Subgroups — C₁₉×#33956 #18039915

Order 4864.

472 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3380	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2255	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2228	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2228	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2224	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2183	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2177	C₂	1	2	yes	maximal
9	C₄×C₁₉×D₁₆	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#554	—	2	2	no	—
11	C₂×C₁₉×D₁₆	C₂²	1	1	yes	characteristic
12	C₁₉×#500	C₂²	1	2	yes	—
13	C₁₉×#499	C₂²	1	2	yes	—
14	C₁₉×#499	C₂²	1	2	yes	—
15	C₁₉×#478	—	2	2	no	—
16	C₁₉×#478	—	2	2	no	—
17	C₁₉×#476	—	2	2	no	—
18	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×D₈×C₁₉	C₂²	1	2	yes	—
20	C₄×D₈×C₁₉	C₂²	1	2	yes	—
21	C₄×D₈×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#367	C₂²	1	2	yes	—
23	C₁₉×#367	C₂²	1	2	yes	—
24	C₁₉×#366	C₂²	1	1	yes	characteristic
25	C₁₉×#366	C₂²	1	1	yes	characteristic
26	C₁₉×#366	C₂²	1	2	yes	—
27	C₁₉×#366	C₂²	1	1	yes	characteristic
28	C₁₉×C₄⋊C₁₆	C₂²	1	2	yes	—
29	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₁₉×#357	C₂²	1	2	yes	—
31	C₁₉×#357	C₂²	1	2	yes	—
32	C₁₉×#357	C₂²	1	2	yes	—
33	C₁₉×#346	C₂²	1	2	yes	—
34	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
35	C₂×D₈×C₁₉	C₂³	1	2	yes	—
36	C₁₉×C₄⋊Q₈	—	2	2	no	—
37	C₁₉×#125	—	2	2	no	—
38	C₁₉×#125	—	2	2	no	—
39	C₁₉×C₂²⋊Q₈	—	4	2	no	—
40	C₁₉×C₂²⋊Q₈	—	4	2	no	—
41	C₁₉×C₂²⋊Q₈	—	4	2	no	—
42	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×D₄×C₁₉	—	2	2	no	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₄×D₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
47	C₁₉×D₁₆	Q₈	1	4	yes	complemented
48	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
50	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
51	C₁₉×#107	—	2	2	no	—
52	C₁₉×#107	C₂³	1	2	yes	—
53	C₁₉×#107	C₂³	1	2	yes	—
54	C₁₉×#107	C₂³	1	2	yes	—
55	C₁₉×#106	—	2	2	no	—
56	C₁₉×#106	—	2	2	no	—
57	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
58	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
59	C₁₉×#102	—	2	2	no	—
60	C₁₉×#102	—	2	2	no	—
61	C₁₉×#102	—	2	2	no	—
62	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₄×C₈×C₁₉	C₂³	1	2	yes	—
64	C₂×Q₈×C₁₉	—	4	2	no	—
65	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	D₈×C₁₉	—	2	2	no	—
71	D₈×C₁₉	C₂×Q₈	1	4	yes	—
72	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	4	2	no	—
79	C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₄⋊C₄×C₁₉	—	4	2	no	—
81	C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₄⋊C₄×C₁₉	—	4	2	no	—
83	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
84	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
85	C₂²⋊C₄×C₁₉	—	4	2	no	—
86	C₂²⋊C₄×C₁₉	—	4	2	no	—
87	C₂²⋊C₄×C₁₉	—	4	2	no	—
88	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₄²×C₁₉	C₂×D₄	1	2	yes	—
90	C₁₆×C₁₉	—	2	1	no	—
