Subgroups — C₁₉×#13243 #18019202

Order 4864.

410 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#508	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2158	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2145	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1976	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#135	C₂²	1	2	yes	—
7	C₁₉×#508	—	2	1	no	—
8	C₁₉×#508	—	2	1	no	—
9	C₁₉×#508	—	2	1	no	—
10	C₁₉×#508	—	2	1	no	—
11	C₂×C₁₉×Q₃₂	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₉×SD₃₂	C₄	1	2	yes	complemented
13	C₂×C₁₉×D₁₆	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
15	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#427	C₂²	1	2	yes	—
17	C₁₉×#421	—	2	2	no	—
18	C₁₉×#410	—	2	2	no	—
19	C₁₉×#405	C₂²	1	1	yes	characteristic
20	C₁₉×#367	—	2	1	no	—
21	C₁₉×#366	—	2	1	no	—
22	C₁₉×#360	—	2	4	no	—
23	C₁₉×#346	—	2	1	no	—
24	C₄×C₁₆×C₁₉	—	2	1	no	—
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₁₉×#135	—	2	2	no	—
27	C₁₉×#135	—	2	2	no	—
28	C₁₉×#135	—	2	2	no	—
29	C₁₉×#135	—	2	2	no	—
30	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×SD₁₆×C₁₉	—	2	2	no	—
32	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
35	C₁₉×#117	—	2	2	no	—
36	C₁₉×#117	D₄	1	1	yes	characteristic
37	C₁₉×Q₃₂	—	2	1	no	—
38	C₁₉×Q₃₂	—	2	1	no	—
39	C₁₉×SD₃₂	—	2	2	no	—
40	C₁₉×SD₃₂	—	2	2	no	—
41	C₁₉×D₁₆	—	2	1	no	—
42	C₁₉×D₁₆	—	2	1	no	—
43	C₁₉×M₃₂	—	2	1	no	—
44	C₁₉×M₃₂	D₄	1	2	yes	—
45	C₂×C₁₆×C₁₉	—	2	1	no	—
46	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
52	C₁₉×#107	—	2	2	no	—
53	C₁₉×#106	—	2	2	no	—
54	C₁₉×#104	—	4	4	no	—
55	C₁₉×#99	—	4	4	no	—
56	C₁₉×#97	—	2	1	no	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	#41×C₁₉	—	4	2	no	—
59	#41×C₁₉	—	4	2	no	—
60	#41×C₁₉	—	4	2	no	—
61	#41×C₁₉	—	4	2	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂×D₄×C₁₉	—	2	2	no	—
64	C₂×D₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	Q₁₆×C₁₉	—	2	2	no	—
68	Q₁₆×C₁₉	—	2	2	no	—
69	SD₁₆×C₁₉	—	4	2	no	—
70	SD₁₆×C₁₉	—	4	2	no	—
71	D₈×C₁₉	—	2	2	no	—
72	D₈×C₁₉	—	2	2	no	—
73	M₁₆×C₁₉	—	2	1	no	—
74	M₁₆×C₁₉	D₈	1	2	yes	—
75	C₂×C₈×C₁₉	—	2	1	no	—
76	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
81	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
82	C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₄⋊C₄×C₁₉	—	4	2	no	—
84	C₂²⋊C₄×C₁₉	—	4	2	no	—
85	C₂²⋊C₄×C₁₉	D₈	1	2	yes	—
86	C₄²×C₁₉	—	2	1	no	—
87	C₄²×C₁₉	—	4	2	no	—
88	C₁₆×C₁₉	—	2	2	no	—
89	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	#13243	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
96	Q₈×C₁₉	—	4	2	no	—
97	Q₈×C₁₉	—	4	2	no	—
98	D₄×C₁₉	—	4	2	no	—
99	D₄×C₁₉	—	4	2	no	—
100	D₄×C₁₉	—	8	2	no	—
101	D₄×C₁₉	—	8	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	8	2	no	—
105	C₂×C₄×C₁₉	—	8	2	no	—
106	C₂×C₄×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
113	C₈×C₁₉	—	2	2	no	—
114	C₈×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
116	C₈×C₁₉	#121	1	1	yes	characteristic
117	C₈×C₁₉	#124	1	1	yes	characteristic
118	C₂×#508	C₂×C₁₉	1	1	yes	characteristic
119	#2158	C₂×C₁₉	1	1	yes	characteristic, complemented
120	#2145	C₂×C₁₉	1	2	yes	complemented
121	#2108	C₂×C₁₉	1	1	yes	characteristic, complemented
122	#1976	C₂×C₁₉	1	2	yes	complemented
123	C₂²×C₁₉	—	4	1	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	—	16	2	no	—
126	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
127	C₂²×C₁₉	#466	1	1	yes	characteristic
128	C₂²×C₁₉	#493	1	1	yes	characteristic
129	C₄×C₁₉	—	4	2	no	—
130	C₄×C₁₉	—	8	2	no	—
131	C₄×C₁₉	—	16	2	no	—
132	C₄×C₁₉	#390	1	1	yes	characteristic
133	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
134	C₄×C₁₉	#466	1	1	yes	characteristic
135	C₄×C₁₉	#495	1	1	yes	characteristic
136	C₂×#135	C₂²×C₁₉	1	2	yes	—
137	#508	—	2	1	no	—
138	#508	—	2	1	no	—
139	#508	—	2	1	no	—
140	#508	—	2	1	no	—
141	C₂×Q₃₂	C₄×C₁₉	1	1	yes	characteristic, complemented
142	C₂×SD₃₂	C₄×C₁₉	1	2	yes	complemented
143	C₂×D₁₆	C₄×C₁₉	1	1	yes	characteristic, complemented
144	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
145	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
146	#427	C₂²×C₁₉	1	2	yes	—
147	#421	—	2	2	no	—
148	#410	—	2	2	no	—
149	#405	C₂²×C₁₉	1	1	yes	characteristic
150	#367	—	2	1	no	—
151	#366	—	2	1	no	—
152	#360	—	2	4	no	—
153	#346	—	2	1	no	—
154	C₄×C₁₆	—	2	1	no	—
155	C₂×C₁₉	—	2	1	no	—
156	C₂×C₁₉	—	2	1	no	—
157	C₂×C₁₉	—	2	1	no	—
158	C₂×C₁₉	—	16	2	no	—
159	C₂×C₁₉	#1970	1	1	yes	characteristic
160	C₂×#41	—	2	2	no	—
161	#135	—	2	2	no	—
