Subgroups — C₁₉×#13453 #18019412

Order 4864.

350 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#367	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#366	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1942	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1380	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1374	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#125	—	2	1	no	—
9	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#499	—	2	2	no	—
12	C₁₉×#499	—	2	2	no	—
13	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#106	—	2	1	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#389	—	2	1	no	—
20	C₁₉×#367	—	2	2	no	—
21	C₁₉×#366	—	2	2	no	—
22	C₁₉×#340	—	2	1	no	—
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₁₉×#125	—	2	4	no	—
26	C₁₉×#125	—	4	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₁₉	—	2	1	no	—
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	C₂×C₁₆×C₁₉	Q₈	1	2	yes	—
41	C₁₉×#107	—	2	1	no	—
42	C₁₉×#107	—	2	1	no	—
43	C₁₉×#107	—	2	1	no	—
44	C₁₉×#107	—	2	1	no	—
45	C₁₉×#107	—	2	1	no	—
46	C₁₉×#107	D₄	1	2	yes	—
47	C₁₉×#107	D₄	1	2	yes	—
48	C₁₉×#107	Q₈	1	2	yes	—
49	C₁₉×#106	—	2	4	no	—
50	C₄×C₈×C₁₉	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₁₉×#95	—	4	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₉	—	2	1	no	—
61	C₂×C₈×C₁₉	—	2	1	no	—
62	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
63	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	4	4	no	—
73	C₄⋊C₄×C₁₉	—	4	4	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	4	1	no	—
79	C₄⋊C₄×C₁₉	—	8	2	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	C₁₆×C₁₉	—	2	2	no	—
83	C₁₆×C₁₉	—	2	2	no	—
84	#13453	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	—	8	1	no	—
99	C₂×C₄×C₁₉	—	8	1	no	—
100	C₂×C₄×C₁₉	—	8	1	no	—
101	C₂×C₄×C₁₉	—	8	1	no	—
102	C₂×C₄×C₁₉	—	8	1	no	—
103	C₂×C₄×C₁₉	—	8	1	no	—
104	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
110	C₈×C₁₉	—	2	2	no	—
111	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
112	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
113	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
114	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
115	C₂×#499	C₂×C₁₉	1	1	yes	characteristic
116	C₂×#367	C₂×C₁₉	1	1	yes	characteristic
117	C₂×#366	C₂×C₁₉	1	1	yes	characteristic
118	#1942	C₂×C₁₉	1	1	yes	characteristic
119	#1380	C₂×C₁₉	1	1	yes	characteristic
120	#1380	C₂×C₁₉	1	1	yes	characteristic
121	#1374	C₂×C₁₉	1	1	yes	characteristic
122	C₂²×C₁₉	#447	1	1	yes	characteristic
123	C₂²×C₁₉	#474	1	1	yes	characteristic
124	C₂²×C₁₉	#500	1	1	yes	characteristic
125	C₂²×C₁₉	#508	1	1	yes	characteristic
126	C₂²×C₁₉	#508	1	1	yes	characteristic
127	C₂²×C₁₉	#509	1	1	yes	characteristic
128	C₂²×C₁₉	#510	1	1	yes	characteristic
129	C₄×C₁₉	—	4	1	no	—
130	C₄×C₁₉	—	4	1	no	—
131	C₄×C₁₉	—	8	2	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	—	16	1	no	—
135	C₄×C₁₉	#395	1	1	yes	characteristic
136	C₄×C₁₉	#451	1	1	yes	characteristic
137	C₄×C₁₉	#477	1	1	yes	characteristic
138	C₄×C₁₉	#501	1	1	yes	characteristic
139	C₂×#125	—	2	1	no	—
140	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
141	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
142	#499	—	2	2	no	—
143	#499	—	2	2	no	—
144	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
145	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
146	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
147	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
148	C₂×#106	—	2	1	no	—
149	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
150	#389	—	2	1	no	—
151	#367	—	2	2	no	—
152	#366	—	2	2	no	—
153	#340	—	2	1	no	—
154	C₂×C₁₉	#2057	1	1	yes	characteristic
155	C₂×C₁₉	#2186	1	1	yes	characteristic
156	C₂×C₁₉	#2189	1	1	yes	characteristic
