Subgroups — C₁₉×#13143 #18019102

Order 4864.

338 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#365	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#360	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2139	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1975	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1776	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1387	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1375	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#135	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×#108	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#104	—	2	1	no	—
15	C₁₉×#408	—	2	1	no	—
16	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₁₉×#365	—	2	2	no	—
19	C₁₉×#360	—	2	2	no	—
20	C₁₉×#358	C₄	1	2	yes	complemented
21	C₁₉×#357	C₄	1	2	yes	complemented
22	C₁₉×#340	—	2	1	no	—
23	C₂×#41×C₁₉	—	2	1	no	—
24	C₁₉×#135	—	2	1	no	—
25	C₁₉×#135	—	2	1	no	—
26	C₁₉×#135	—	2	1	no	—
27	C₁₉×#135	—	2	1	no	—
28	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×SD₁₆×C₁₉	—	2	1	no	—
30	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	—	4	1	no	—
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₁₉×M₃₂	—	2	1	no	—
39	C₁₉×M₃₂	—	2	1	no	—
40	C₁₉×M₃₂	—	2	1	no	—
41	C₁₉×M₃₂	—	2	1	no	—
42	C₂×C₁₆×C₁₉	—	2	1	no	—
43	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	—
44	C₁₉×#108	—	2	1	no	—
45	C₁₉×#108	—	2	1	no	—
46	C₁₉×#107	—	2	1	no	—
47	C₁₉×#107	C₂×C₄	1	2	yes	—
48	C₁₉×#106	—	2	1	no	—
49	C₁₉×#106	D₄	1	2	yes	—
50	C₁₉×#104	—	4	2	no	—
51	C₁₉×C₂²⋊C₈	—	4	2	no	—
52	C₁₉×#97	—	2	1	no	—
53	C₁₉×#97	—	2	1	no	—
54	C₁₉×#95	—	4	1	no	—
55	#41×C₁₉	—	4	1	no	—
56	#41×C₁₉	—	4	1	no	—
57	#41×C₁₉	—	4	1	no	—
58	#41×C₁₉	—	4	1	no	—
59	C₂×Q₈×C₁₉	—	2	1	no	—
60	C₂×D₄×C₁₉	—	2	1	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	Q₁₆×C₁₉	—	2	1	no	—
68	Q₁₆×C₁₉	—	2	1	no	—
69	SD₁₆×C₁₉	—	4	1	no	—
70	SD₁₆×C₁₉	—	4	1	no	—
71	D₈×C₁₉	—	2	1	no	—
72	D₈×C₁₉	—	2	1	no	—
73	M₁₆×C₁₉	—	4	1	no	—
74	M₁₆×C₁₉	—	4	1	no	—
75	C₂×C₈×C₁₉	—	2	1	no	—
76	C₂×C₈×C₁₉	—	2	1	no	—
77	C₂×C₈×C₁₉	—	2	1	no	—
78	C₂×C₈×C₁₉	—	4	1	no	—
79	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
82	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
83	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
84	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	4	1	no	—
88	C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₄²×C₁₉	—	2	1	no	—
90	C₄²×C₁₉	—	8	2	no	—
91	C₄²×C₁₉	SD₁₆	1	2	yes	—
92	C₁₆×C₁₉	—	2	2	no	—
93	C₁₆×C₁₉	—	4	1	no	—
94	#13143	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂³×C₁₉	—	4	1	no	—
96	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
97	Q₈×C₁₉	—	4	1	no	—
98	Q₈×C₁₉	—	4	1	no	—
99	D₄×C₁₉	—	4	1	no	—
100	D₄×C₁₉	—	4	1	no	—
101	D₄×C₁₉	—	8	1	no	—
102	D₄×C₁₉	—	8	1	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	—	8	1	no	—
111	C₂×C₄×C₁₉	—	8	1	no	—
112	C₂×C₄×C₁₉	—	8	1	no	—
113	C₂×C₄×C₁₉	—	8	1	no	—
114	C₂×C₄×C₁₉	—	8	1	no	—
115	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
117	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
120	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
