Subgroups — C₁₉×#13146 #18019105

Order 4864.

312 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2148	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#359	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1976	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1953	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1382	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	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#430	—	2	1	no	—
12	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
14	C₁₉×#427	C₂²	1	1	yes	characteristic
15	C₁₉×#421	—	2	1	no	—
16	C₁₉×#410	—	2	1	no	—
17	C₁₉×#405	C₂²	1	1	yes	characteristic
18	C₁₉×#362	C₄	1	2	yes	complemented
19	C₁₉×#361	C₄	1	2	yes	complemented
20	C₁₉×#359	—	2	1	no	—
21	C₁₉×#359	—	2	1	no	—
22	C₁₉×#346	—	2	1	no	—
23	C₄×C₁₆×C₁₉	—	2	1	no	—
24	C₁₉×#344	—	2	1	no	—
25	C₂×#41×C₁₉	—	2	1	no	—
26	C₁₉×#135	—	2	1	no	—
27	C₁₉×#135	—	2	1	no	—
28	C₁₉×#135	—	2	1	no	—
29	C₁₉×#135	—	2	1	no	—
30	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×SD₁₆×C₁₉	—	2	1	no	—
32	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	D₄	1	1	yes	characteristic
39	C₁₉×M₃₂	—	2	1	no	—
40	C₁₉×M₃₂	C₂×C₄	1	2	yes	—
41	C₂×C₁₆×C₁₉	—	2	1	no	—
42	C₂×C₁₆×C₁₉	—	2	1	no	—
43	C₂×C₁₆×C₁₉	—	2	1	no	—
44	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
46	C₁₉×#108	—	2	1	no	—
47	C₁₉×#108	—	2	1	no	—
48	C₁₉×#108	—	2	1	no	—
49	C₁₉×#108	—	4	2	no	—
50	C₁₉×#108	C₂×C₄	1	2	yes	—
51	C₁₉×#107	—	2	1	no	—
52	C₁₉×#106	—	2	1	no	—
53	C₁₉×#104	—	4	2	no	—
54	C₁₉×#99	—	4	2	no	—
55	C₁₉×#97	—	2	1	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	#41×C₁₉	—	4	1	no	—
58	#41×C₁₉	—	4	1	no	—
59	#41×C₁₉	—	4	1	no	—
60	#41×C₁₉	—	4	1	no	—
61	C₂×Q₈×C₁₉	—	2	1	no	—
62	C₂×D₄×C₁₉	—	2	1	no	—
63	C₂×D₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	Q₁₆×C₁₉	—	2	1	no	—
67	Q₁₆×C₁₉	—	2	1	no	—
68	SD₁₆×C₁₉	—	4	1	no	—
69	SD₁₆×C₁₉	—	4	1	no	—
70	D₈×C₁₉	—	2	1	no	—
71	D₈×C₁₉	—	2	1	no	—
72	M₁₆×C₁₉	—	2	1	no	—
73	M₁₆×C₁₉	—	2	2	no	—
74	M₁₆×C₁₉	—	4	1	no	—
75	M₁₆×C₁₉	—	4	1	no	—
76	M₁₆×C₁₉	—	4	1	no	—
77	M₁₆×C₁₉	D₈	1	2	yes	—
78	C₂×C₈×C₁₉	—	2	1	no	—
79	C₂×C₈×C₁₉	—	4	1	no	—
80	C₂×C₈×C₁₉	—	4	1	no	—
81	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
84	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
85	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
86	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
87	C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₂²⋊C₄×C₁₉	—	4	1	no	—
90	C₂²⋊C₄×C₁₉	SD₁₆	1	2	yes	—
91	C₄²×C₁₉	—	2	1	no	—
92	C₄²×C₁₉	—	4	1	no	—
93	C₁₆×C₁₉	—	2	2	no	—
94	C₁₆×C₁₉	—	2	1	no	—
95	C₁₆×C₁₉	—	2	1	no	—
96	#13146	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂³×C₁₉	—	4	1	no	—
98	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
99	Q₈×C₁₉	—	4	1	no	—
100	Q₈×C₁₉	—	4	1	no	—
101	D₄×C₁₉	—	4	1	no	—
102	D₄×C₁₉	—	4	1	no	—
103	D₄×C₁₉	—	8	1	no	—
104	D₄×C₁₉	—	8	1	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	4	1	no	—
107	C₂×C₄×C₁₉	—	8	1	no	—
108	C₂×C₄×C₁₉	—	8	1	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
