Subgroups — C₁₉×#18703 #18024662

Order 4864.

812 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	C₁₉×#3556	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3255	C₂	1	2	yes	maximal
3	C₁₉×#3160	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1653	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1648	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1561	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1493	C₂	1	2	yes	maximal
8	C₁₉×#564	—	2	2	no	—
9	C₁₉×#557	—	2	2	no	—
10	C₁₉×#557	—	2	2	no	—
11	C₁₉×#557	C₂²	1	4	yes	—
12	C₁₉×#541	—	2	4	no	—
13	C₁₉×#541	—	2	2	no	—
14	C₁₉×#533	C₂²	1	1	yes	characteristic
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#500	C₂²	1	2	yes	—
18	C₁₉×#499	—	2	2	no	—
19	C₁₉×#498	C₂²	1	2	yes	—
20	C₁₉×#475	—	2	2	no	—
21	C₁₉×#475	C₂²	1	4	yes	—
22	C₁₉×#470	—	2	4	no	—
23	C₁₉×#462	—	2	2	no	—
24	C₁₉×#462	C₂²	1	4	yes	—
25	C₁₉×#427	—	2	2	no	—
26	C₁₉×#423	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#332	C₂²	1	4	yes	—
29	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
30	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	—
31	C₂×Q₁₆×C₁₉	—	2	4	no	—
32	C₂×M₁₆×C₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	2	no	—
35	C₁₉×C₄⋊Q₈	—	2	4	no	—
36	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
37	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
38	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
39	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
40	C₁₉×#126	—	2	8	no	—
41	C₁₉×#125	—	2	2	no	—
42	C₁₉×#125	—	2	8	no	—
43	C₁₉×#125	—	2	8	no	—
44	C₁₉×#125	—	2	4	no	—
45	C₁₉×#125	—	2	8	no	—
46	C₁₉×#125	—	2	2	no	—
47	C₁₉×#125	—	2	1	no	—
48	C₁₉×#125	D₄	1	2	yes	—
49	C₁₉×C₂²⋊Q₈	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
53	C₄×Q₈×C₁₉	—	2	4	no	—
54	C₄×Q₈×C₁₉	—	2	4	no	—
55	C₄×Q₈×C₁₉	—	2	4	no	—
56	C₄×Q₈×C₁₉	—	2	2	no	—
57	C₄×Q₈×C₁₉	—	2	2	no	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	D₄	1	2	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#107	—	2	4	no	—
65	C₁₉×#106	—	2	4	no	—
66	C₁₉×#106	—	2	4	no	—
67	C₁₉×C₄⋊C₈	—	2	2	no	—
68	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
69	C₁₉×#103	—	2	4	no	—
70	C₁₉×#103	—	2	4	no	—
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×Q₈×C₁₉	—	2	2	no	—
75	C₂×Q₈×C₁₉	—	2	2	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	Q₁₆×C₁₉	—	8	4	no	—
81	M₁₆×C₁₉	—	8	2	no	—
82	C₂×C₈×C₁₉	—	2	4	no	—
83	C₂×C₈×C₁₉	—	2	1	no	—
84	C₂×C₈×C₁₉	—	2	1	no	—
85	C₂×C₈×C₁₉	—	2	4	no	—
86	C₄⋊C₄×C₁₉	—	2	8	no	—
87	C₄⋊C₄×C₁₉	—	2	8	no	—
88	C₄⋊C₄×C₁₉	—	2	8	no	—
89	C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	—	2	4	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	—	2	4	no	—
96	C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	4	2	no	—
99	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
100	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
101	C₂²⋊C₄×C₁₉	—	2	4	no	—
102	C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂²⋊C₄×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	2	8	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	4	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	C₂×D₄	1	2	yes	—
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
111	#18703	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₉	#120	1	1	yes	characteristic
113	Q₈×C₁₉	—	2	4	no	—
114	Q₈×C₁₉	—	2	4	no	—
115	Q₈×C₁₉	—	4	2	no	—
116	Q₈×C₁₉	—	4	2	no	—
117	Q₈×C₁₉	—	4	4	no	—
118	Q₈×C₁₉	—	4	2	no	—
119	Q₈×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	2	4	no	—
125	C₂×C₄×C₁₉	—	2	4	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	#120	1	2	yes	—
128	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
131	C₈×C₁₉	—	2	2	no	—
132	C₈×C₁₉	—	2	2	no	—
133	C₈×C₁₉	—	4	4	no	—
134	#3556	C₂×C₁₉	1	1	yes	characteristic
135	#3255	C₂×C₁₉	1	2	yes	—
136	#3160	C₂×C₁₉	1	1	yes	characteristic
137	#1653	C₂×C₁₉	1	4	yes	complemented
138	#1648	C₂×C₁₉	1	4	yes	complemented
139	#1561	C₂×C₁₉	1	1	yes	characteristic
140	#1493	C₂×C₁₉	1	2	yes	—
141	C₂²×C₁₉	—	2	2	no	—
142	C₂²×C₁₉	—	2	1	no	—
143	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
144	C₄×C₁₉	—	2	2	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	4	4	no	—
147	C₄×C₁₉	—	4	4	no	—
148	C₄×C₁₉	—	4	4	no	—
149	C₄×C₁₉	—	8	2	no	—
150	C₄×C₁₉	#456	1	2	yes	—
151	C₄×C₁₉	#577	1	2	yes	—
152	C₄×C₁₉	#578	1	2	yes	—
153	#564	—	2	2	no	—
154	#557	—	2	2	no	—
155	#557	—	2	2	no	—
