Subgroups — C₁₉×#33803 #18039762

Order 4864.

456 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×#3170	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3160	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2255	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2245	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2237	C₂	1	4	yes	maximal
6	C₁₉×#2227	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2225	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2163	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#533	—	2	1	no	—
10	C₁₉×#533	—	2	1	no	—
11	C₁₉×#500	C₂²	1	1	yes	characteristic
12	C₁₉×#500	C₂²	1	1	yes	characteristic
13	C₁₉×#500	C₂²	1	1	yes	characteristic
14	C₁₉×#499	—	2	1	no	—
15	C₁₉×#499	C₂²	1	2	yes	—
16	C₁₉×#498	—	2	1	no	—
17	C₁₉×#494	C₂²	1	1	yes	characteristic
18	C₁₉×#487	—	2	1	no	—
19	C₁₉×#467	—	2	1	no	—
20	C₁₉×#467	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₁₉	—	2	1	no	—
22	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#427	—	2	1	no	—
24	C₁₉×#427	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#367	C₂²	1	4	yes	—
27	C₁₉×#366	C₂²	1	4	yes	—
28	C₁₉×C₄⋊C₁₆	C₂²	1	2	yes	—
29	C₁₉×#358	C₂²	1	4	yes	—
30	C₁₉×#358	C₂²	1	4	yes	—
31	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₁₉×#346	C₂²	1	2	yes	—
33	C₂×Q₁₆×C₁₉	—	2	1	no	—
34	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	2	1	no	—
40	C₁₉×C₄⋊Q₈	—	2	1	no	—
41	C₁₉×#125	—	2	2	no	—
42	C₁₉×#125	—	4	1	no	—
43	C₁₉×C₂²⋊Q₈	—	2	2	no	—
44	C₁₉×C₂²⋊Q₈	—	4	1	no	—
45	C₁₉×C₂²⋊Q₈	—	4	1	no	—
46	C₁₉×C₂²⋊Q₈	—	4	1	no	—
47	C₄×Q₈×C₁₉	—	2	2	no	—
48	C₄×Q₈×C₁₉	—	4	1	no	—
49	C₄×Q₈×C₁₉	—	4	1	no	—
50	C₄×Q₈×C₁₉	—	4	1	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	—	4	1	no	—
53	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
54	C₂×C₁₆×C₁₉	C₂³	1	4	yes	—
55	C₁₉×#107	—	2	1	no	—
56	C₁₉×#107	—	2	1	no	—
57	C₁₉×#107	—	2	1	no	—
58	C₁₉×#107	C₂³	1	2	yes	—
59	C₁₉×#107	C₂³	1	2	yes	—
60	C₁₉×#107	C₂³	1	2	yes	—
61	C₁₉×#106	—	2	2	no	—
62	C₁₉×#106	—	2	2	no	—
63	C₁₉×#103	—	2	2	no	—
64	C₁₉×#103	—	2	2	no	—
65	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
66	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
67	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₁₉	—	2	2	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	Q₁₆×C₁₉	—	2	4	no	—
77	Q₁₆×C₁₉	—	4	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	—	2	2	no	—
80	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	—	2	2	no	—
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	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	4	2	no	—
91	C₄⋊C₄×C₁₉	—	4	2	no	—
92	C₄⋊C₄×C₁₉	—	4	2	no	—
93	C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₂²⋊C₄×C₁₉	—	4	2	no	—
97	C₂²⋊C₄×C₁₉	—	4	2	no	—
98	C₄²×C₁₉	—	4	2	no	—
99	C₄²×C₁₉	—	4	2	no	—
100	C₄²×C₁₉	D₈	1	1	yes	characteristic
101	C₄²×C₁₉	D₈	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₁₆×C₁₉	—	2	4	no	—
105	#33803	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
107	Q₈×C₁₉	—	4	2	no	—
108	Q₈×C₁₉	—	4	2	no	—
