Subgroups — C₁₉×#34375 #18040334

Order 4864.

1898 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2381	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2371	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2355	C₂	1	8	yes	maximal, complemented
5	C₁₉×#2332	C₂	1	8	yes	maximal
6	C₁₉×#2314	C₂	1	4	yes	maximal
7	C₁₉×#2283	C₂	1	2	yes	maximal
8	C₁₉×#533	C₄	1	16	yes	complemented
9	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₂×C₁₉×#125	C₂²	1	2	yes	—
11	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
13	C₂×C₁₉×#117	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#391	C₂²	1	16	yes	—
16	C₁₉×#388	C₂²	1	16	yes	—
17	C₁₉×#387	C₂²	1	16	yes	—
18	C₁₉×#387	C₂²	1	16	yes	—
19	C₁₉×#387	C₂²	1	16	yes	—
20	C₁₉×#384	C₂²	1	4	yes	—
21	C₁₉×#383	C₂²	1	4	yes	—
22	C₁₉×#382	C₂²	1	4	yes	—
23	C₁₉×#382	C₂²	1	4	yes	—
24	C₁₉×#381	C₂²	1	4	yes	—
25	C₁₉×#380	C₂²	1	4	yes	—
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	—
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
30	C₁₉×#376	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
34	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
35	C₁₉×#125	C₂×C₄	1	16	yes	—
36	C₁₉×C₂²⋊Q₈	C₂×C₄	1	32	yes	—
37	C₄×Q₈×C₁₉	C₂×C₄	1	32	yes	—
38	C₁₉×#117	C₂×C₄	1	16	yes	—
39	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
40	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
41	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
42	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
44	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
45	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
46	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
47	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
48	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#95	C₂³	1	8	yes	—
54	C₁₉×#95	C₂³	1	8	yes	—
55	C₁₉×#95	C₂³	1	8	yes	—
56	C₁₉×#95	C₂³	1	8	yes	—
57	C₁₉×#95	C₂³	1	16	yes	—
58	C₁₉×#95	C₂³	1	16	yes	—
59	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
60	C₂×Q₈×C₁₉	—	4	4	no	—
61	C₂×Q₈×C₁₉	—	4	4	no	—
62	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	4	4	no	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
66	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
67	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
68	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
70	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
72	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₄⋊C₄×C₁₉	—	2	16	no	—
74	C₄⋊C₄×C₁₉	—	4	16	no	—
75	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
76	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
77	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
78	C₂²⋊C₄×C₁₉	—	4	8	no	—
79	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
80	C₄²×C₁₉	—	4	8	no	—
81	C₄²×C₁₉	—	4	16	no	—
82	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
83	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
84	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
85	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
86	#34375	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂³×C₁₉	—	2	2	no	—
88	C₂³×C₁₉	—	2	4	no	—
89	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
90	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
91	Q₈×C₁₉	—	4	16	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	4	no	—
94	C₂×C₄×C₁₉	—	2	8	no	—
95	C₂×C₄×C₁₉	—	2	8	no	—
96	C₂×C₄×C₁₉	—	2	4	no	—
97	C₂×C₄×C₁₉	—	2	8	no	—
98	C₂×C₄×C₁₉	—	2	16	no	—
99	C₂×C₄×C₁₉	—	2	16	no	—
100	C₂×C₄×C₁₉	—	2	16	no	—
101	C₂×C₄×C₁₉	—	4	8	no	—
102	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
103	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
104	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
105	C₂×C₄×C₁₉	C₂³×C₄	1	16	yes	—
106	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
107	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
108	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
109	#2381	C₂×C₁₉	1	4	yes	complemented
110	#2371	C₂×C₁₉	1	4	yes	complemented
111	#2355	C₂×C₁₉	1	8	yes	complemented
112	#2332	C₂×C₁₉	1	8	yes	—
113	#2314	C₂×C₁₉	1	4	yes	—
114	#2283	C₂×C₁₉	1	2	yes	—
115	C₂²×C₁₉	—	2	2	no	—
116	C₂²×C₁₉	—	2	4	no	—
117	C₂²×C₁₉	—	4	4	no	—
118	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
119	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
120	C₂²×C₁₉	#585	1	4	yes	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	2	4	no	—
123	C₄×C₁₉	—	2	4	no	—
124	C₄×C₁₉	—	2	16	no	—
125	C₄×C₁₉	—	4	16	no	—
126	C₄×C₁₉	#519	1	4	yes	—
127	#533	C₄×C₁₉	1	16	yes	complemented
128	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
129	C₂×#125	C₂²×C₁₉	1	2	yes	—
130	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
131	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
132	C₂×#117	C₂²×C₁₉	1	2	yes	—
133	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
134	#391	C₂²×C₁₉	1	16	yes	—
135	#388	C₂²×C₁₉	1	16	yes	—
136	#387	C₂²×C₁₉	1	16	yes	—
137	#387	C₂²×C₁₉	1	16	yes	—
138	#387	C₂²×C₁₉	1	16	yes	—