162	#135	—	2	2	no	—
163	#135	—	2	2	no	—
164	#135	—	2	2	no	—
165	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
166	C₂×SD₁₆	—	2	2	no	—
167	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
168	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
169	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
170	#117	—	2	2	no	—
171	#117	D₄×C₁₉	1	1	yes	characteristic
172	Q₃₂	—	2	1	no	—
173	Q₃₂	—	2	1	no	—
174	SD₃₂	—	2	2	no	—
175	SD₃₂	—	2	2	no	—
176	D₁₆	—	2	1	no	—
177	D₁₆	—	2	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	D₄×C₁₉	1	2	yes	—
180	C₂×C₁₆	—	2	1	no	—
181	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
182	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
183	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
184	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
185	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
186	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
187	#107	—	2	2	no	—
188	#106	—	2	2	no	—
189	#104	—	4	4	no	—
190	#99	—	4	4	no	—
191	#97	—	2	1	no	—
192	C₄×C₈	—	2	1	no	—
193	C₁₉	#13243	1	1	yes	characteristic, direct product factor, Sylow
194	#41	—	4	2	no	—
195	#41	—	4	2	no	—
196	#41	—	4	2	no	—
197	#41	—	4	2	no	—
198	C₂×Q₈	—	2	2	no	—
199	C₂×D₄	—	2	2	no	—
200	C₂×D₄	—	4	2	no	—
201	C₂²×C₄	—	4	2	no	—
202	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
203	Q₁₆	—	2	2	no	—
204	Q₁₆	—	2	2	no	—
205	SD₁₆	—	4	2	no	—
206	SD₁₆	—	4	2	no	—
207	D₈	—	2	2	no	—
208	D₈	—	2	2	no	—
209	M₁₆	—	2	1	no	—
210	M₁₆	D₈×C₁₉	1	2	yes	—
211	C₂×C₈	—	2	1	no	—
212	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
213	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
214	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
215	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
216	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
217	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
218	C₄⋊C₄	—	2	1	no	—
219	C₄⋊C₄	—	4	2	no	—
220	C₂²⋊C₄	—	4	2	no	—
221	C₂²⋊C₄	D₈×C₁₉	1	2	yes	—
222	C₄²	—	2	1	no	—
223	C₄²	—	4	2	no	—
224	C₁₆	—	2	2	no	—
225	C₁₆	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
226	C₁₆	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
227	C₁₆	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
228	C₁₆	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
229	C₂³	—	4	2	no	—
230	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
231	Q₈	—	4	2	no	—
232	Q₈	—	4	2	no	—
233	D₄	—	4	2	no	—
234	D₄	—	4	2	no	—
235	D₄	—	8	2	no	—
236	D₄	—	8	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	—	8	2	no	—
241	C₂×C₄	—	8	2	no	—
242	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
243	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
244	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
245	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
246	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
247	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
250	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
251	C₈	C₁₉×#121	1	1	yes	characteristic
252	C₈	C₁₉×#124	1	1	yes	characteristic
253	C₂²	—	4	1	no	—
254	C₂²	—	8	2	no	—
255	C₂²	—	16	2	no	—
256	C₂²	C₄×D₈×C₁₉	1	1	yes	characteristic
257	C₂²	C₁₉×#466	1	1	yes	characteristic
258	C₂²	C₁₉×#493	1	1	yes	characteristic
259	C₄	—	4	2	no	—
260	C₄	—	8	2	no	—
261	C₄	—	16	2	no	—
262	C₄	C₁₉×#390	1	1	yes	characteristic
263	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
264	C₄	C₁₉×#466	1	1	yes	characteristic
265	C₄	C₁₉×#495	1	1	yes	characteristic
266	C₂	—	2	1	no	—
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	—	16	2	no	—
270	C₂	C₁₉×#1970	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#466
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1970
prime radical	C₂×C₁₉×#508	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2158	C₂	semidirect
3. C₁₉×#2145	C₂	semidirect
4. C₁₉×#2108	C₂	semidirect
5. C₁₉×#1976	C₂	semidirect
11. C₂×C₁₉×Q₃₂	C₄	semidirect
12. C₂×C₁₉×SD₃₂	C₄	semidirect
13. C₂×C₁₉×D₁₆	C₄	semidirect
93. #13243	C₁₉	direct (N × H)
119. #2158	C₂×C₁₉	semidirect
120. #2145	C₂×C₁₉	semidirect
121. #2108	C₂×C₁₉	semidirect
122. #1976	C₂×C₁₉	semidirect
141. C₂×Q₃₂	C₄×C₁₉	semidirect
142. C₂×SD₃₂	C₄×C₁₉	semidirect
143. C₂×D₁₆	C₄×C₁₉	semidirect
193. C₁₉	#13243	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×#508	2
C₁₉×#2158	2
C₁₉×#2145	2
C₁₉×#2108	2
C₁₉×#1976	2
#13243	19

Subgroups — C19×#13243 #18019202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13243 #18019202