Subgroups — C₁₉×#14655 #18020614

Order 4864.

1094 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#395	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1446	C₂	1	2	yes	maximal
3	C₁₉×#1445	C₂	1	3	yes	maximal
4	C₁₉×#1443	C₂	1	6	yes	maximal
5	C₁₉×#1436	C₂	1	3	yes	maximal
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#395	C₄	1	8	yes	complemented
10	C₂×C₁₉×#95	C₂²	1	6	yes	—
11	C₂×C₁₉×#95	C₂²	1	6	yes	—
12	C₂×C₁₉×#95	C₂²	1	3	yes	—
13	C₂×C₁₉×#95	C₂²	1	3	yes	—
14	C₂×C₁₉×#95	C₂²	1	3	yes	—
15	C₂×C₁₉×#95	C₂²	1	6	yes	—
16	C₂×C₁₉×#95	C₂²	1	3	yes	—
17	C₂²×Q₈×C₁₉	—	4	3	no	—
18	C₂²×Q₈×C₁₉	—	4	3	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
22	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
25	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
26	C₂×C₄⋊C₄×C₁₉	—	4	3	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
28	C₂×C₄²×C₁₉	—	4	3	no	—
29	C₁₉×#95	—	2	12	no	—
30	C₁₉×#95	—	4	6	no	—
31	C₁₉×#95	—	4	3	no	—
32	C₁₉×#95	—	4	3	no	—
33	C₁₉×#95	—	4	3	no	—
34	C₁₉×#95	—	4	6	no	—
35	C₁₉×#95	C₂×C₄	1	12	yes	—
36	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
37	C₂×Q₈×C₁₉	—	4	12	no	—
38	C₂×Q₈×C₁₉	—	4	12	no	—
39	C₂×Q₈×C₁₉	—	4	4	no	—
40	C₂²×C₄×C₁₉	—	2	6	no	—
41	C₂²×C₄×C₁₉	—	2	3	no	—
42	C₂²×C₄×C₁₉	—	2	6	no	—
43	C₂²×C₄×C₁₉	—	2	3	no	—
44	C₂²×C₄×C₁₉	—	2	3	no	—
45	C₂²×C₄×C₁₉	—	2	3	no	—
46	C₂²×C₄×C₁₉	—	2	3	no	—
47	C₂²×C₄×C₁₉	—	2	3	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	6	no	—
52	C₂²×C₄×C₁₉	—	2	6	no	—
53	C₂²×C₄×C₁₉	—	2	6	no	—
54	C₂²×C₄×C₁₉	—	2	6	no	—
55	C₂²×C₄×C₁₉	—	2	6	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	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
62	C₂²×C₄×C₁₉	#41	1	4	yes	—
63	C₄⋊C₄×C₁₉	—	4	12	no	—
64	C₄²×C₁₉	—	4	4	no	—
65	#14655	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
67	C₂³×C₁₉	C₂×#41	1	2	yes	—
68	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
69	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
70	C₂³×C₁₉	2₋¹⁺⁴	1	6	yes	—
71	Q₈×C₁₉	—	4	16	no	—
72	C₂×C₄×C₁₉	—	2	6	no	—
73	C₂×C₄×C₁₉	—	2	6	no	—
74	C₂×C₄×C₁₉	—	2	6	no	—
75	C₂×C₄×C₁₉	—	2	6	no	—
76	C₂×C₄×C₁₉	—	2	12	no	—
77	C₂×C₄×C₁₉	—	2	6	no	—
78	C₂×C₄×C₁₉	—	2	12	no	—
79	C₂×C₄×C₁₉	—	4	6	no	—
80	C₂×C₄×C₁₉	—	4	6	no	—
81	C₂×C₄×C₁₉	—	4	3	no	—
82	C₂×C₄×C₁₉	—	4	6	no	—
83	C₂×C₄×C₁₉	—	4	3	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	3	no	—
87	C₂×C₄×C₁₉	—	4	6	no	—
88	C₂×C₄×C₁₉	—	4	6	no	—
89	C₂×C₄×C₁₉	—	4	6	no	—
90	C₂×C₄×C₁₉	—	4	6	no	—
91	C₂×C₄×C₁₉	—	4	6	no	—
92	C₂×C₄×C₁₉	—	4	6	no	—
93	C₂×C₄×C₁₉	—	4	6	no	—
94	C₂×C₄×C₁₉	—	4	6	no	—
95	C₂×#395	C₂×C₁₉	1	1	yes	characteristic
96	#1446	C₂×C₁₉	1	2	yes	—
97	#1445	C₂×C₁₉	1	3	yes	—
98	#1443	C₂×C₁₉	1	6	yes	—
99	#1436	C₂×C₁₉	1	3	yes	—
100	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
101	C₂²×C₁₉	#518	1	3	yes	—
102	C₂²×C₁₉	#519	1	3	yes	—
103	C₂²×C₁₉	#539	1	6	yes	—
104	C₂²×C₁₉	#542	1	6	yes	—
105	C₂²×C₁₉	#560	1	3	yes	—
106	C₂²×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
107	C₂²×C₁₉	#563	1	6	yes	—
108	C₂²×C₁₉	#563	1	3	yes	—
109	C₂²×C₁₉	#563	1	3	yes	—
110	C₄×C₁₉	—	4	4	no	—
111	C₄×C₁₉	—	4	6	no	—
112	C₄×C₁₉	—	4	2	no	—
113	C₄×C₁₉	—	4	6	no	—
114	C₄×C₁₉	—	8	6	no	—
115	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
116	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
117	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
118	#395	C₄×C₁₉	1	8	yes	complemented
119	C₂×#95	C₂²×C₁₉	1	6	yes	—
120	C₂×#95	C₂²×C₁₉	1	6	yes	—
121	C₂×#95	C₂²×C₁₉	1	3	yes	—
122	C₂×#95	C₂²×C₁₉	1	3	yes	—
