Subgroups — C₁₉×#9418 #18015377

Order 4864.

402 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3182	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2987	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1515	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1514	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1291	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#533	C₂²	1	1	yes	characteristic
9	C₁₉×#532	C₂²	1	1	yes	characteristic
10	C₁₉×#500	C₄	1	1	yes	characteristic, complemented
11	C₁₉×#492	C₄	1	1	yes	characteristic, complemented
12	C₁₉×#487	C₄	1	1	yes	characteristic, complemented
13	C₁₉×#486	C₄	1	1	yes	characteristic, complemented
14	C₁₉×#468	—	2	2	no	—
15	C₁₉×#446	—	2	2	no	—
16	C₁₉×#446	—	2	2	no	—
17	C₁₉×#440	—	2	2	no	—
18	C₁₉×#433	—	2	2	no	—
19	C₁₉×#432	C₂²	1	1	yes	characteristic
20	C₁₉×#432	C₂²	1	1	yes	characteristic
21	C₁₉×#432	C₂²	1	1	yes	characteristic
22	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#383	C₂²	1	1	yes	characteristic
24	C₁₉×#329	—	2	2	no	—
25	C₁₉×#328	—	2	2	no	—
26	C₁₉×#327	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	1	no	—
28	C₂×SD₁₆×C₁₉	—	2	2	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
31	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
32	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
33	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
34	C₁₉×#125	—	2	1	no	—
35	C₁₉×#124	—	2	1	no	—
36	C₁₉×C₂²⋊Q₈	—	2	1	no	—
37	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
38	C₁₉×#121	—	2	1	no	—
39	C₁₉×#121	—	2	1	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	D₄	1	2	yes	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
46	C₁₉×#107	—	2	2	no	—
47	C₁₉×C₄⋊C₈	—	2	4	no	—
48	C₁₉×C₄⋊C₈	—	2	1	no	—
49	C₁₉×C₄⋊C₈	—	2	1	no	—
50	C₁₉×C₄⋊C₈	—	2	1	no	—
51	C₁₉×#103	—	2	2	no	—
52	C₁₉×#102	—	2	2	no	—
53	C₁₉×C₂²⋊C₈	—	2	1	no	—
54	C₁₉×C₂²⋊C₈	—	2	1	no	—
55	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
56	C₁₉×#97	—	2	2	no	—
57	C₁₉×#97	—	2	1	no	—
58	C₁₉×#97	—	2	1	no	—
59	C₁₉×#97	—	2	1	no	—
60	C₁₉×#97	D₄	1	2	yes	—
61	C₄×C₈×C₁₉	—	2	2	no	—
62	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#95	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	1	no	—
67	#41×C₁₉	—	8	2	no	—
68	C₂×Q₈×C₁₉	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
71	C₂×D₄×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	SD₁₆×C₁₉	—	4	4	no	—
81	M₁₆×C₁₉	—	4	2	no	—
82	C₂×C₈×C₁₉	—	2	1	no	—
83	C₂×C₈×C₁₉	—	2	1	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	2	2	no	—
86	C₂×C₈×C₁₉	—	4	1	no	—
87	C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂²⋊C₄×C₁₉	—	2	2	no	—
96	C₂²⋊C₄×C₁₉	—	4	1	no	—
97	C₂²⋊C₄×C₁₉	—	4	1	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	#41	1	1	yes	characteristic
103	#9418	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂³×C₁₉	—	4	1	no	—
105	C₂³×C₁₉	#121	1	1	yes	characteristic
106	Q₈×C₁₉	—	4	2	no	—
107	Q₈×C₁₉	—	8	1	no	—
108	Q₈×C₁₉	—	8	1	no	—
109	D₄×C₁₉	—	4	2	no	—
110	D₄×C₁₉	—	8	1	no	—
111	D₄×C₁₉	—	8	1	no	—
112	D₄×C₁₉	—	8	2	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	1	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	1	no	—