121	C₈×C₁₉	—	4	1	no	—
122	C₈×C₁₉	—	8	1	no	—
123	C₈×C₁₉	#117	1	1	yes	characteristic
124	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
125	C₈×C₁₉	#124	1	1	yes	characteristic
126	C₈×C₁₉	#126	1	1	yes	characteristic
127	C₂×#365	C₂×C₁₉	1	1	yes	characteristic, complemented
128	C₂×#360	C₂×C₁₉	1	1	yes	characteristic
129	#2139	C₂×C₁₉	1	1	yes	characteristic
130	#1975	C₂×C₁₉	1	1	yes	characteristic
131	#1776	C₂×C₁₉	1	1	yes	characteristic, complemented
132	#1387	C₂×C₁₉	1	1	yes	characteristic, complemented
133	#1375	C₂×C₁₉	1	1	yes	characteristic, complemented
134	C₂²×C₁₉	—	2	1	no	—
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	—	8	1	no	—
137	C₂²×C₁₉	—	8	1	no	—
138	C₂²×C₁₉	—	8	1	no	—
139	C₂²×C₁₉	#442	1	1	yes	characteristic
140	C₂²×C₁₉	#463	1	1	yes	characteristic
141	C₂²×C₁₉	#481	1	1	yes	characteristic
142	C₄×C₁₉	—	4	2	no	—
143	C₄×C₁₉	—	8	2	no	—
144	C₄×C₁₉	—	8	2	no	—
145	C₄×C₁₉	—	8	1	no	—
146	C₄×C₁₉	#388	1	1	yes	characteristic
147	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
148	C₄×C₁₉	#460	1	1	yes	characteristic
149	C₄×C₁₉	#482	1	1	yes	characteristic
150	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
151	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
152	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
153	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
154	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
155	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
156	C₂×#104	—	2	1	no	—
157	#408	—	2	1	no	—
158	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
159	C₄×C₄⋊C₄	—	2	1	no	—
160	#365	—	2	2	no	—
161	#360	—	2	2	no	—
162	#358	C₄×C₁₉	1	2	yes	complemented
163	#357	C₄×C₁₉	1	2	yes	complemented
164	#340	—	2	1	no	—
165	C₂×C₁₉	—	2	1	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	—	16	1	no	—
168	C₂×C₁₉	#1926	1	1	yes	characteristic
169	C₂×C₁₉	#2180	1	1	yes	characteristic
170	C₂×C₁₉	AGL(1,ℤ/16)	1	1	yes	characteristic
171	C₂×#41	—	2	1	no	—
172	#135	—	2	1	no	—
173	#135	—	2	1	no	—
174	#135	—	2	1	no	—
175	#135	—	2	1	no	—
176	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
177	C₂×SD₁₆	—	2	1	no	—
178	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
179	C₂×M₁₆	—	2	1	no	—
180	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
181	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₄²	—	4	1	no	—
185	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
186	M₃₂	—	2	1	no	—
187	M₃₂	—	2	1	no	—
188	M₃₂	—	2	1	no	—
189	M₃₂	—	2	1	no	—
190	C₂×C₁₆	—	2	1	no	—
191	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	—
192	#108	—	2	1	no	—
193	#108	—	2	1	no	—
194	#107	—	2	1	no	—
195	#107	C₂×C₄×C₁₉	1	2	yes	—
196	#106	—	2	1	no	—
197	#106	D₄×C₁₉	1	2	yes	—
198	#104	—	4	2	no	—
199	C₂²⋊C₈	—	4	2	no	—
200	#97	—	2	1	no	—
201	#97	—	2	1	no	—
202	#95	—	4	1	no	—
203	C₁₉	#13143	1	1	yes	characteristic, direct product factor, Sylow
204	#41	—	4	1	no	—
205	#41	—	4	1	no	—
206	#41	—	4	1	no	—
207	#41	—	4	1	no	—
208	C₂×Q₈	—	2	1	no	—
209	C₂×D₄	—	2	1	no	—
210	C₂×D₄	—	4	1	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	4	1	no	—
213	C₂²×C₄	—	4	1	no	—
214	C₂²×C₄	—	4	1	no	—
215	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
