Subgroups — C₁₉×#9662 #18015621

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1984	C₂	1	2	yes	maximal
3	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
8	C₄×Q₁₆×C₁₉	—	2	2	no	—
9	C₄×Q₁₆×C₁₉	—	2	2	no	—
10	C₂×C₁₉×#107	C₄	1	1	yes	characteristic
11	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₉×#103	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#336	—	2	4	no	—
17	C₁₉×#335	—	2	2	no	—
18	C₁₉×Q₈⋊C₈	—	2	4	no	—
19	C₁₉×#322	—	2	2	no	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×Q₁₆×C₁₉	—	2	4	no	—
22	C₂×Q₁₆×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	D₄	1	2	yes	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₄×Q₈×C₁₉	—	2	2	no	—
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₉	—	2	2	no	—
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	C₄×C₈×C₁₉	—	2	1	no	—
41	C₄×C₈×C₁₉	—	2	1	no	—
42	C₄×C₈×C₁₉	—	2	1	no	—
43	C₄×C₈×C₁₉	D₄	1	2	yes	—
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	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	Q₁₆×C₁₉	—	2	8	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	4	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₁₉	Q₁₆	1	4	yes	complemented
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₄⋊C₄×C₁₉	—	4	2	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	#41	1	1	yes	characteristic
79	#9662	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
81	Q₈×C₁₉	—	2	4	no	—
82	Q₈×C₁₉	—	2	4	no	—
83	Q₈×C₁₉	—	4	2	no	—
84	Q₈×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	4	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
98	C₂×C₄×C₁₉	#131	1	2	yes	—
99	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
100	C₂×C₄×C₁₉	#135	1	2	yes	—
101	C₈×C₁₉	—	2	2	no	—
102	C₈×C₁₉	—	2	2	no	—
103	C₈×C₁₉	—	2	4	no	—
104	C₈×C₁₉	—	4	2	no	—
105	C₈×C₁₉	—	8	2	no	—
106	C₂×C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
107	#1984	C₂×C₁₉	1	2	yes	—
108	C₂×#335	C₂×C₁₉	1	1	yes	characteristic
109	C₂×Q₈⋊C₈	C₂×C₁₉	1	2	yes	—
110	C₂×#322	C₂×C₁₉	1	1	yes	characteristic
111	C₂²×C₁₉	#390	1	1	yes	characteristic
112	C₂²×C₁₉	#435	1	2	yes	—
113	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
114	C₂²×C₁₉	#444	1	2	yes	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	4	4	no	—
118	C₄×C₁₉	—	8	2	no	—
119	C₄×C₁₉	#407	1	1	yes	characteristic
120	C₄×C₁₉	#408	1	1	yes	characteristic
121	C₄×C₁₉	#435	1	2	yes	—
122	C₄×C₁₉	#467	1	2	yes	—
123	C₄×C₁₉	#494	1	1	yes	characteristic
124	C₄×C₁₉	#495	1	1	yes	characteristic
125	C₂²×Q₁₆	C₄×C₁₉	1	1	yes	characteristic
126	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
127	C₄×Q₁₆	—	2	2	no	—
128	C₄×Q₁₆	—	2	2	no	—
129	C₂×#107	C₄×C₁₉	1	1	yes	characteristic
130	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
131	C₂×#103	C₄×C₁₉	1	2	yes	—
132	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
135	#336	—	2	4	no	—
136	#335	—	2	2	no	—
137	Q₈⋊C₈	—	2	4	no	—
138	#322	—	2	2	no	—
139	C₂×C₁₉	#1584	1	4	yes	—
140	C₂×C₁₉	#1955	1	1	yes	characteristic
141	C₂×C₁₉	#1969	1	1	yes	characteristic
142	C₂×C₁₉	#1975	1	1	yes	characteristic
143	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
144	C₂×Q₁₆	—	2	4	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	—	2	2	no	—
148	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
149	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
150	C₂²×C₈	D₄×C₁₉	1	2	yes	—
151	C₄×Q₈	—	2	2	no	—
152	C₄×Q₈	—	2	2	no	—
153	C₄×Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	2	no	—
156	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
157	C₂×C₄²	—	2	2	no	—
158	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
159	#107	—	2	2	no	—
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	2	2	no	—
162	#103	—	2	4	no	—
163	C₄×C₈	—	2	1	no	—
164	C₄×C₈	—	2	1	no	—
165	C₄×C₈	—	2	1	no	—
166	C₄×C₈	D₄×C₁₉	1	2	yes	—
167	C₄×C₈	D₄×C₁₉	1	2	yes	—
168	C₄×C₈	D₄×C₁₉	1	2	yes	—
169	C₁₉	#9662	1	1	yes	characteristic, direct product factor, Sylow
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	M₁₆×C₁₉	1	4	yes	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
180	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
181	Q₁₆	—	2	8	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	2	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	4	no	—
190	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
191	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
192	C₂×C₈	Q₁₆×C₁₉	1	4	yes	complemented
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄²	—	4	2	no	—
198	C₄²	—	4	2	no	—
199	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
200	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
201	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
202	C₄²	#41×C₁₉	1	1	yes	characteristic
203	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
204	Q₈	—	2	4	no	—
205	Q₈	—	2	4	no	—
206	Q₈	—	4	2	no	—
207	Q₈	—	4	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
215	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
216	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
217	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
218	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
219	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
220	C₂×C₄	C₂×M₁₆×C₁₉	1	2	yes	—
221	C₂×C₄	C₁₉×#131	1	2	yes	—
222	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
223	C₂×C₄	C₁₉×#135	1	2	yes	—
224	C₈	—	2	2	no	—
225	C₈	—	2	2	no	—
226	C₈	—	2	4	no	—
227	C₈	—	4	2	no	—
228	C₈	—	8	2	no	—
229	C₂²	C₁₉×#390	1	1	yes	characteristic
230	C₂²	C₁₉×#435	1	2	yes	—
231	C₂²	C₄×Q₁₆×C₁₉	1	2	yes	—
232	C₂²	C₁₉×#444	1	2	yes	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	4	no	—
236	C₄	—	8	2	no	—
237	C₄	C₁₉×#407	1	1	yes	characteristic
238	C₄	C₁₉×#408	1	1	yes	characteristic
239	C₄	C₁₉×#435	1	2	yes	—
240	C₄	C₁₉×#467	1	2	yes	—
241	C₄	C₁₉×#494	1	1	yes	characteristic
242	C₄	C₁₉×#495	1	1	yes	characteristic
243	C₂	C₁₉×#1584	1	4	yes	—
244	C₂	C₁₉×#1955	1	1	yes	characteristic
245	C₂	C₁₉×#1969	1	1	yes	characteristic
246	C₂	C₁₉×#1975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₄×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
68. C₂×C₈×C₁₉	Q₁₆	semidirect
79. #9662	C₁₉	direct (N × H)
169. C₁₉	#9662	direct (N × H)
192. C₂×C₈	Q₁₆×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₁₉	2
C₁₉×#1984	2
C₂×C₁₉×#335	2
C₂×C₁₉×Q₈⋊C₈	2
C₂×C₁₉×#322	2
#9662	19

Subgroups — C19×#9662 #18015621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9662 #18015621