Subgroups — C₁₉×#34530 #18040489

Order 4864.

1800 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#564	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2382	C₂	1	3	yes	maximal
3	C₁₉×#2371	C₂	1	6	yes	maximal
4	C₁₉×#2370	C₂	1	6	yes	maximal
5	C₁₉×#2336	C₂	1	6	yes	maximal
6	C₁₉×#2330	C₂	1	6	yes	maximal
7	C₄×C₁₉×#125	C₂	1	3	yes	maximal
8	C₁₉×#564	C₄	1	16	yes	complemented
9	C₂×C₁₉×#125	C₂²	1	3	yes	—
10	C₂×C₁₉×#125	C₂²	1	6	yes	—
11	C₂×C₁₉×#125	C₂²	1	6	yes	—
12	C₁₉×#389	C₂²	1	3	yes	—
13	C₁₉×#389	C₂²	1	3	yes	—
14	C₁₉×#389	C₂²	1	6	yes	—
15	C₁₉×#389	C₂²	1	6	yes	—
16	C₁₉×#389	C₂²	1	6	yes	—
17	C₁₉×#389	C₂²	1	6	yes	—
18	C₁₉×#387	C₂²	1	6	yes	—
19	C₁₉×#387	C₂²	1	6	yes	—
20	C₁₉×#387	C₂²	1	6	yes	—
21	C₁₉×#387	C₂²	1	6	yes	—
22	C₁₉×#387	C₂²	1	6	yes	—
23	C₁₉×#387	C₂²	1	6	yes	—
24	C₁₉×#387	C₂²	1	6	yes	—
25	C₁₉×#387	C₂²	1	6	yes	—
26	C₁₉×#387	C₂²	1	6	yes	—
27	C₁₉×#387	C₂²	1	6	yes	—
28	C₁₉×#384	C₂²	1	2	yes	—
29	C₁₉×#383	C₂²	1	2	yes	—
30	C₁₉×#382	C₂²	1	3	yes	—
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
38	C₁₉×#376	C₂²	1	6	yes	—
39	C₄³×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#125	C₂×C₄	1	24	yes	—
41	C₁₉×#125	C₂×C₄	1	48	yes	—
42	C₁₉×#125	C₂×C₄	1	48	yes	—
43	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
44	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
48	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
49	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
50	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
55	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
56	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
57	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
58	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
59	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
60	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
61	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#95	C₂³	1	6	yes	—
65	C₁₉×#95	C₂³	1	6	yes	—
66	C₁₉×#95	C₂³	1	6	yes	—
67	C₁₉×#95	C₂³	1	6	yes	—
68	C₁₉×#95	C₂³	1	6	yes	—
69	C₁₉×#95	C₂³	1	6	yes	—
70	C₁₉×#95	C₂³	1	6	yes	—
71	C₁₉×#95	C₂³	1	6	yes	—
72	C₁₉×#95	C₂³	1	6	yes	—
73	C₁₉×#95	C₂³	1	6	yes	—
74	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
75	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
77	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
78	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
79	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
80	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
81	C₄⋊C₄×C₁₉	—	2	12	no	—
82	C₄⋊C₄×C₁₉	—	4	6	no	—
83	C₄⋊C₄×C₁₉	—	4	3	no	—
84	C₄⋊C₄×C₁₉	—	4	6	no	—
85	C₄⋊C₄×C₁₉	—	4	6	no	—
86	C₄⋊C₄×C₁₉	—	4	3	no	—
87	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
88	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
89	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
90	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
91	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
92	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
93	C₄²×C₁₉	—	2	6	no	—
94	C₄²×C₁₉	—	2	12	no	—
95	C₄²×C₁₉	—	4	6	no	—
96	C₄²×C₁₉	—	4	3	no	—
97	C₄²×C₁₉	—	4	6	no	—
98	C₄²×C₁₉	—	4	6	no	—
99	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
100	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