216	Q₁₆	—	2	1	no	—
217	Q₁₆	—	2	1	no	—
218	SD₁₆	—	4	1	no	—
219	SD₁₆	—	4	1	no	—
220	D₈	—	2	1	no	—
221	D₈	—	2	1	no	—
222	M₁₆	—	4	1	no	—
223	M₁₆	—	4	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	—	2	1	no	—
227	C₂×C₈	—	4	1	no	—
228	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
229	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
230	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
231	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
232	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
233	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	4	1	no	—
237	C₄⋊C₄	—	4	1	no	—
238	C₄²	—	2	1	no	—
239	C₄²	—	8	2	no	—
240	C₄²	SD₁₆×C₁₉	1	2	yes	—
241	C₁₆	—	2	2	no	—
242	C₁₆	—	4	1	no	—
243	C₂³	—	4	1	no	—
244	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
245	Q₈	—	4	1	no	—
246	Q₈	—	4	1	no	—
247	D₄	—	4	1	no	—
248	D₄	—	4	1	no	—
249	D₄	—	8	1	no	—
250	D₄	—	8	1	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	1	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	8	1	no	—
258	C₂×C₄	—	8	1	no	—
259	C₂×C₄	—	8	1	no	—
260	C₂×C₄	—	8	1	no	—
261	C₂×C₄	—	8	1	no	—
262	C₂×C₄	—	8	1	no	—
263	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
265	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
266	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
267	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
268	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₈	—	4	1	no	—
270	C₈	—	8	1	no	—
271	C₈	C₁₉×#117	1	1	yes	characteristic
272	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
273	C₈	C₁₉×#124	1	1	yes	characteristic
274	C₈	C₁₉×#126	1	1	yes	characteristic
275	C₂²	—	2	1	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	8	1	no	—
278	C₂²	—	8	1	no	—
279	C₂²	—	8	1	no	—
280	C₂²	C₁₉×#442	1	1	yes	characteristic
281	C₂²	C₁₉×#463	1	1	yes	characteristic
282	C₂²	C₁₉×#481	1	1	yes	characteristic
283	C₄	—	4	2	no	—
284	C₄	—	8	2	no	—
285	C₄	—	8	2	no	—
286	C₄	—	8	1	no	—
287	C₄	C₁₉×#388	1	1	yes	characteristic
288	C₄	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
289	C₄	C₁₉×#460	1	1	yes	characteristic
290	C₄	C₁₉×#482	1	1	yes	characteristic
291	C₂	—	2	1	no	—
292	C₂	—	2	1	no	—
293	C₂	—	16	1	no	—
294	C₂	C₁₉×#1926	1	1	yes	characteristic
295	C₂	C₁₉×#2180	1	1	yes	characteristic
296	C₂	C₁₉×AGL(1,ℤ/16)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#442
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×C₁₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#365	C₂	semidirect
5. C₁₉×#1776	C₂	semidirect
6. C₁₉×#1387	C₂	semidirect
7. C₁₉×#1375	C₂	semidirect
20. C₁₉×#358	C₄	semidirect
21. C₁₉×#357	C₄	semidirect
94. #13143	C₁₉	direct (N × H)
127. C₂×#365	C₂×C₁₉	semidirect
131. #1776	C₂×C₁₉	semidirect
132. #1387	C₂×C₁₉	semidirect
133. #1375	C₂×C₁₉	semidirect
162. #358	C₄×C₁₉	semidirect
163. #357	C₄×C₁₉	semidirect
203. C₁₉	#13143	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×#365	2
C₂×C₁₉×#360	2
C₁₉×#2139	2
C₁₉×#1975	2
C₁₉×#1776	2
C₁₉×#1387	2
C₁₉×#1375	2
#13143	19

Subgroups — C19×#13143 #18019102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13143 #18019102