116	C₈×C₁₉	—	2	2	no	—
117	C₈×C₁₉	—	4	2	no	—
118	C₈×C₁₉	—	8	1	no	—
119	C₈×C₁₉	#117	1	1	yes	characteristic
120	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
121	C₈×C₁₉	#123	1	1	yes	characteristic
122	C₈×C₁₉	#126	1	1	yes	characteristic
123	#2148	C₂×C₁₉	1	1	yes	characteristic
124	C₂×#359	C₂×C₁₉	1	1	yes	characteristic
125	#2108	C₂×C₁₉	1	1	yes	characteristic, complemented
126	#1976	C₂×C₁₉	1	1	yes	characteristic
127	#1953	C₂×C₁₉	1	1	yes	characteristic, complemented
128	#1389	C₂×C₁₉	1	1	yes	characteristic, complemented
129	#1382	C₂×C₁₉	1	1	yes	characteristic, complemented
130	C₂²×C₁₉	—	4	1	no	—
131	C₂²×C₁₉	—	8	1	no	—
132	C₂²×C₁₉	—	16	1	no	—
133	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
134	C₂²×C₁₉	#465	1	1	yes	characteristic
135	C₂²×C₁₉	#486	1	1	yes	characteristic
136	C₄×C₁₉	—	4	2	no	—
137	C₄×C₁₉	—	8	1	no	—
138	C₄×C₁₉	—	16	1	no	—
139	C₄×C₁₉	#388	1	1	yes	characteristic
140	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
141	C₄×C₁₉	#466	1	1	yes	characteristic
142	C₄×C₁₉	#488	1	1	yes	characteristic
143	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
144	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
145	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
146	#430	—	2	1	no	—
147	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
148	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
149	#427	C₂²×C₁₉	1	1	yes	characteristic
150	#421	—	2	1	no	—
151	#410	—	2	1	no	—
152	#405	C₂²×C₁₉	1	1	yes	characteristic
153	#362	C₄×C₁₉	1	2	yes	complemented
154	#361	C₄×C₁₉	1	2	yes	complemented
155	#359	—	2	1	no	—
156	#359	—	2	1	no	—
157	#346	—	2	1	no	—
158	C₄×C₁₆	—	2	1	no	—
159	#344	—	2	1	no	—
160	C₂×C₁₉	—	2	1	no	—
161	C₂×C₁₉	—	2	1	no	—
162	C₂×C₁₉	—	2	1	no	—
163	C₂×C₁₉	—	16	1	no	—
164	C₂×C₁₉	#1934	1	1	yes	characteristic
165	C₂×#41	—	2	1	no	—
166	#135	—	2	1	no	—
167	#135	—	2	1	no	—
168	#135	—	2	1	no	—
169	#135	—	2	1	no	—
170	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
171	C₂×SD₁₆	—	2	1	no	—
172	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
173	C₂×M₁₆	—	2	1	no	—
174	C₂×M₁₆	—	2	1	no	—
175	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
176	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
177	#117	—	2	1	no	—
178	#117	D₄×C₁₉	1	1	yes	characteristic
179	M₃₂	—	2	1	no	—
180	M₃₂	C₂×C₄×C₁₉	1	2	yes	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	2	1	no	—
184	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
185	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
186	#108	—	2	1	no	—
187	#108	—	2	1	no	—
188	#108	—	2	1	no	—
189	#108	—	4	2	no	—
190	#108	C₂×C₄×C₁₉	1	2	yes	—
191	#107	—	2	1	no	—
192	#106	—	2	1	no	—
193	#104	—	4	2	no	—
194	#99	—	4	2	no	—
195	#97	—	2	1	no	—
196	C₄×C₈	—	2	1	no	—
197	C₁₉	#13146	1	1	yes	characteristic, direct product factor, Sylow
198	#41	—	4	1	no	—
199	#41	—	4	1	no	—
200	#41	—	4	1	no	—
201	#41	—	4	1	no	—
202	C₂×Q₈	—	2	1	no	—
203	C₂×D₄	—	2	1	no	—
204	C₂×D₄	—	4	1	no	—
205	C₂²×C₄	—	4	1	no	—
206	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