101	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
102	#34530	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
104	C₂×C₄×C₁₉	—	2	3	no	—
105	C₂×C₄×C₁₉	—	2	6	no	—
106	C₂×C₄×C₁₉	—	2	3	no	—
107	C₂×C₄×C₁₉	—	2	6	no	—
108	C₂×C₄×C₁₉	—	2	3	no	—
109	C₂×C₄×C₁₉	—	2	6	no	—
110	C₂×C₄×C₁₉	—	2	3	no	—
111	C₂×C₄×C₁₉	—	2	6	no	—
112	C₂×C₄×C₁₉	—	2	6	no	—
113	C₂×C₄×C₁₉	—	2	6	no	—
114	C₂×C₄×C₁₉	—	2	6	no	—
115	C₂×C₄×C₁₉	—	2	6	no	—
116	C₂×C₄×C₁₉	—	2	6	no	—
117	C₂×C₄×C₁₉	—	2	3	no	—
118	C₂×C₄×C₁₉	—	2	6	no	—
119	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
120	C₂×C₄×C₁₉	C₂³×C₄	1	12	yes	—
121	C₂×C₄×C₁₉	C₂³×C₄	1	12	yes	—
122	C₂×C₄×C₁₉	2₋¹⁺⁴	1	6	yes	—
123	C₂×#564	C₂×C₁₉	1	1	yes	characteristic
124	#2382	C₂×C₁₉	1	3	yes	—
125	#2371	C₂×C₁₉	1	6	yes	—
126	#2370	C₂×C₁₉	1	6	yes	—
127	#2336	C₂×C₁₉	1	6	yes	—
128	#2330	C₂×C₁₉	1	6	yes	—
129	C₄×#125	C₂×C₁₉	1	3	yes	—
130	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
131	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	3	yes	—
132	C₂²×C₁₉	#585	1	3	yes	—
133	C₄×C₁₉	—	2	6	no	—
134	C₄×C₁₉	—	2	12	no	—
135	C₄×C₁₉	—	2	12	no	—
136	C₄×C₁₉	—	2	6	no	—
137	C₄×C₁₉	—	4	6	no	—
138	C₄×C₁₉	—	4	6	no	—
139	C₄×C₁₉	—	4	1	no	—
140	#564	C₄×C₁₉	1	16	yes	complemented
141	C₂×#125	C₂²×C₁₉	1	3	yes	—
142	C₂×#125	C₂²×C₁₉	1	6	yes	—
143	C₂×#125	C₂²×C₁₉	1	6	yes	—
144	#389	C₂²×C₁₉	1	3	yes	—
145	#389	C₂²×C₁₉	1	3	yes	—
146	#389	C₂²×C₁₉	1	6	yes	—
147	#389	C₂²×C₁₉	1	6	yes	—
148	#389	C₂²×C₁₉	1	6	yes	—
149	#389	C₂²×C₁₉	1	6	yes	—
150	#387	C₂²×C₁₉	1	6	yes	—
151	#387	C₂²×C₁₉	1	6	yes	—
152	#387	C₂²×C₁₉	1	6	yes	—
153	#387	C₂²×C₁₉	1	6	yes	—
154	#387	C₂²×C₁₉	1	6	yes	—
155	#387	C₂²×C₁₉	1	6	yes	—
156	#387	C₂²×C₁₉	1	6	yes	—
157	#387	C₂²×C₁₉	1	6	yes	—
158	#387	C₂²×C₁₉	1	6	yes	—
159	#387	C₂²×C₁₉	1	6	yes	—
160	#384	C₂²×C₁₉	1	2	yes	—
161	#383	C₂²×C₁₉	1	2	yes	—
162	#382	C₂²×C₁₉	1	3	yes	—
163	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
164	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
165	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
166	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
167	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
168	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
169	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
170	#376	C₂²×C₁₉	1	6	yes	—
171	C₄³	C₂²×C₁₉	1	1	yes	characteristic
172	C₂×C₁₉	C₄×2₋¹⁺⁴	1	3	yes	—
173	C₂×C₁₉	#3563	1	3	yes	—
174	C₂×C₁₉	#3567	1	1	yes	characteristic
175	#125	C₂×C₄×C₁₉	1	24	yes	—
176	#125	C₂×C₄×C₁₉	1	48	yes	—
177	#125	C₂×C₄×C₁₉	1	48	yes	—
178	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
179	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
180	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
181	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
182	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
183	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
184	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
185	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
186	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
187	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
188	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
189	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
190	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