123	C₂×#95	C₂²×C₁₉	1	3	yes	—
124	C₂×#95	C₂²×C₁₉	1	6	yes	—
125	C₂×#95	C₂²×C₁₉	1	3	yes	—
126	C₂×C₁₉	#2332	1	3	yes	—
127	C₂×C₁₉	#2375	1	1	yes	characteristic
128	C₂×C₁₉	#2381	1	3	yes	—
129	C₂×C₁₉	#2835	1	2	yes	—
130	C₂×C₁₉	#2838	1	6	yes	—
131	C₂²×Q₈	—	4	3	no	—
132	C₂²×Q₈	—	4	3	no	—
133	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
134	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
135	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
136	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
137	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
138	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
139	C₂×C₄⋊C₄	—	4	3	no	—
140	C₂×C₄⋊C₄	—	4	3	no	—
141	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
142	C₂×C₄²	—	4	3	no	—
143	#95	—	2	12	no	—
144	#95	—	4	6	no	—
145	#95	—	4	3	no	—
146	#95	—	4	3	no	—
147	#95	—	4	3	no	—
148	#95	—	4	6	no	—
149	#95	C₂×C₄×C₁₉	1	12	yes	—
150	C₁₉	#14655	1	1	yes	characteristic, direct product factor, Sylow
151	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
152	C₂×Q₈	—	4	12	no	—
153	C₂×Q₈	—	4	12	no	—
154	C₂×Q₈	—	4	4	no	—
155	C₂²×C₄	—	2	6	no	—
156	C₂²×C₄	—	2	6	no	—
157	C₂²×C₄	—	2	3	no	—
158	C₂²×C₄	—	2	3	no	—
159	C₂²×C₄	—	2	3	no	—
160	C₂²×C₄	—	2	6	no	—
161	C₂²×C₄	—	2	6	no	—
162	C₂²×C₄	—	2	3	no	—
163	C₂²×C₄	—	2	3	no	—
164	C₂²×C₄	—	2	3	no	—
165	C₂²×C₄	—	2	6	no	—
166	C₂²×C₄	—	2	6	no	—
167	C₂²×C₄	—	2	6	no	—
168	C₂²×C₄	—	2	6	no	—
169	C₂²×C₄	—	2	6	no	—
170	C₂²×C₄	—	2	6	no	—
171	C₂²×C₄	—	2	6	no	—
172	C₂²×C₄	—	2	6	no	—
173	C₂²×C₄	—	2	6	no	—
174	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
176	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
177	C₂²×C₄	#41×C₁₉	1	4	yes	—
178	C₄⋊C₄	—	4	12	no	—
179	C₄²	—	4	4	no	—
180	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
181	C₂³	C₂×#41×C₁₉	1	2	yes	—
182	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
183	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
184	C₂³	C₁₉×2₋¹⁺⁴	1	6	yes	—
185	Q₈	—	4	16	no	—
186	C₂×C₄	—	2	6	no	—
187	C₂×C₄	—	2	6	no	—
188	C₂×C₄	—	2	6	no	—
189	C₂×C₄	—	2	6	no	—
190	C₂×C₄	—	2	12	no	—
191	C₂×C₄	—	2	6	no	—
192	C₂×C₄	—	2	12	no	—
193	C₂×C₄	—	4	6	no	—
194	C₂×C₄	—	4	6	no	—
195	C₂×C₄	—	4	3	no	—
196	C₂×C₄	—	4	6	no	—
197	C₂×C₄	—	4	3	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	3	no	—
201	C₂×C₄	—	4	6	no	—
202	C₂×C₄	—	4	6	no	—
203	C₂×C₄	—	4	6	no	—
204	C₂×C₄	—	4	6	no	—
205	C₂×C₄	—	4	6	no	—
206	C₂×C₄	—	4	6	no	—
207	C₂×C₄	—	4	6	no	—
208	C₂×C₄	—	4	6	no	—
209	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
210	C₂²	C₁₉×#518	1	3	yes	—
211	C₂²	C₁₉×#519	1	3	yes	—
212	C₂²	C₁₉×#539	1	6	yes	—
213	C₂²	C₁₉×#542	1	6	yes	—
214	C₂²	C₁₉×#560	1	3	yes	—
215	C₂²	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
216	C₂²	C₁₉×#563	1	6	yes	—
217	C₂²	C₁₉×#563	1	3	yes	—
218	C₂²	C₁₉×#563	1	3	yes	—
219	C₄	—	4	4	no	—
220	C₄	—	4	6	no	—
221	C₄	—	4	6	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	6	no	—
224	C₂	C₁₉×#2332	1	3	yes	—
225	C₂	C₁₉×#2375	1	1	yes	characteristic
226	C₂	C₁₉×#2381	1	3	yes	—
227	C₂	C₁₉×#2835	1	2	yes	—
228	C₂	C₁₉×#2838	1	6	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
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
9. C₁₉×#395	C₄	semidirect
65. #14655	C₁₉	direct (N × H)
118. #395	C₄×C₁₉	semidirect
150. C₁₉	#14655	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×#395	2
C₁₉×#1446	2
C₁₉×#1445	2
C₁₉×#1443	2
C₁₉×#1436	2
#14655	19

Subgroups — C19×#14655 #18020614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14655 #18020614