Subgroups — C₁₉×#9836 #18015795

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1990	C₂	1	2	yes	maximal
3	C₁₉×#1956	C₂	1	2	yes	maximal
4	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₁₉×#500	—	2	2	no	—
8	C₁₉×#500	C₄	1	4	yes	complemented
9	C₂×C₁₉×#107	—	2	2	no	—
10	C₂×C₁₉×#106	—	2	2	no	—
11	C₂×C₁₉×#103	—	2	4	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#384	C₂²	1	2	yes	—
16	C₁₉×#340	—	2	4	no	—
17	C₁₉×#322	—	2	2	no	—
18	C₂²×Q₈×C₁₉	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×#107	—	2	8	no	—
33	C₁₉×#106	—	4	4	no	—
34	C₁₉×#103	—	4	8	no	—
35	C₄×C₈×C₁₉	—	2	1	no	—
36	C₄×C₈×C₁₉	—	2	1	no	—
37	C₄×C₈×C₁₉	—	2	1	no	—
38	C₄×C₈×C₁₉	—	2	1	no	—
39	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₂×Q₈×C₁₉	—	2	4	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	—	4	4	no	—
44	C₂×Q₈×C₁₉	—	4	4	no	—
45	C₂²×C₄×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	—	4	2	no	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	4	no	—
53	C₂×C₈×C₁₉	—	2	4	no	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
55	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
56	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
57	C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₄⋊C₄×C₁₉	—	4	4	no	—
62	C₄⋊C₄×C₁₉	—	4	4	no	—
63	C₄⋊C₄×C₁₉	—	4	4	no	—
64	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	#9836	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₉	#127	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	8	no	—
71	Q₈×C₁₉	—	8	4	no	—
72	C₂×C₄×C₁₉	—	4	4	no	—
73	C₂×C₄×C₁₉	—	8	2	no	—
74	C₂×C₄×C₁₉	—	8	2	no	—
75	C₂×C₄×C₁₉	—	8	2	no	—
76	C₂×C₄×C₁₉	—	8	2	no	—
77	C₂×C₄×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
87	C₂×C₄×C₁₉	#137	1	4	yes	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	—	4	2	no	—
90	C₈×C₁₉	#103	1	8	yes	complemented
91	C₂×#500	C₂×C₁₉	1	1	yes	characteristic
92	#1990	C₂×C₁₉	1	2	yes	—
93	#1956	C₂×C₁₉	1	2	yes	—
94	#1844	C₂×C₁₉	1	1	yes	characteristic
95	C₂×#322	C₂×C₁₉	1	1	yes	characteristic
96	C₂²×C₁₉	#390	1	1	yes	characteristic
97	C₂²×C₁₉	#492	1	1	yes	characteristic
98	C₂²×C₁₉	#494	1	1	yes	characteristic
99	C₂²×C₁₉	#496	1	2	yes	—
100	C₂²×C₁₉	#497	1	2	yes	—
101	C₄×C₁₉	—	8	4	no	—
102	C₄×C₁₉	—	16	2	no	—
103	C₄×C₁₉	C₂×#103	1	2	yes	—
104	C₄×C₁₉	#441	1	2	yes	—
105	C₄×C₁₉	#442	1	2	yes	—
106	C₄×C₁₉	#469	1	2	yes	—
107	C₄×C₁₉	#470	1	2	yes	—
108	C₄×C₁₉	#487	1	2	yes	—
109	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
110	#500	—	2	2	no	—
111	#500	C₄×C₁₉	1	4	yes	complemented
112	C₂×#107	—	2	2	no	—
113	C₂×#106	—	2	2	no	—
114	C₂×#103	—	2	4	no	—
115	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
116	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
118	#384	C₂²×C₁₉	1	2	yes	—
119	#340	—	2	4	no	—
120	#322	—	2	2	no	—
121	C₂×C₁₉	#1714	1	2	yes	—
122	C₂×C₁₉	#1723	1	2	yes	—
123	C₂×C₁₉	#1956	1	1	yes	characteristic
124	C₂×C₁₉	#1971	1	1	yes	characteristic
125	C₂×C₁₉	#1972	1	1	yes	characteristic
126	C₂²×Q₈	—	2	2	no	—
127	C₂²×C₈	D₄×C₁₉	1	2	yes	—
128	C₂²×C₈	D₄×C₁₉	1	2	yes	—
129	C₂²×C₈	D₄×C₁₉	1	2	yes	—
130	C₄⋊Q₈	—	2	2	no	—
