Subgroups — C₁₉×#14609 #18020568

Order 4864.

1354 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#393	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1446	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1440	C₂	1	3	yes	maximal
4	C₁₉×#1437	C₂	1	3	yes	maximal
5	C₁₉×#1434	C₂	1	6	yes	maximal, complemented
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
11	C₁₉×#393	C₄	1	8	yes	complemented
12	C₂×C₁₉×#95	C₂²	1	6	yes	—
13	C₂×C₁₉×#95	C₂²	1	3	yes	—
14	C₂×C₁₉×#95	C₂²	1	6	yes	—
15	C₂×C₁₉×#95	C₂²	1	6	yes	—
16	C₂×C₁₉×#95	C₂²	1	3	yes	—
17	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	—	4	3	no	—
19	C₂²×Q₈×C₁₉	—	4	3	no	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
22	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	4	3	no	—
30	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
31	C₂×C₄²×C₁₉	—	2	12	no	—
32	C₂×C₄²×C₁₉	—	4	3	no	—
33	C₁₉×#95	—	2	12	no	—
34	C₁₉×#95	—	4	6	no	—
35	C₁₉×#95	—	4	3	no	—
36	C₁₉×#95	—	4	6	no	—
37	C₁₉×#95	C₂×C₄	1	12	yes	—
38	C₂⁴×C₁₉	—	2	6	no	—
39	C₂⁴×C₁₉	—	2	3	no	—
40	C₂⁴×C₁₉	—	2	3	no	—
41	C₂⁴×C₁₉	—	2	2	no	—
42	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
43	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂×Q₈×C₁₉	—	4	12	no	—
45	C₂×Q₈×C₁₉	—	4	12	no	—
46	C₂×Q₈×C₁₉	—	4	4	no	—
47	C₂²×C₄×C₁₉	—	2	6	no	—
48	C₂²×C₄×C₁₉	—	2	6	no	—
49	C₂²×C₄×C₁₉	—	2	6	no	—
50	C₂²×C₄×C₁₉	—	2	6	no	—
51	C₂²×C₄×C₁₉	—	2	3	no	—
52	C₂²×C₄×C₁₉	—	2	6	no	—
53	C₂²×C₄×C₁₉	—	2	3	no	—
54	C₂²×C₄×C₁₉	—	2	3	no	—
55	C₂²×C₄×C₁₉	—	2	3	no	—
56	C₂²×C₄×C₁₉	—	2	6	no	—
57	C₂²×C₄×C₁₉	—	2	6	no	—
58	C₂²×C₄×C₁₉	—	2	6	no	—
59	C₂²×C₄×C₁₉	—	2	6	no	—
60	C₂²×C₄×C₁₉	—	2	6	no	—
61	C₂²×C₄×C₁₉	—	2	6	no	—
62	C₂²×C₄×C₁₉	—	2	6	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
66	C₂²×C₄×C₁₉	#41	1	12	yes	—
67	C₂²⋊C₄×C₁₉	—	4	12	no	—
68	C₂²⋊C₄×C₁₉	—	4	12	no	—
69	C₂²⋊C₄×C₁₉	—	4	4	no	—
70	C₄²×C₁₉	—	4	12	no	—
71	#14609	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂³×C₁₉	—	2	6	no	—
73	C₂³×C₁₉	—	2	6	no	—
74	C₂³×C₁₉	—	2	2	no	—
75	C₂³×C₁₉	—	4	6	no	—
76	C₂³×C₁₉	—	4	6	no	—
77	C₂³×C₁₉	—	4	3	no	—
78	C₂³×C₁₉	—	4	3	no	—
79	C₂³×C₁₉	—	4	6	no	—
80	C₂³×C₁₉	—	4	3	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
83	C₂³×C₁₉	C₂×#41	1	6	yes	—
84	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
85	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
86	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
87	Q₈×C₁₉	—	4	16	no	—
88	C₂×C₄×C₁₉	—	2	12	no	—
89	C₂×C₄×C₁₉	—	2	6	no	—
90	C₂×C₄×C₁₉	—	2	6	no	—
91	C₂×C₄×C₁₉	—	2	12	no	—
92	C₂×C₄×C₁₉	—	2	12	no	—
93	C₂×C₄×C₁₉	—	2	12	no	—
94	C₂×C₄×C₁₉	—	2	12	no	—
95	C₂×C₄×C₁₉	—	4	6	no	—
96	C₂×C₄×C₁₉	—	4	6	no	—
97	C₂×C₄×C₁₉	—	4	3	no	—
98	C₂×C₄×C₁₉	—	4	3	no	—