191	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
192	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
193	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
194	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
195	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
196	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
197	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
198	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
199	#95	C₂³×C₁₉	1	6	yes	—
200	#95	C₂³×C₁₉	1	6	yes	—
201	#95	C₂³×C₁₉	1	6	yes	—
202	#95	C₂³×C₁₉	1	6	yes	—
203	#95	C₂³×C₁₉	1	6	yes	—
204	#95	C₂³×C₁₉	1	6	yes	—
205	#95	C₂³×C₁₉	1	6	yes	—
206	#95	C₂³×C₁₉	1	6	yes	—
207	#95	C₂³×C₁₉	1	6	yes	—
208	#95	C₂³×C₁₉	1	6	yes	—
209	C₁₉	#34530	1	1	yes	characteristic, direct product factor, Sylow
210	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
211	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
212	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
213	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
214	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
215	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
216	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
217	C₄⋊C₄	—	2	12	no	—
218	C₄⋊C₄	—	4	6	no	—
219	C₄⋊C₄	—	4	3	no	—
220	C₄⋊C₄	—	4	6	no	—
221	C₄⋊C₄	—	4	6	no	—
222	C₄⋊C₄	—	4	3	no	—
223	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
224	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
225	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
226	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
227	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
228	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
229	C₄²	—	2	6	no	—
230	C₄²	—	2	12	no	—
231	C₄²	—	4	6	no	—
232	C₄²	—	4	3	no	—
233	C₄²	—	4	6	no	—
234	C₄²	—	4	6	no	—
235	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
236	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
237	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
238	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
239	C₂×C₄	—	2	3	no	—
240	C₂×C₄	—	2	6	no	—
241	C₂×C₄	—	2	3	no	—
242	C₂×C₄	—	2	6	no	—
243	C₂×C₄	—	2	3	no	—
244	C₂×C₄	—	2	6	no	—
245	C₂×C₄	—	2	3	no	—
246	C₂×C₄	—	2	6	no	—
247	C₂×C₄	—	2	6	no	—
248	C₂×C₄	—	2	6	no	—
249	C₂×C₄	—	2	6	no	—
250	C₂×C₄	—	2	6	no	—
251	C₂×C₄	—	2	6	no	—
252	C₂×C₄	—	2	3	no	—
253	C₂×C₄	—	2	6	no	—
254	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
255	C₂×C₄	C₂³×C₄×C₁₉	1	12	yes	—
256	C₂×C₄	C₂³×C₄×C₁₉	1	12	yes	—
257	C₂×C₄	C₁₉×2₋¹⁺⁴	1	6	yes	—
258	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
259	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	3	yes	—
260	C₂²	C₁₉×#585	1	3	yes	—
261	C₄	—	2	6	no	—
262	C₄	—	2	12	no	—
263	C₄	—	2	12	no	—
264	C₄	—	2	6	no	—
265	C₄	—	4	6	no	—
266	C₄	—	4	6	no	—
267	C₄	—	4	1	no	—
268	C₂	C₄×C₁₉×2₋¹⁺⁴	1	3	yes	—
269	C₂	C₁₉×#3563	1	3	yes	—
270	C₂	C₁₉×#3567	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₉×#564	C₄	semidirect
102. #34530	C₁₉	direct (N × H)
140. #564	C₄×C₁₉	semidirect
209. C₁₉	#34530	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#564	2
C₁₉×#2382	2
C₁₉×#2371	2
C₁₉×#2370	2
C₁₉×#2336	2
C₁₉×#2330	2
C₄×C₁₉×#125	2
#34530	19

Subgroups — C19×#34530 #18040489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34530 #18040489