119	C₂×C₄×C₁₉	—	8	2	no	—
120	C₂×C₄×C₁₉	—	8	1	no	—
121	C₂×C₄×C₁₉	—	8	1	no	—
122	C₂×C₄×C₁₉	—	8	1	no	—
123	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
129	C₈×C₁₉	—	2	2	no	—
130	C₈×C₁₉	—	4	2	no	—
131	C₈×C₁₉	—	4	2	no	—
132	C₈×C₁₉	—	4	1	no	—
133	C₈×C₁₉	—	8	1	no	—
134	#3182	C₂×C₁₉	1	1	yes	characteristic
135	#2987	C₂×C₁₉	1	1	yes	characteristic, complemented
136	#1536	C₂×C₁₉	1	1	yes	characteristic
137	#1515	C₂×C₁₉	1	1	yes	characteristic, complemented
138	#1514	C₂×C₁₉	1	1	yes	characteristic
139	#1291	C₂×C₁₉	1	1	yes	characteristic, complemented
140	#1288	C₂×C₁₉	1	1	yes	characteristic, complemented
141	C₂²×C₁₉	—	2	1	no	—
142	C₂²×C₁₉	—	2	1	no	—
143	C₂²×C₁₉	—	2	1	no	—
144	C₂²×C₁₉	—	8	1	no	—
145	C₂²×C₁₉	—	8	1	no	—
146	C₂²×C₁₉	—	8	1	no	—
147	C₂²×C₁₉	#386	1	1	yes	characteristic
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	2	1	no	—
152	C₄×C₁₉	—	2	1	no	—
153	C₄×C₁₉	—	2	1	no	—
154	C₄×C₁₉	—	4	2	no	—
155	C₄×C₁₉	—	4	2	no	—
156	C₄×C₁₉	—	8	1	no	—
157	C₄×C₁₉	—	16	1	no	—
158	#533	C₂²×C₁₉	1	1	yes	characteristic
159	#532	C₂²×C₁₉	1	1	yes	characteristic
160	#500	C₄×C₁₉	1	1	yes	characteristic, complemented
161	#492	C₄×C₁₉	1	1	yes	characteristic, complemented
162	#487	C₄×C₁₉	1	1	yes	characteristic, complemented
163	#486	C₄×C₁₉	1	1	yes	characteristic, complemented
164	#468	—	2	2	no	—
165	#446	—	2	2	no	—
166	#446	—	2	2	no	—
167	#440	—	2	2	no	—
168	#433	—	2	2	no	—
169	#432	C₂²×C₁₉	1	1	yes	characteristic
170	#432	C₂²×C₁₉	1	1	yes	characteristic
171	#432	C₂²×C₁₉	1	1	yes	characteristic
172	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
173	#383	C₂²×C₁₉	1	1	yes	characteristic
174	#329	—	2	2	no	—
175	#328	—	2	2	no	—
176	#327	—	2	2	no	—
177	C₂×C₁₉	—	4	1	no	—
178	C₂×C₁₉	—	16	1	no	—
179	C₂×C₁₉	#1884	1	1	yes	characteristic
180	C₂×C₁₉	#1903	1	1	yes	characteristic
181	C₂×C₁₉	#1905	1	1	yes	characteristic
182	C₂×#41	—	2	1	no	—
183	C₂×SD₁₆	—	2	2	no	—
184	C₂×M₁₆	—	2	1	no	—
185	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
186	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
187	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
188	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
189	#125	—	2	1	no	—
190	#124	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
193	#121	—	2	1	no	—
194	#121	—	2	1	no	—
195	C₄×Q₈	—	2	1	no	—
196	C₄×Q₈	D₄×C₁₉	1	2	yes	—
197	C₄×D₄	—	2	1	no	—
198	C₄×D₄	—	2	1	no	—
199	#117	—	2	1	no	—
200	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
201	#107	—	2	2	no	—
202	C₄⋊C₈	—	2	4	no	—
203	C₄⋊C₈	—	2	1	no	—
204	C₄⋊C₈	—	2	1	no	—
205	C₄⋊C₈	—	2	1	no	—
206	#103	—	2	2	no	—
207	#102	—	2	2	no	—
208	C₂²⋊C₈	—	2	1	no	—
209	C₂²⋊C₈	—	2	1	no	—
210	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
211	#97	—	2	2	no	—
212	#97	—	2	1	no	—
213	#97	—	2	1	no	—
214	#97	—	2	1	no	—
215	#97	D₄×C₁₉	1	2	yes	—
216	C₄×C₈	—	2	2	no	—
217	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
218	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
219	#95	—	2	1	no	—
220	#95	—	2	1	no	—
221	#95	—	2	1	no	—
222	C₁₉	#9418	1	1	yes	characteristic, direct product factor, Sylow
223	#41	—	8	2	no	—
224	C₂×Q₈	—	2	1	no	—
