	1	1	yes	characteristic, direct product factor, Sylow
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
164	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
165	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
166	Q₁₆	—	4	4	no	—
167	M₁₆	—	4	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
173	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₂²⋊C₄	—	4	2	no	—
181	C₄²	—	2	4	no	—
182	C₄²	—	2	4	no	—
183	C₄²	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
186	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
187	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
188	C₄²	#41×C₁₉	1	1	yes	characteristic
189	C₂³	C₁₉×#121	1	1	yes	characteristic
190	Q₈	—	4	4	no	—
191	Q₈	—	4	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
200	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
201	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
202	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
203	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
204	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
205	C₂×C₄	C₁₉×#137	1	4	yes	—
206	C₈	—	2	4	no	—
207	C₈	—	2	2	no	—
208	C₈	—	8	2	no	—
209	C₈	C₁₉×#104	1	4	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	C₁₉×#390	1	1	yes	characteristic
213	C₂²	C₁₉×#470	1	2	yes	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	4	4	no	—
217	C₄	—	8	2	no	—
218	C₄	—	8	2	no	—
219	C₄	C₂×C₁₉×#104	1	2	yes	—
220	C₄	C₁₉×#441	1	2	yes	—
221	C₄	C₁₉×#444	1	2	yes	—
222	C₄	C₁₉×#497	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	C₁₉×#1962	1	1	yes	characteristic
225	C₂	C₁₉×#1971	1	1	yes	characteristic
226	C₂	C₁₉×#1975	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₉×#500	C₄	semidirect
8. C₁₉×#494	C₄	semidirect
9. C₁₉×#487	C₄	semidirect
75. #9850	C₁₉	direct (N × H)
116. #500	C₄×C₁₉	semidirect
117. #494	C₄×C₁₉	semidirect
118. #487	C₄×C₁₉	semidirect
159. C₁₉	#9850	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×#3170	2
C₁₉×#1994	2
C₄×C₁₉×#97	2
C₁₉×#1566	2
C₁₉×#1493	2
#9850	19

Subgroups — C19×#9850 #18015809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9850 #18015809