131	C₄⋊Q₈	—	2	2	no	—
132	C₄⋊Q₈	—	2	2	no	—
133	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	2	2	no	—
139	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
140	#107	—	2	8	no	—
141	#106	—	4	4	no	—
142	#103	—	4	8	no	—
143	C₄×C₈	—	2	1	no	—
144	C₄×C₈	—	2	1	no	—
145	C₄×C₈	—	2	1	no	—
146	C₄×C₈	—	2	1	no	—
147	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
148	C₄×C₈	D₄×C₁₉	1	2	yes	—
149	C₁₉	#9836	1	1	yes	characteristic, direct product factor, Sylow
150	C₂×Q₈	—	2	4	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	4	4	no	—
153	C₂×Q₈	—	4	4	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	—	4	2	no	—
156	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
157	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
158	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
164	C₂×C₈	SD₁₆×C₁₉	1	4	yes	—
165	C₂×C₈	Q₁₆×C₁₉	1	4	yes	—
166	C₄⋊C₄	—	2	4	no	—
167	C₄⋊C₄	—	2	4	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	4	no	—
171	C₄⋊C₄	—	4	4	no	—
172	C₄⋊C₄	—	4	4	no	—
173	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
174	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
175	C₄²	#41×C₁₉	1	1	yes	characteristic
176	C₄²	#41×C₁₉	1	1	yes	characteristic
177	C₂³	C₁₉×#127	1	1	yes	characteristic
178	Q₈	—	4	8	no	—
179	Q₈	—	8	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	8	2	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	8	2	no	—
184	C₂×C₄	—	8	2	no	—
185	C₂×C₄	—	8	2	no	—
186	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
187	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
188	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
189	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
190	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
191	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
192	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
193	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
194	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
195	C₂×C₄	C₁₉×#137	1	4	yes	—
196	C₈	—	4	2	no	—
197	C₈	—	4	2	no	—
198	C₈	C₁₉×#103	1	8	yes	complemented
199	C₂²	C₁₉×#390	1	1	yes	characteristic
200	C₂²	C₁₉×#492	1	1	yes	characteristic
201	C₂²	C₁₉×#494	1	1	yes	characteristic
202	C₂²	C₁₉×#496	1	2	yes	—
203	C₂²	C₁₉×#497	1	2	yes	—
204	C₄	—	8	4	no	—
205	C₄	—	16	2	no	—
206	C₄	C₂×C₁₉×#103	1	2	yes	—
207	C₄	C₁₉×#441	1	2	yes	—
208	C₄	C₁₉×#442	1	2	yes	—
209	C₄	C₁₉×#469	1	2	yes	—
210	C₄	C₁₉×#470	1	2	yes	—
211	C₄	C₁₉×#487	1	2	yes	—
212	C₂	C₁₉×#1714	1	2	yes	—
213	C₂	C₁₉×#1723	1	2	yes	—
214	C₂	C₁₉×#1956	1	1	yes	characteristic
215	C₂	C₁₉×#1971	1	1	yes	characteristic
216	C₂	C₁₉×#1972	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
8. C₁₉×#500	C₄	semidirect
68. #9836	C₁₉	direct (N × H)
90. C₈×C₁₉	#103	semidirect
111. #500	C₄×C₁₉	semidirect
149. C₁₉	#9836	direct (N × H)
198. C₈	C₁₉×#103	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#500	2
C₁₉×#1990	2
C₁₉×#1956	2
C₁₉×#1844	2
C₂×C₁₉×#322	2
#9836	19

Subgroups — C19×#9836 #18015795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9836 #18015795