91	C₁₆×C₁₉	—	2	2	no	—
92	C₁₆×C₁₉	C₂×Q₈	1	2	yes	—
93	#33956	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂³×C₁₉	—	4	2	no	—
95	Q₈×C₁₉	—	4	1	no	—
96	Q₈×C₁₉	—	16	2	no	—
97	D₄×C₁₉	—	2	4	no	—
98	D₄×C₁₉	—	4	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	8	4	no	—
103	C₂×C₄×C₁₉	—	16	2	no	—
104	C₂×C₄×C₁₉	—	16	2	no	—
105	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
108	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	2	no	—
112	C₈×C₁₉	C₂²×Q₈	1	1	yes	characteristic
113	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
114	#3380	C₂×C₁₉	1	2	yes	complemented
115	#2255	C₂×C₁₉	1	2	yes	complemented
116	#2253	C₂×C₁₉	1	1	yes	characteristic, complemented
117	#2228	C₂×C₁₉	1	2	yes	complemented
118	#2228	C₂×C₁₉	1	2	yes	complemented
119	#2224	C₂×C₁₉	1	2	yes	complemented
120	#2183	C₂×C₁₉	1	1	yes	characteristic, complemented
121	#2177	C₂×C₁₉	1	2	yes	—
122	C₄×D₁₆	C₂×C₁₉	1	1	yes	characteristic
123	C₂²×C₁₉	—	4	4	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	—	8	2	no	—
126	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
127	C₄×C₁₉	—	2	2	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	—	8	2	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	D₄×Q₈	1	1	yes	characteristic
135	C₄×C₁₉	#578	1	1	yes	characteristic
136	#554	—	2	2	no	—
137	C₂×D₁₆	C₂²×C₁₉	1	1	yes	characteristic
138	#500	C₂²×C₁₉	1	2	yes	—
139	#499	C₂²×C₁₉	1	2	yes	—
140	#499	C₂²×C₁₉	1	2	yes	—
141	#478	—	2	2	no	—
142	#478	—	2	2	no	—
143	#476	—	2	2	no	—
144	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
145	C₄×D₈	C₂²×C₁₉	1	2	yes	—
146	C₄×D₈	C₂²×C₁₉	1	2	yes	—
147	C₄×D₈	C₂²×C₁₉	1	2	yes	—
148	#367	C₂²×C₁₉	1	2	yes	—
149	#367	C₂²×C₁₉	1	2	yes	—
150	#366	C₂²×C₁₉	1	1	yes	characteristic
151	#366	C₂²×C₁₉	1	1	yes	characteristic
152	#366	C₂²×C₁₉	1	2	yes	—
153	#366	C₂²×C₁₉	1	1	yes	characteristic
154	C₄⋊C₁₆	C₂²×C₁₉	1	2	yes	—
155	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
156	#357	C₂²×C₁₉	1	2	yes	—
157	#357	C₂²×C₁₉	1	2	yes	—
158	#357	C₂²×C₁₉	1	2	yes	—
159	#346	C₂²×C₁₉	1	2	yes	—
160	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
161	C₂×C₁₉	—	8	4	no	—
162	C₂×C₁₉	Q₈×D₈	1	1	yes	characteristic
163	C₂×C₁₉	#3414	1	1	yes	characteristic
164	C₂×C₁₉	#3415	1	1	yes	characteristic
165	C₂×D₈	C₂³×C₁₉	1	2	yes	—
166	C₄⋊Q₈	—	2	2	no	—
167	#125	—	2	2	no	—
168	#125	—	2	2	no	—
169	C₂²⋊Q₈	—	4	2	no	—
170	C₂²⋊Q₈	—	4	2	no	—
171	C₂²⋊Q₈	—	4	2	no	—
172	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	2	2	no	—
175	C₄×D₄	—	2	2	no	—
176	C₂×C₄⋊C₄	—	4	2	no	—
177	D₁₆	Q₈×C₁₉	1	4	yes	complemented
178	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
179	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
180	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
181	#107	—	2	2	no	—
182	#107	C₂³×C₁₉	1	2	yes	—
183	#107	C₂³×C₁₉	1	2	yes	—
184	#107	C₂³×C₁₉	1	2	yes	—
185	#106	—	2	2	no	—
186	#106	—	2	2	no	—
187	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
