Subgroups — C₁₉×#13108 #18019067

Order 4864.

246 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×#2153	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2110	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1773	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1378	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1378	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1377	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1375	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#108	C₄	1	1	yes	characteristic
13	C₁₉×#427	C₄	1	1	yes	characteristic
14	C₁₉×#405	C₂²	1	1	yes	characteristic
15	C₁₉×#405	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
17	C₁₉×#364	—	2	2	no	—
18	C₁₉×#347	—	2	2	no	—
19	C₁₉×#339	C₄	1	1	yes	characteristic
20	C₁₉×#339	C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
26	C₁₉×#117	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₉×M₃₂	—	2	1	no	—
29	C₁₉×M₃₂	—	2	1	no	—
30	C₁₉×M₃₂	—	2	1	no	—
31	C₁₉×M₃₂	—	2	1	no	—
32	C₁₉×M₃₂	—	2	1	no	—
33	C₁₉×M₃₂	—	2	1	no	—
34	C₁₉×M₃₂	—	2	1	no	—
35	C₁₉×M₃₂	D₄	1	2	yes	—
36	C₂×C₁₆×C₁₉	—	2	1	no	—
37	C₂×C₁₆×C₁₉	—	2	1	no	—
38	C₂×C₁₆×C₁₉	—	2	1	no	—
39	C₂×C₁₆×C₁₉	Q₈	1	2	yes	—
40	C₁₉×#108	—	2	2	no	—
41	C₁₉×#107	—	2	1	no	—
42	C₁₉×#106	—	2	1	no	—
43	C₁₉×#97	—	2	1	no	—
44	C₁₉×#97	—	2	1	no	—
45	C₁₉×#97	—	2	1	no	—
46	C₁₉×#97	—	2	1	no	—
47	C₄×C₈×C₁₉	—	2	1	no	—
48	C₄×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	M₁₆×C₁₉	—	2	1	no	—
52	M₁₆×C₁₉	—	2	1	no	—
53	M₁₆×C₁₉	—	2	1	no	—
54	M₁₆×C₁₉	M₁₆	1	2	yes	—
55	C₂×C₈×C₁₉	—	2	1	no	—
56	C₂×C₈×C₁₉	—	2	1	no	—
57	C₂×C₈×C₁₉	—	2	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
60	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
61	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
64	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
65	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
66	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
67	C₄⋊C₄×C₁₉	—	2	1	no	—
68	C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₄²×C₁₉	—	2	1	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	—	2	1	no	—
74	C₄²×C₁₉	—	2	1	no	—
75	C₁₆×C₁₉	—	2	2	no	—
76	C₁₆×C₁₉	—	2	2	no	—
77	C₁₆×C₁₉	—	4	1	no	—
78	C₁₆×C₁₉	—	4	1	no	—
79	#13108	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂³×C₁₉	#131	1	1	yes	characteristic
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	8	1	no	—
85	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
91	C₈×C₁₉	—	2	1	no	—
92	C₈×C₁₉	—	2	1	no	—
93	C₈×C₁₉	—	2	2	no	—
94	C₈×C₁₉	—	4	1	no	—
95	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
96	C₈×C₁₉	#123	1	1	yes	characteristic
97	C₈×C₁₉	#125	1	1	yes	characteristic
98	C₈×C₁₉	#126	1	1	yes	characteristic
99	#2153	C₂×C₁₉	1	1	yes	characteristic
100	#2110	C₂×C₁₉	1	1	yes	characteristic
101	#1773	C₂×C₁₉	1	1	yes	characteristic
102	#1378	C₂×C₁₉	1	1	yes	characteristic
103	#1378	C₂×C₁₉	1	1	yes	characteristic
104	#1377	C₂×C₁₉	1	1	yes	characteristic
105	#1375	C₂×C₁₉	1	1	yes	characteristic
106	C₂²×C₁₉	—	4	1	no	—
107	C₂²×C₁₉	#433	1	1	yes	characteristic
108	C₂²×C₁₉	#436	1	1	yes	characteristic
109	C₂²×C₁₉	#446	1	1	yes	characteristic
110	C₄×C₁₉	—	8	1	no	—
111	C₄×C₁₉	—	8	1	no	—
112	C₄×C₁₉	—	8	1	no	—
113	C₄×C₁₉	#387	1	1	yes	characteristic
114	C₄×C₁₉	#432	1	1	yes	characteristic
115	C₄×C₁₉	#435	1	1	yes	characteristic
116	C₄×C₁₉	#446	1	1	yes	characteristic
117	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
118	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
119	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
120	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
121	C₂×#108	C₄×C₁₉	1	1	yes	characteristic
