Subgroups — C₁₉×#2565 #14560422

Order 2432.

452 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#398	C₂	1	4	yes	maximal
4	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#387	C₂	1	4	yes	maximal
7	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#382	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#125	—	2	4	no	—
12	C₄×Q₈×C₁₉	—	2	4	no	—
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#95	C₂²	1	2	yes	—
26	C₁₉×#95	C₂²	1	4	yes	—
27	C₁₉×#95	C₂²	1	4	yes	—
28	C₁₉×#95	C₂²	1	4	yes	—
29	C₂×Q₈×C₁₉	—	2	2	no	—
30	C₂×Q₈×C₁₉	—	2	2	no	—
31	C₂×Q₈×C₁₉	Q₈	1	4	yes	—
32	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₄⋊C₄×C₁₉	—	2	4	no	—
45	C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₄⋊C₄×C₁₉	—	2	8	no	—
49	C₄²×C₁₉	—	2	4	no	—
50	C₄²×C₁₉	—	2	2	no	—
51	C₄²×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	D₄	1	4	yes	—
53	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
54	Q₈×C₁₉	—	2	8	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	2	4	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	4	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
74	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
75	C₂×C₄×C₁₉	#41	1	4	yes	—
76	C₂×C₄×C₁₉	#41	1	2	yes	—
77	#2565	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
79	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
80	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
81	C₂²×C₁₉	C₂×#41	1	2	yes	—
82	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
83	C₄×C₁₉	—	2	4	no	—
84	C₄×C₁₉	—	2	2	no	—
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	2	4	no	—
87	C₄×C₁₉	—	4	2	no	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
92	C₂×#125	C₂×C₁₉	1	1	yes	characteristic
93	C₂×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
94	#398	C₂×C₁₉	1	4	yes	—
95	#391	C₂×C₁₉	1	1	yes	characteristic
96	#391	C₂×C₁₉	1	1	yes	characteristic
97	#387	C₂×C₁₉	1	4	yes	—
98	#384	C₂×C₁₉	1	1	yes	characteristic
99	#382	C₂×C₁₉	1	1	yes	characteristic
100	C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
101	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₁₉	#532	1	1	yes	characteristic
103	C₂×C₁₉	#536	1	1	yes	characteristic
104	C₂×C₁₉	#552	1	2	yes	—
105	C₂×C₁₉	#557	1	2	yes	—
106	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
107	#125	—	2	4	no	—
108	C₄×Q₈	—	2	4	no	—
109	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
110	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
111	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
112	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
113	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
114	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
116	C₂×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
117	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
118	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
120	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
121	#95	C₂²×C₁₉	1	2	yes	—
122	#95	C₂²×C₁₉	1	4	yes	—
123	#95	C₂²×C₁₉	1	4	yes	—
124	#95	C₂²×C₁₉	1	4	yes	—
125	C₁₉	#2565	1	1	yes	characteristic, direct product factor, Sylow
126	C₂×Q₈	—	2	2	no	—
127	C₂×Q₈	—	2	2	no	—
128	C₂×Q₈	Q₈×C₁₉	1	4	yes	—
129	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
130	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
131	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
132	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
133	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
134	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
136	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
137	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	2	2	no	—
140	C₄⋊C₄	—	2	4	no	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	2	2	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	2	4	no	—
145	C₄⋊C₄	—	2	8	no	—
146	C₄²	—	2	4	no	—
147	C₄²	—	2	2	no	—
148	C₄²	—	2	2	no	—
149	C₄²	D₄×C₁₉	1	4	yes	—
150	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
151	Q₈	—	2	8	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
168	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
169	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
170	C₂×C₄	C₂×Q₈×C₁₉	1	4	yes	—
171	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
172	C₂×C₄	#41×C₁₉	1	4	yes	—
173	C₂×C₄	#41×C₁₉	1	2	yes	—
174	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
175	C₂²	C₂²×Q₈×C₁₉	1	1	yes	characteristic
176	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
177	C₂²	C₂×#41×C₁₉	1	2	yes	—
178	C₂²	C₁₉×2₋¹⁺⁴	1	2	yes	—
179	C₄	—	2	4	no	—
180	C₄	—	2	2	no	—
181	C₄	—	2	2	no	—
182	C₄	—	2	4	no	—
183	C₄	—	4	2	no	—
184	C₄	—	4	2	no	—
185	C₄	—	4	2	no	—
186	C₄	—	4	2	no	—
187	C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
188	C₂	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
189	C₂	C₁₉×#532	1	1	yes	characteristic
190	C₂	C₁₉×#536	1	1	yes	characteristic
191	C₂	C₁₉×#552	1	2	yes	—
192	C₂	C₁₉×#557	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
77. #2565	C₁₉	direct (N × H)
125. C₁₉	#2565	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×#125	2
C₂×C₄×Q₈×C₁₉	2
C₁₉×#398	2
C₁₉×#391	2
C₁₉×#387	2
C₁₉×#384	2
C₁₉×#382	2
C₄×C₄⋊C₄×C₁₉	2
#2565	19

Subgroups — C19×#2565 #14560422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2565 #14560422