157	C₂×C₁₉	#2228	1	1	yes	characteristic
158	C₂×C₁₉	#2229	1	1	yes	characteristic
159	C₂×C₁₉	#2253	1	1	yes	characteristic
160	C₂×C₁₉	#2255	1	1	yes	characteristic
161	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
162	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
163	#125	—	2	4	no	—
164	#125	—	4	2	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	—	2	1	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	4	1	no	—
170	C₂×C₄⋊C₄	—	4	1	no	—
171	C₂×C₄⋊C₄	—	4	1	no	—
172	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
173	C₂×C₁₆	—	2	1	no	—
174	C₂×C₁₆	—	2	1	no	—
175	C₂×C₁₆	—	2	1	no	—
176	C₂×C₁₆	—	2	1	no	—
177	C₂×C₁₆	Q₈×C₁₉	1	2	yes	—
178	C₂×C₁₆	Q₈×C₁₉	1	2	yes	—
179	#107	—	2	1	no	—
180	#107	—	2	1	no	—
181	#107	—	2	1	no	—
182	#107	—	2	1	no	—
183	#107	—	2	1	no	—
184	#107	D₄×C₁₉	1	2	yes	—
185	#107	D₄×C₁₉	1	2	yes	—
186	#107	Q₈×C₁₉	1	2	yes	—
187	#106	—	2	4	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	2	1	no	—
190	#95	—	4	1	no	—
191	C₁₉	#13453	1	1	yes	characteristic, direct product factor, Sylow
192	C₂²×C₄	—	4	1	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
197	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
198	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
199	C₂×C₈	—	2	1	no	—
200	C₂×C₈	—	2	1	no	—
201	C₂×C₈	Q₁₆×C₁₉	1	2	yes	—
202	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
203	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
204	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
205	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
206	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
207	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	—	2	2	no	—
211	C₄⋊C₄	—	4	4	no	—
212	C₄⋊C₄	—	4	4	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	1	no	—
215	C₄⋊C₄	—	4	1	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	8	2	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	2	1	no	—
221	C₁₆	—	2	2	no	—
222	C₁₆	—	2	2	no	—
223	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	8	1	no	—
234	C₂×C₄	—	8	1	no	—
235	C₂×C₄	—	8	1	no	—
236	C₂×C₄	—	8	1	no	—
237	C₂×C₄	—	8	1	no	—
238	C₂×C₄	—	8	1	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	—	8	1	no	—
241	C₂×C₄	—	8	1	no	—
242	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
243	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
245	C₂×C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
246	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
250	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
251	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
252	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
253	C₂²	C₁₉×#447	1	1	yes	characteristic
254	C₂²	C₁₉×#474	1	1	yes	characteristic
255	C₂²	C₁₉×#500	1	1	yes	characteristic
256	C₂²	C₁₉×#508	1	1	yes	characteristic
257	C₂²	C₁₉×#508	1	1	yes	characteristic
258	C₂²	C₁₉×#509	1	1	yes	characteristic
259	C₂²	C₁₉×#510	1	1	yes	characteristic
260	C₄	—	4	1	no	—
261	C₄	—	4	1	no	—
262	C₄	—	8	2	no	—
263	C₄	—	8	2	no	—
264	C₄	—	8	2	no	—
265	C₄	—	16	1	no	—
266	C₄	C₁₉×#395	1	1	yes	characteristic
267	C₄	C₁₉×#451	1	1	yes	characteristic
268	C₄	C₁₉×#477	1	1	yes	characteristic
269	C₄	C₁₉×#501	1	1	yes	characteristic
270	C₂	C₁₉×#2057	1	1	yes	characteristic
271	C₂	C₁₉×#2186	1	1	yes	characteristic
272	C₂	C₁₉×#2189	1	1	yes	characteristic
273	C₂	C₁₉×#2228	1	1	yes	characteristic
274	C₂	C₁₉×#2229	1	1	yes	characteristic
275	C₂	C₁₉×#2253	1	1	yes	characteristic
276	C₂	C₁₉×#2255	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
84. #13453	C₁₉	direct (N × H)
191. C₁₉	#13453	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×#499	2
C₂×C₁₉×#367	2
C₂×C₁₉×#366	2
C₁₉×#1942	2
C₁₉×#1380	2
C₁₉×#1374	2
#13453	19

Subgroups — C19×#13453 #18019412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13453 #18019412