225	C₂×Q₈	—	2	1	no	—
226	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
227	C₂×D₄	—	2	1	no	—
228	C₂×D₄	—	2	1	no	—
229	C₂×D₄	—	2	1	no	—
230	C₂×D₄	—	4	1	no	—
231	C₂²×C₄	—	4	1	no	—
232	C₂²×C₄	—	4	1	no	—
233	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
235	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
236	SD₁₆	—	4	4	no	—
237	M₁₆	—	4	2	no	—
238	C₂×C₈	—	2	1	no	—
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	4	1	no	—
243	C₄⋊C₄	—	2	1	no	—
244	C₄⋊C₄	—	2	1	no	—
245	C₄⋊C₄	—	2	1	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₄⋊C₄	—	2	2	no	—
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	1	no	—
250	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
251	C₂²⋊C₄	—	2	2	no	—
252	C₂²⋊C₄	—	4	1	no	—
253	C₂²⋊C₄	—	4	1	no	—
254	C₄²	—	2	2	no	—
255	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
256	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
257	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
258	C₄²	#41×C₁₉	1	1	yes	characteristic
259	C₂³	—	4	1	no	—
260	C₂³	C₁₉×#121	1	1	yes	characteristic
261	Q₈	—	4	2	no	—
262	Q₈	—	8	1	no	—
263	Q₈	—	8	1	no	—
264	D₄	—	4	2	no	—
265	D₄	—	8	1	no	—
266	D₄	—	8	1	no	—
267	D₄	—	8	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	1	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	4	1	no	—
274	C₂×C₄	—	8	2	no	—
275	C₂×C₄	—	8	1	no	—
276	C₂×C₄	—	8	1	no	—
277	C₂×C₄	—	8	1	no	—
278	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
279	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
280	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
281	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
282	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
283	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
284	C₈	—	2	2	no	—
285	C₈	—	4	1	no	—
286	C₈	—	4	2	no	—
287	C₈	—	4	2	no	—
288	C₈	—	8	1	no	—
289	C₂²	—	2	1	no	—
290	C₂²	—	2	1	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	8	1	no	—
293	C₂²	—	8	1	no	—
294	C₂²	—	8	1	no	—
295	C₂²	C₁₉×#386	1	1	yes	characteristic
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	2	1	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	4	2	no	—
303	C₄	—	4	2	no	—
304	C₄	—	8	1	no	—
305	C₄	—	16	1	no	—
306	C₂	—	4	1	no	—
307	C₂	—	16	1	no	—
308	C₂	C₁₉×#1884	1	1	yes	characteristic
309	C₂	C₁₉×#1903	1	1	yes	characteristic
310	C₂	C₁₉×#1905	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2987	C₂	semidirect
4. C₁₉×#1515	C₂	semidirect
6. C₁₉×#1291	C₂	semidirect
7. C₁₉×#1288	C₂	semidirect
10. C₁₉×#500	C₄	semidirect
11. C₁₉×#492	C₄	semidirect
12. C₁₉×#487	C₄	semidirect
13. C₁₉×#486	C₄	semidirect
103. #9418	C₁₉	direct (N × H)
135. #2987	C₂×C₁₉	semidirect
137. #1515	C₂×C₁₉	semidirect
139. #1291	C₂×C₁₉	semidirect
140. #1288	C₂×C₁₉	semidirect
160. #500	C₄×C₁₉	semidirect
161. #492	C₄×C₁₉	semidirect
162. #487	C₄×C₁₉	semidirect
163. #486	C₄×C₁₉	semidirect
222. C₁₉	#9418	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×#3182	2
C₁₉×#2987	2
C₁₉×#1536	2
C₁₉×#1515	2
C₁₉×#1514	2
C₁₉×#1291	2
C₁₉×#1288	2
#9418	19

Subgroups — C19×#9418 #18015377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9418 #18015377