139	#384	C₂²×C₁₉	1	4	yes	—
140	#383	C₂²×C₁₉	1	4	yes	—
141	#382	C₂²×C₁₉	1	4	yes	—
142	#382	C₂²×C₁₉	1	4	yes	—
143	#381	C₂²×C₁₉	1	4	yes	—
144	#380	C₂²×C₁₉	1	4	yes	—
145	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
146	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	—
147	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
148	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
149	#376	C₂²×C₁₉	1	4	yes	—
150	C₂×C₁₉	—	4	2	no	—
151	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
152	C₂×C₁₉	#3428	1	2	yes	—
153	C₂×C₁₉	#3557	1	4	yes	—
154	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
155	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
156	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
157	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
158	#125	C₂×C₄×C₁₉	1	16	yes	—
159	C₂²⋊Q₈	C₂×C₄×C₁₉	1	32	yes	—
160	C₄×Q₈	C₂×C₄×C₁₉	1	32	yes	—
161	#117	C₂×C₄×C₁₉	1	16	yes	—
162	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
163	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
164	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
165	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
166	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
167	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
168	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
169	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
170	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
171	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
172	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
173	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
174	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
175	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
176	#95	C₂³×C₁₉	1	8	yes	—
177	#95	C₂³×C₁₉	1	8	yes	—
178	#95	C₂³×C₁₉	1	8	yes	—
179	#95	C₂³×C₁₉	1	8	yes	—
180	#95	C₂³×C₁₉	1	16	yes	—
181	#95	C₂³×C₁₉	1	16	yes	—
182	C₁₉	#34375	1	1	yes	characteristic, direct product factor, Sylow
183	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
187	C₂²×C₄	—	2	4	no	—
188	C₂²×C₄	—	4	4	no	—
189	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
190	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
191	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
192	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
193	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
194	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
195	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
196	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
197	C₄⋊C₄	—	2	16	no	—
198	C₄⋊C₄	—	4	16	no	—
199	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
200	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
201	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
202	C₂²⋊C₄	—	4	8	no	—
203	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
204	C₄²	—	4	8	no	—
205	C₄²	—	4	16	no	—
206	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
207	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
208	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
209	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
210	C₂³	—	2	2	no	—
211	C₂³	—	2	4	no	—
212	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
213	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
214	Q₈	—	4	16	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	8	no	—
218	C₂×C₄	—	2	8	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	8	no	—
221	C₂×C₄	—	2	16	no	—
222	C₂×C₄	—	2	16	no	—
223	C₂×C₄	—	2	16	no	—
224	C₂×C₄	—	4	8	no	—
225	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
226	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
227	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
228	C₂×C₄	C₂³×C₄×C₁₉	1	16	yes	—
229	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
230	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	4	no	—
233	C₂²	—	4	4	no	—
234	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
235	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
236	C₂²	C₁₉×#585	1	4	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	4	no	—
239	C₄	—	2	4	no	—
240	C₄	—	2	16	no	—
241	C₄	—	4	16	no	—
242	C₄	C₁₉×#519	1	4	yes	—
243	C₂	—	4	2	no	—
244	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
245	C₂	C₁₉×#3428	1	2	yes	—
246	C₂	C₁₉×#3557	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
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
2. C₁₉×#2381	C₂	semidirect
3. C₁₉×#2371	C₂	semidirect
4. C₁₉×#2355	C₂	semidirect
8. C₁₉×#533	C₄	semidirect
86. #34375	C₁₉	direct (N × H)
109. #2381	C₂×C₁₉	semidirect
110. #2371	C₂×C₁₉	semidirect
111. #2355	C₂×C₁₉	semidirect
127. #533	C₄×C₁₉	semidirect
182. C₁₉	#34375	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×#533	2
C₁₉×#2381	2
C₁₉×#2371	2
C₁₉×#2355	2
C₁₉×#2332	2
C₁₉×#2314	2
C₁₉×#2283	2
#34375	19

Subgroups — C19×#34375 #18040334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34375 #18040334