188	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
189	#102	—	2	2	no	—
190	#102	—	2	2	no	—
191	#102	—	2	2	no	—
192	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
193	C₄×C₈	C₂³×C₁₉	1	2	yes	—
194	C₁₉	#33956	1	1	yes	characteristic, direct product factor, Sylow
195	C₂×Q₈	—	4	2	no	—
196	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
197	C₂×D₄	—	2	2	no	—
198	C₂²×C₄	—	4	2	no	—
199	C₂²×C₄	—	4	2	no	—
200	C₂²×C₄	—	4	2	no	—
201	D₈	—	2	2	no	—
202	D₈	C₂×Q₈×C₁₉	1	4	yes	—
203	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
204	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
205	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	—	4	2	no	—
211	C₄⋊C₄	—	4	2	no	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	4	2	no	—
214	C₄⋊C₄	D₈×C₁₉	1	2	yes	—
215	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
216	C₂²⋊C₄	—	4	2	no	—
217	C₂²⋊C₄	—	4	2	no	—
218	C₂²⋊C₄	—	4	2	no	—
219	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
220	C₄²	C₂×D₄×C₁₉	1	2	yes	—
221	C₁₆	—	2	1	no	—
222	C₁₆	—	2	2	no	—
223	C₁₆	C₂×Q₈×C₁₉	1	2	yes	—
224	C₂³	—	4	2	no	—
225	Q₈	—	4	1	no	—
226	Q₈	—	16	2	no	—
227	D₄	—	2	4	no	—
228	D₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	8	4	no	—
233	C₂×C₄	—	16	2	no	—
234	C₂×C₄	—	16	2	no	—
235	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
236	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
237	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
238	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
239	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
240	C₈	—	2	1	no	—
241	C₈	—	2	2	no	—
242	C₈	C₂²×Q₈×C₁₉	1	1	yes	characteristic
243	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
244	C₂²	—	4	4	no	—
245	C₂²	—	8	2	no	—
246	C₂²	—	8	2	no	—
247	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	2	no	—
252	C₄	—	8	2	no	—
253	C₄	—	8	2	no	—
254	C₄	—	8	2	no	—
255	C₄	D₄×Q₈×C₁₉	1	1	yes	characteristic
256	C₄	C₁₉×#578	1	1	yes	characteristic
257	C₂	—	8	4	no	—
258	C₂	Q₈×D₈×C₁₉	1	1	yes	characteristic
259	C₂	C₁₉×#3414	1	1	yes	characteristic
260	C₂	C₁₉×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×Q₈×C₁₉ ◁ C₈×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3380	C₂	semidirect
2. C₁₉×#2255	C₂	semidirect
3. C₁₉×#2253	C₂	semidirect
4. C₁₉×#2228	C₂	semidirect
5. C₁₉×#2228	C₂	semidirect
6. C₁₉×#2224	C₂	semidirect
7. C₁₉×#2183	C₂	semidirect
47. C₁₉×D₁₆	Q₈	semidirect
93. #33956	C₁₉	direct (N × H)
114. #3380	C₂×C₁₉	semidirect
115. #2255	C₂×C₁₉	semidirect
116. #2253	C₂×C₁₉	semidirect
117. #2228	C₂×C₁₉	semidirect
118. #2228	C₂×C₁₉	semidirect
119. #2224	C₂×C₁₉	semidirect
120. #2183	C₂×C₁₉	semidirect
177. D₁₆	Q₈×C₁₉	semidirect
194. C₁₉	#33956	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×#3380	2
C₁₉×#2255	2
C₁₉×#2253	2
C₁₉×#2228	2
C₁₉×#2224	2
C₁₉×#2183	2
C₁₉×#2177	2
C₄×C₁₉×D₁₆	2
#33956	19

Subgroups — C19×#33956 #18039915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33956 #18039915