99	C₂×C₄×C₁₉	—	4	6	no	—
100	C₂×C₄×C₁₉	—	4	6	no	—
101	C₂×C₄×C₁₉	—	4	6	no	—
102	C₂×C₄×C₁₉	—	4	6	no	—
103	C₂×C₄×C₁₉	—	4	3	no	—
104	C₂×C₄×C₁₉	—	4	3	no	—
105	C₂×C₄×C₁₉	—	4	6	no	—
106	C₂×C₄×C₁₉	—	4	6	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×#393	C₂×C₁₉	1	1	yes	characteristic
109	#1446	C₂×C₁₉	1	2	yes	complemented
110	#1440	C₂×C₁₉	1	3	yes	—
111	#1437	C₂×C₁₉	1	3	yes	—
112	#1434	C₂×C₁₉	1	6	yes	complemented
113	C₂²×C₁₉	—	4	6	no	—
114	C₂²×C₁₉	—	4	6	no	—
115	C₂²×C₁₉	—	4	2	no	—
116	C₂²×C₁₉	—	8	6	no	—
117	C₂²×C₁₉	—	8	2	no	—
118	C₂²×C₁₉	C₄×#41	1	3	yes	—
119	C₂²×C₁₉	#518	1	3	yes	—
120	C₂²×C₁₉	#519	1	1	yes	characteristic
121	C₂²×C₁₉	#539	1	6	yes	—
122	C₂²×C₁₉	#542	1	6	yes	—
123	C₂²×C₁₉	#551	1	3	yes	—
124	C₂²×C₁₉	#551	1	3	yes	—
125	C₂²×C₁₉	#555	1	6	yes	—
126	C₂²×C₁₉	#560	1	3	yes	—
127	C₂²×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
128	C₄×C₁₉	—	4	6	no	—
129	C₄×C₁₉	—	4	6	no	—
130	C₄×C₁₉	—	4	12	no	—
131	C₄×C₁₉	—	8	2	no	—
132	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
133	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
134	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
135	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
136	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
137	#393	C₄×C₁₉	1	8	yes	complemented
138	C₂×#95	C₂²×C₁₉	1	6	yes	—
139	C₂×#95	C₂²×C₁₉	1	3	yes	—
140	C₂×#95	C₂²×C₁₉	1	6	yes	—
141	C₂×#95	C₂²×C₁₉	1	6	yes	—
142	C₂×#95	C₂²×C₁₉	1	3	yes	—
143	C₂×C₁₉	—	8	2	no	—
144	C₂×C₁₉	#2332	1	3	yes	—
145	C₂×C₁₉	#2372	1	3	yes	—
146	C₂×C₁₉	#2375	1	1	yes	characteristic
147	C₂×C₁₉	#2737	1	6	yes	—
148	C₂×C₁₉	#2785	1	2	yes	—
149	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
150	C₂²×Q₈	—	4	3	no	—
151	C₂²×Q₈	—	4	3	no	—
152	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
153	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
154	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
155	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
156	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
157	C₂×C₂²⋊C₄	—	2	12	no	—
158	C₂×C₂²⋊C₄	—	4	3	no	—
159	C₂×C₂²⋊C₄	—	4	3	no	—
160	C₂×C₂²⋊C₄	—	4	3	no	—
161	C₂×C₂²⋊C₄	—	4	3	no	—
162	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
163	C₂×C₄²	—	2	12	no	—
164	C₂×C₄²	—	4	3	no	—
165	#95	—	2	12	no	—
166	#95	—	4	3	no	—
167	#95	—	4	6	no	—
168	#95	—	4	6	no	—
169	#95	C₂×C₄×C₁₉	1	12	yes	—
170	C₁₉	#14609	1	1	yes	characteristic, direct product factor, Sylow
171	C₂⁴	—	2	6	no	—
172	C₂⁴	—	2	3	no	—
173	C₂⁴	—	2	3	no	—
174	C₂⁴	—	2	2	no	—
175	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
176	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
177	C₂×Q₈	—	4	12	no	—
178	C₂×Q₈	—	4	12	no	—
179	C₂×Q₈	—	4	4	no	—
180	C₂²×C₄	—	2	6	no	—