109	Q₈×C₁₉	—	8	2	no	—
110	Q₈×C₁₉	—	8	2	no	—
111	Q₈×C₁₉	—	8	2	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	2	no	—
117	C₂×C₄×C₁₉	—	4	2	no	—
118	C₂×C₄×C₁₉	—	4	2	no	—
119	C₂×C₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
123	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
126	C₈×C₁₉	—	2	1	no	—
127	C₈×C₁₉	—	2	1	no	—
128	C₈×C₁₉	#137	1	2	yes	—
129	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
130	#3170	C₂×C₁₉	1	1	yes	characteristic
131	#3160	C₂×C₁₉	1	1	yes	characteristic
132	#2255	C₂×C₁₉	1	2	yes	complemented
133	#2245	C₂×C₁₉	1	2	yes	complemented
134	#2237	C₂×C₁₉	1	4	yes	—
135	#2227	C₂×C₁₉	1	2	yes	complemented
136	#2225	C₂×C₁₉	1	2	yes	complemented
137	#2163	C₂×C₁₉	1	1	yes	characteristic
138	C₂²×C₁₉	—	2	1	no	—
139	C₂²×C₁₉	—	2	1	no	—
140	C₂²×C₁₉	—	2	1	no	—
141	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	8	2	no	—
147	C₄×C₁₉	—	8	2	no	—
148	C₄×C₁₉	—	8	2	no	—
149	C₄×C₁₉	—	8	2	no	—
150	C₄×C₁₉	#510	1	2	yes	—
151	C₄×C₁₉	#536	1	1	yes	characteristic
152	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
153	#533	—	2	1	no	—
154	#533	—	2	1	no	—
155	#500	C₂²×C₁₉	1	1	yes	characteristic
156	#500	C₂²×C₁₉	1	1	yes	characteristic
157	#500	C₂²×C₁₉	1	1	yes	characteristic
158	#499	—	2	1	no	—
159	#499	C₂²×C₁₉	1	2	yes	—
160	#498	—	2	1	no	—
161	#494	C₂²×C₁₉	1	1	yes	characteristic
162	#487	—	2	1	no	—
163	#467	—	2	1	no	—
164	#467	C₂²×C₁₉	1	2	yes	—
165	C₄×Q₁₆	—	2	1	no	—
166	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
167	#427	—	2	1	no	—
168	#427	C₂²×C₁₉	1	2	yes	—
169	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
170	#367	C₂²×C₁₉	1	4	yes	—
171	#366	C₂²×C₁₉	1	4	yes	—
172	C₄⋊C₁₆	C₂²×C₁₉	1	2	yes	—
173	#358	C₂²×C₁₉	1	4	yes	—
174	#358	C₂²×C₁₉	1	4	yes	—
175	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	—
176	#346	C₂²×C₁₉	1	2	yes	—
177	C₂×C₁₉	—	4	1	no	—
178	C₂×C₁₉	#3226	1	1	yes	characteristic
179	C₂×C₁₉	C₂×#510	1	1	yes	characteristic
180	C₂×C₁₉	#3414	1	1	yes	characteristic
181	C₂×Q₁₆	—	2	1	no	—
182	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
183	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
184	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
185	C₄⋊Q₈	—	2	1	no	—
186	C₄⋊Q₈	—	2	1	no	—
187	C₄⋊Q₈	—	2	1	no	—
188	C₄⋊Q₈	—	2	1	no	—
189	#125	—	2	2	no	—
190	#125	—	4	1	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	4	1	no	—
193	C₂²⋊Q₈	—	4	1	no	—
194	C₂²⋊Q₈	—	4	1	no	—
195	C₄×Q₈	—	2	2	no	—
196	C₄×Q₈	—	4	1	no	—
197	C₄×Q₈	—	4	1	no	—
198	C₄×Q₈	—	4	1	no	—
199	#117	—	2	2	no	—
200	#117	—	4	1	no	—
201	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
202	C₂×C₁₆	C₂³×C₁₉	1	4	yes	—
203	#107	—	2	1	no	—
204	#107	—	2	1	no	—
205	#107	—	2	1	no	—
206	#107	C₂³×C₁₉	1	2	yes	—
207	#107	C₂³×C₁₉	1	2	yes	—
208	#107	C₂³×C₁₉	1	2	yes	—
209	#106	—	2	2	no	—
210	#106	—	2	2	no	—
211	#103	—	2	2	no	—
212	#103	—	2	2	no	—
213	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
214	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
215	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