207	Q₁₆	—	2	1	no	—
208	Q₁₆	—	2	1	no	—
209	SD₁₆	—	4	1	no	—
210	SD₁₆	—	4	1	no	—
211	D₈	—	2	1	no	—
212	D₈	—	2	1	no	—
213	M₁₆	—	2	1	no	—
214	M₁₆	—	2	2	no	—
215	M₁₆	—	4	1	no	—
216	M₁₆	—	4	1	no	—
217	M₁₆	—	4	1	no	—
218	M₁₆	D₈×C₁₉	1	2	yes	—
219	C₂×C₈	—	2	1	no	—
220	C₂×C₈	—	4	1	no	—
221	C₂×C₈	—	4	1	no	—
222	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
223	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
224	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
225	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
226	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
227	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
228	C₄⋊C₄	—	2	1	no	—
229	C₄⋊C₄	—	4	1	no	—
230	C₂²⋊C₄	—	4	1	no	—
231	C₂²⋊C₄	SD₁₆×C₁₉	1	2	yes	—
232	C₄²	—	2	1	no	—
233	C₄²	—	4	1	no	—
234	C₁₆	—	2	2	no	—
235	C₁₆	—	2	1	no	—
236	C₁₆	—	2	1	no	—
237	C₂³	—	4	1	no	—
238	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
239	Q₈	—	4	1	no	—
240	Q₈	—	4	1	no	—
241	D₄	—	4	1	no	—
242	D₄	—	4	1	no	—
243	D₄	—	8	1	no	—
244	D₄	—	8	1	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	8	1	no	—
248	C₂×C₄	—	8	1	no	—
249	C₂×C₄	—	8	1	no	—
250	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
251	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
252	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
253	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
254	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
255	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
256	C₈	—	2	2	no	—
257	C₈	—	4	2	no	—
258	C₈	—	8	1	no	—
259	C₈	C₁₉×#117	1	1	yes	characteristic
260	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
261	C₈	C₁₉×#123	1	1	yes	characteristic
262	C₈	C₁₉×#126	1	1	yes	characteristic
263	C₂²	—	4	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	—	16	1	no	—
266	C₂²	C₄×SD₁₆×C₁₉	1	1	yes	characteristic
267	C₂²	C₁₉×#465	1	1	yes	characteristic
268	C₂²	C₁₉×#486	1	1	yes	characteristic
269	C₄	—	4	2	no	—
270	C₄	—	8	1	no	—
271	C₄	—	16	1	no	—
272	C₄	C₁₉×#388	1	1	yes	characteristic
273	C₄	C₄×D₈×C₁₉	1	1	yes	characteristic
274	C₄	C₁₉×#466	1	1	yes	characteristic
275	C₄	C₁₉×#488	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	2	1	no	—
279	C₂	—	16	1	no	—
280	C₂	C₁₉×#1934	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	#1934
prime radical	C₂×C₁₉×#135	C₂²
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
3. C₁₉×#2108	C₂	semidirect
5. C₁₉×#1953	C₂	semidirect
6. C₁₉×#1389	C₂	semidirect
7. C₁₉×#1382	C₂	semidirect
18. C₁₉×#362	C₄	semidirect
19. C₁₉×#361	C₄	semidirect
96. #13146	C₁₉	direct (N × H)
125. #2108	C₂×C₁₉	semidirect
127. #1953	C₂×C₁₉	semidirect
128. #1389	C₂×C₁₉	semidirect
129. #1382	C₂×C₁₉	semidirect
153. #362	C₄×C₁₉	semidirect
154. #361	C₄×C₁₉	semidirect
197. C₁₉	#13146	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×#2148	2
C₂×C₁₉×#359	2
C₁₉×#2108	2
C₁₉×#1976	2
C₁₉×#1953	2
C₁₉×#1389	2
C₁₉×#1382	2
#13146	19

Subgroups — C19×#13146 #18019105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13146 #18019105