181	C₂²×C₄	—	2	6	no	—
182	C₂²×C₄	—	2	6	no	—
183	C₂²×C₄	—	2	6	no	—
184	C₂²×C₄	—	2	6	no	—
185	C₂²×C₄	—	2	6	no	—
186	C₂²×C₄	—	2	3	no	—
187	C₂²×C₄	—	2	6	no	—
188	C₂²×C₄	—	2	6	no	—
189	C₂²×C₄	—	2	6	no	—
190	C₂²×C₄	—	2	3	no	—
191	C₂²×C₄	—	2	3	no	—
192	C₂²×C₄	—	2	3	no	—
193	C₂²×C₄	—	2	6	no	—
194	C₂²×C₄	—	2	6	no	—
195	C₂²×C₄	—	2	6	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
198	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
199	C₂²×C₄	#41×C₁₉	1	12	yes	—
200	C₂²⋊C₄	—	4	12	no	—
201	C₂²⋊C₄	—	4	12	no	—
202	C₂²⋊C₄	—	4	4	no	—
203	C₄²	—	4	12	no	—
204	C₂³	—	2	6	no	—
205	C₂³	—	2	6	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	4	6	no	—
208	C₂³	—	4	6	no	—
209	C₂³	—	4	3	no	—
210	C₂³	—	4	3	no	—
211	C₂³	—	4	6	no	—
212	C₂³	—	4	3	no	—
213	C₂³	—	4	1	no	—
214	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
215	C₂³	C₂×#41×C₁₉	1	6	yes	—
216	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
217	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
218	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
219	Q₈	—	4	16	no	—
220	C₂×C₄	—	2	12	no	—
221	C₂×C₄	—	2	6	no	—
222	C₂×C₄	—	2	6	no	—
223	C₂×C₄	—	2	12	no	—
224	C₂×C₄	—	2	12	no	—
225	C₂×C₄	—	2	12	no	—
226	C₂×C₄	—	2	12	no	—
227	C₂×C₄	—	4	6	no	—
228	C₂×C₄	—	4	6	no	—
229	C₂×C₄	—	4	3	no	—
230	C₂×C₄	—	4	3	no	—
231	C₂×C₄	—	4	6	no	—
232	C₂×C₄	—	4	6	no	—
233	C₂×C₄	—	4	3	no	—
234	C₂×C₄	—	4	6	no	—
235	C₂×C₄	—	4	6	no	—
236	C₂×C₄	—	4	3	no	—
237	C₂×C₄	—	4	6	no	—
238	C₂×C₄	—	4	6	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂²	—	4	6	no	—
241	C₂²	—	4	6	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	6	no	—
244	C₂²	—	8	2	no	—
245	C₂²	C₄×#41×C₁₉	1	3	yes	—
246	C₂²	C₁₉×#518	1	3	yes	—
247	C₂²	C₁₉×#519	1	1	yes	characteristic
248	C₂²	C₁₉×#539	1	6	yes	—
249	C₂²	C₁₉×#542	1	6	yes	—
250	C₂²	C₁₉×#551	1	3	yes	—
251	C₂²	C₁₉×#551	1	3	yes	—
252	C₂²	C₁₉×#555	1	6	yes	—
253	C₂²	C₁₉×#560	1	3	yes	—
254	C₂²	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
255	C₄	—	4	12	no	—
256	C₄	—	4	6	no	—
257	C₄	—	4	6	no	—
258	C₄	—	8	2	no	—
259	C₂	—	8	2	no	—
260	C₂	C₁₉×#2332	1	3	yes	—
261	C₂	C₁₉×#2372	1	3	yes	—
262	C₂	C₁₉×#2375	1	1	yes	characteristic
263	C₂	C₁₉×#2737	1	6	yes	—
264	C₂	C₁₉×#2785	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1446	C₂	semidirect
5. C₁₉×#1434	C₂	semidirect
11. C₁₉×#393	C₄	semidirect
71. #14609	C₁₉	direct (N × H)
109. #1446	C₂×C₁₉	semidirect
112. #1434	C₂×C₁₉	semidirect
137. #393	C₄×C₁₉	semidirect
170. C₁₉	#14609	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×#393	2
C₁₉×#1446	2
C₁₉×#1440	2
C₁₉×#1437	2
C₁₉×#1434	2
#14609	19

Subgroups — C19×#14609 #18020568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14609 #18020568