156	#557	C₂²×C₁₉	1	4	yes	—
157	#541	—	2	4	no	—
158	#541	—	2	2	no	—
159	#533	C₂²×C₁₉	1	1	yes	characteristic
160	#533	C₂²×C₁₉	1	2	yes	—
161	#533	C₂²×C₁₉	1	1	yes	characteristic
162	#500	C₂²×C₁₉	1	2	yes	—
163	#499	—	2	2	no	—
164	#498	C₂²×C₁₉	1	2	yes	—
165	#475	—	2	2	no	—
166	#475	C₂²×C₁₉	1	4	yes	—
167	#470	—	2	4	no	—
168	#462	—	2	2	no	—
169	#462	C₂²×C₁₉	1	4	yes	—
170	#427	—	2	2	no	—
171	#423	C₂²×C₁₉	1	2	yes	—
172	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
173	#332	C₂²×C₁₉	1	4	yes	—
174	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
175	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	—
176	C₂×C₁₉	—	4	1	no	—
177	C₂×C₁₉	#3013	1	2	yes	—
178	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
179	C₂×Q₁₆	—	2	4	no	—
180	C₂×M₁₆	—	2	2	no	—
181	C₂²×C₈	—	2	1	no	—
182	C₄⋊Q₈	—	2	2	no	—
183	C₄⋊Q₈	—	2	4	no	—
184	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
185	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
186	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
187	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
188	#126	—	2	8	no	—
189	#125	—	2	2	no	—
190	#125	—	2	8	no	—
191	#125	—	2	8	no	—
192	#125	—	2	4	no	—
193	#125	—	2	8	no	—
194	#125	—	2	2	no	—
195	#125	—	2	1	no	—
196	#125	D₄×C₁₉	1	2	yes	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	2	no	—
200	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
201	C₄×Q₈	—	2	4	no	—
202	C₄×Q₈	—	2	4	no	—
203	C₄×Q₈	—	2	4	no	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	—	2	2	no	—
207	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
208	#117	—	2	2	no	—
209	#117	—	2	1	no	—
210	#117	D₄×C₁₉	1	2	yes	—
211	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
212	#107	—	2	4	no	—
213	#106	—	2	4	no	—
214	#106	—	2	4	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
217	#103	—	2	4	no	—
218	#103	—	2	4	no	—
219	C₄×C₈	—	2	1	no	—
220	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
221	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
222	C₁₉	#18703	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×Q₈	—	2	2	no	—
224	C₂×Q₈	—	2	2	no	—
225	C₂×Q₈	—	2	2	no	—
226	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
227	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
229	Q₁₆	—	8	4	no	—
230	M₁₆	—	8	2	no	—
231	C₂×C₈	—	2	4	no	—
232	C₂×C₈	—	2	1	no	—
233	C₂×C₈	—	2	1	no	—
234	C₂×C₈	—	2	4	no	—
235	C₄⋊C₄	—	2	8	no	—
236	C₄⋊C₄	—	2	8	no	—
237	C₄⋊C₄	—	2	8	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	2	2	no	—
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	—	2	4	no	—
243	C₄⋊C₄	—	2	2	no	—
244	C₄⋊C₄	—	2	4	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
249	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
250	C₂²⋊C₄	—	2	4	no	—
251	C₂²⋊C₄	—	2	2	no	—
252	C₂²⋊C₄	—	4	1	no	—
253	C₄²	—	2	8	no	—
254	C₄²	—	2	2	no	—
255	C₄²	—	2	4	no	—
256	C₄²	—	4	1	no	—
257	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
258	C₄²	C₂×D₄×C₁₉	1	2	yes	—
259	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
260	C₂³	C₁₉×#120	1	1	yes	characteristic
261	Q₈	—	2	4	no	—
262	Q₈	—	2	4	no	—
263	Q₈	—	4	4	no	—
264	Q₈	—	4	2	no	—
265	Q₈	—	4	2	no	—
266	Q₈	—	4	2	no	—
267	Q₈	—	4	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	C₁₉×#120	1	2	yes	—
276	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
277	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
278	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
279	C₈	—	2	2	no	—
280	C₈	—	2	2	no	—
281	C₈	—	4	4	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	2	1	no	—
284	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
285	C₄	—	2	2	no	—
286	C₄	—	2	1	no	—
287	C₄	—	4	4	no	—
288	C₄	—	4	4	no	—
289	C₄	—	4	4	no	—
290	C₄	—	8	2	no	—
291	C₄	C₁₉×#456	1	2	yes	—
292	C₄	C₁₉×#577	1	2	yes	—
293	C₄	C₁₉×#578	1	2	yes	—
294	C₂	—	4	1	no	—
295	C₂	C₁₉×#3013	1	2	yes	—
296	C₂	C₂×C₁₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	#120
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
4. C₁₉×#1653	C₂	semidirect
5. C₁₉×#1648	C₂	semidirect
111. #18703	C₁₉	direct (N × H)
137. #1653	C₂×C₁₉	semidirect
138. #1648	C₂×C₁₉	semidirect
222. C₁₉	#18703	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×#3556	2
C₁₉×#3255	2
C₁₉×#3160	2
C₁₉×#1653	2
C₁₉×#1648	2
C₁₉×#1561	2
C₁₉×#1493	2
#18703	19

Subgroups — C19×#18703 #18024662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18703 #18024662