216	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
217	C₁₉	#33803	1	1	yes	characteristic, direct product factor, Sylow
218	C₂×Q₈	—	2	2	no	—
219	C₂×Q₈	—	4	1	no	—
220	C₂×Q₈	—	4	1	no	—
221	C₂×Q₈	—	4	1	no	—
222	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
223	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
224	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
225	Q₁₆	—	2	4	no	—
226	Q₁₆	—	4	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
230	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
231	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
232	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
233	C₄⋊C₄	—	2	2	no	—
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	C₄⋊C₄	—	4	2	no	—
239	C₄⋊C₄	—	4	2	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₄⋊C₄	—	4	2	no	—
242	C₄⋊C₄	—	4	1	no	—
243	C₄⋊C₄	—	4	1	no	—
244	C₄⋊C₄	—	4	1	no	—
245	C₂²⋊C₄	—	4	2	no	—
246	C₂²⋊C₄	—	4	2	no	—
247	C₄²	—	4	2	no	—
248	C₄²	—	4	2	no	—
249	C₄²	D₈×C₁₉	1	1	yes	characteristic
250	C₄²	D₈×C₁₉	1	1	yes	characteristic
251	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
252	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
253	C₁₆	—	2	4	no	—
254	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
255	Q₈	—	4	2	no	—
256	Q₈	—	4	2	no	—
257	Q₈	—	8	2	no	—
258	Q₈	—	8	2	no	—
259	Q₈	—	8	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	4	1	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	2	no	—
268	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
269	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
270	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
271	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
272	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
273	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
274	C₈	—	2	1	no	—
275	C₈	—	2	1	no	—
276	C₈	C₁₉×#137	1	2	yes	—
277	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
278	C₂²	—	2	1	no	—
279	C₂²	—	2	1	no	—
280	C₂²	—	2	1	no	—
281	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
282	C₄	—	2	1	no	—
283	C₄	—	2	1	no	—
284	C₄	—	2	1	no	—
285	C₄	—	2	1	no	—
286	C₄	—	8	2	no	—
287	C₄	—	8	2	no	—
288	C₄	—	8	2	no	—
289	C₄	—	8	2	no	—
290	C₄	C₁₉×#510	1	2	yes	—
291	C₄	C₁₉×#536	1	1	yes	characteristic
292	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
293	C₂	—	4	1	no	—
294	C₂	C₁₉×#3226	1	1	yes	characteristic
295	C₂	C₂×C₁₉×#510	1	1	yes	characteristic
296	C₂	C₁₉×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2255	C₂	semidirect
4. C₁₉×#2245	C₂	semidirect
6. C₁₉×#2227	C₂	semidirect
7. C₁₉×#2225	C₂	semidirect
105. #33803	C₁₉	direct (N × H)
132. #2255	C₂×C₁₉	semidirect
133. #2245	C₂×C₁₉	semidirect
135. #2227	C₂×C₁₉	semidirect
136. #2225	C₂×C₁₉	semidirect
217. C₁₉	#33803	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×#3170	2
C₁₉×#3160	2
C₁₉×#2255	2
C₁₉×#2245	2
C₁₉×#2237	2
C₁₉×#2227	2
C₁₉×#2225	2
C₁₉×#2163	2
#33803	19

Subgroups — C19×#33803 #18039762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33803 #18039762