122	#427	C₄×C₁₉	1	1	yes	characteristic
123	#405	C₂²×C₁₉	1	1	yes	characteristic
124	#405	C₂²×C₁₉	1	1	yes	characteristic
125	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
126	#364	—	2	2	no	—
127	#347	—	2	2	no	—
128	#339	C₄×C₁₉	1	1	yes	characteristic
129	#339	C₄×C₁₉	1	1	yes	characteristic
130	C₂×C₁₉	—	2	1	no	—
131	C₂×C₁₉	—	2	1	no	—
132	C₂×C₁₉	—	2	1	no	—
133	C₂×C₁₉	#1917	1	1	yes	characteristic
134	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
135	C₂×M₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
136	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
137	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
138	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
139	#117	C₂×C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
141	M₃₂	—	2	1	no	—
142	M₃₂	—	2	1	no	—
143	M₃₂	—	2	1	no	—
144	M₃₂	—	2	1	no	—
145	M₃₂	—	2	1	no	—
146	M₃₂	—	2	1	no	—
147	M₃₂	—	2	1	no	—
148	M₃₂	D₄×C₁₉	1	2	yes	—
149	C₂×C₁₆	—	2	1	no	—
150	C₂×C₁₆	—	2	1	no	—
151	C₂×C₁₆	—	2	1	no	—
152	C₂×C₁₆	Q₈×C₁₉	1	2	yes	—
153	#108	—	2	2	no	—
154	#107	—	2	1	no	—
155	#106	—	2	1	no	—
156	#97	—	2	1	no	—
157	#97	—	2	1	no	—
158	#97	—	2	1	no	—
159	#97	—	2	1	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	—	2	1	no	—
162	C₁₉	#13108	1	1	yes	characteristic, direct product factor, Sylow
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
165	M₁₆	—	2	1	no	—
166	M₁₆	—	2	1	no	—
167	M₁₆	—	2	1	no	—
168	M₁₆	M₁₆×C₁₉	1	2	yes	—
169	C₂×C₈	—	2	1	no	—
170	C₂×C₈	—	2	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
174	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
175	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
176	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
177	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
178	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
179	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
180	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₂²⋊C₄	—	2	1	no	—
184	C₂²⋊C₄	—	2	1	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₁₆	—	2	2	no	—
190	C₁₆	—	2	2	no	—
191	C₁₆	—	4	1	no	—
192	C₁₆	—	4	1	no	—
193	C₂³	C₁₉×#131	1	1	yes	characteristic
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
199	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
200	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
201	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
202	C₂×C₄	C₂×M₁₆×C₁₉	1	1	yes	characteristic
203	C₂×C₄	C₁₉×#131	1	1	yes	characteristic
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	2	2	no	—
207	C₈	—	4	1	no	—
208	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
209	C₈	C₁₉×#123	1	1	yes	characteristic
210	C₈	C₁₉×#125	1	1	yes	characteristic
211	C₈	C₁₉×#126	1	1	yes	characteristic
212	C₂²	—	4	1	no	—
213	C₂²	C₁₉×#433	1	1	yes	characteristic
214	C₂²	C₁₉×#436	1	1	yes	characteristic
215	C₂²	C₁₉×#446	1	1	yes	characteristic
216	C₄	—	8	1	no	—
217	C₄	—	8	1	no	—
218	C₄	—	8	1	no	—
219	C₄	C₁₉×#387	1	1	yes	characteristic
220	C₄	C₁₉×#432	1	1	yes	characteristic
221	C₄	C₁₉×#435	1	1	yes	characteristic
222	C₄	C₁₉×#446	1	1	yes	characteristic
223	C₂	—	2	1	no	—
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	C₁₉×#1917	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#387
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1917
prime radical	C₂³×C₁₉	#131
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
79. #13108	C₁₉	direct (N × H)
162. C₁₉	#13108	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×#2153	2
C₁₉×#2110	2
C₁₉×#1773	2
C₁₉×#1378	2
C₁₉×#1377	2
C₁₉×#1375	2
#13108	19

Subgroups — C19×#13108 #18019067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13108 #18019067