Subgroups — C₁₉×#3250 #14561107

Order 2432.

360 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#529	C₂	1	2	yes	maximal, complemented
2	C₁₉×#479	C₂	1	2	yes	maximal, complemented
3	C₁₉×#478	C₂	1	2	yes	maximal, complemented
4	C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#466	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#465	C₂	1	2	yes	maximal, complemented
7	C₁₉×#464	C₂	1	2	yes	maximal, complemented
8	C₁₉×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	—
12	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#126	—	2	2	no	—
16	C₁₉×#125	C₂²	1	2	yes	—
17	C₁₉×#124	C₂²	1	2	yes	—
18	C₁₉×#123	—	2	2	no	—
19	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₁₉×#121	C₂²	1	2	yes	—
21	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₄×D₄×C₁₉	—	2	2	no	—
23	C₄×D₄×C₁₉	C₂²	1	2	yes	—
24	C₁₉×#117	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#107	C₂²	1	1	yes	characteristic
27	C₁₉×#107	C₂²	1	1	yes	characteristic
28	C₁₉×#106	C₂²	1	2	yes	—
29	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
31	C₁₉×#103	C₂²	1	2	yes	—
32	C₁₉×#103	C₂²	1	2	yes	—
33	C₁₉×#102	C₂²	1	2	yes	—
34	C₁₉×#102	C₂²	1	2	yes	—
35	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
36	C₂×D₄×C₁₉	—	2	2	no	—
37	C₂×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	Q₁₆×C₁₉	—	4	1	no	—
43	SD₁₆×C₁₉	—	4	2	no	—
44	D₈×C₁₉	—	4	1	no	—
45	C₂×C₈×C₁₉	—	4	1	no	—
46	C₂×C₈×C₁₉	—	4	1	no	—
47	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	D₄	1	2	yes	—
63	C₄²×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
66	Q₈×C₁₉	—	2	2	no	—
67	Q₈×C₁₉	—	2	2	no	—
68	D₄×C₁₉	—	2	2	no	—
69	D₄×C₁₉	—	2	2	no	—
70	D₄×C₁₉	—	4	4	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
83	C₈×C₁₉	—	2	1	no	—
84	C₈×C₁₉	—	2	2	no	—
85	C₈×C₁₉	—	2	1	no	—
86	#3250	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	—	4	2	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	#135	1	2	yes	—
93	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	—	4	2	no	—
100	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
101	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
102	#529	C₂×C₁₉	1	2	yes	complemented
103	#479	C₂×C₁₉	1	2	yes	complemented
104	#478	C₂×C₁₉	1	2	yes	complemented
105	#467	C₂×C₁₉	1	1	yes	characteristic, complemented
106	#466	C₂×C₁₉	1	1	yes	characteristic
107	#465	C₂×C₁₉	1	2	yes	complemented
108	#464	C₂×C₁₉	1	2	yes	complemented
109	#463	C₂×C₁₉	1	2	yes	complemented
110	C₂×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
111	C₂×C₁₉	—	2	2	no	—
112	C₂×C₁₉	—	8	2	no	—
113	C₂×C₁₉	#537	1	1	yes	characteristic
114	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
115	C₂×C₁₉	#575	1	1	yes	characteristic
116	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
117	C₂×SD₁₆	C₂²×C₁₉	1	2	yes	—
118	C₂×D₈	C₂²×C₁₉	1	1	yes	characteristic
119	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
120	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
121	#126	—	2	2	no	—
122	#125	C₂²×C₁₉	1	2	yes	—
123	#124	C₂²×C₁₉	1	2	yes	—
124	#123	—	2	2	no	—
125	C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
126	#121	C₂²×C₁₉	1	2	yes	—
127	C₄×Q₈	C₂²×C₁₉	1	2	yes	—
128	C₄×D₄	—	2	2	no	—
129	C₄×D₄	C₂²×C₁₉	1	2	yes	—
130	#117	—	2	2	no	—
131	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
132	#107	C₂²×C₁₉	1	1	yes	characteristic
133	#107	C₂²×C₁₉	1	1	yes	characteristic
134	#106	C₂²×C₁₉	1	2	yes	—
135	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
136	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
137	#103	C₂²×C₁₉	1	2	yes	—
138	#103	C₂²×C₁₉	1	2	yes	—
139	#102	C₂²×C₁₉	1	2	yes	—
140	#102	C₂²×C₁₉	1	2	yes	—
141	C₁₉	#3250	1	1	yes	characteristic, direct product factor, Sylow
142	C₂×Q₈	C₂³×C₁₉	1	2	yes	—
143	C₂×D₄	—	2	2	no	—
144	C₂×D₄	C₂³×C₁₉	1	2	yes	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
147	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
148	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
149	Q₁₆	—	4	1	no	—
150	SD₁₆	—	4	2	no	—
151	D₈	—	4	1	no	—
152	C₂×C₈	—	4	1	no	—
153	C₂×C₈	—	4	1	no	—
154	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
155	C₂×C₈	C₂³×C₁₉	1	2	yes	—
156	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	2	2	no	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
162	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
163	C₂²⋊C₄	—	2	2	no	—
164	C₂²⋊C₄	—	2	2	no	—
165	C₂²⋊C₄	—	2	2	no	—
166	C₂²⋊C₄	—	2	2	no	—
167	C₂²⋊C₄	—	2	2	no	—
168	C₄²	—	2	2	no	—
169	C₄²	D₄×C₁₉	1	2	yes	—
170	C₄²	C₂³×C₁₉	1	2	yes	—
171	C₂³	—	2	2	no	—
172	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
173	Q₈	—	2	2	no	—
174	Q₈	—	2	2	no	—
175	D₄	—	2	2	no	—
176	D₄	—	2	2	no	—
177	D₄	—	4	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	4	1	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
187	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
188	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
189	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
190	C₈	—	2	1	no	—
191	C₈	—	2	2	no	—
192	C₈	—	2	1	no	—
193	C₂²	—	2	1	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	4	2	no	—
196	C₂²	—	4	2	no	—
197	C₂²	—	4	2	no	—
198	C₂²	C₁₉×#135	1	2	yes	—
199	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
200	C₄	—	2	1	no	—
201	C₄	—	2	2	no	—
202	C₄	—	2	2	no	—
203	C₄	—	4	2	no	—
204	C₄	—	4	2	no	—
205	C₄	—	4	2	no	—
206	C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
207	C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
208	C₂	—	2	2	no	—
209	C₂	—	8	2	no	—
210	C₂	C₁₉×#537	1	1	yes	characteristic
211	C₂	C₂×C₁₉×#135	1	1	yes	characteristic
212	C₂	C₁₉×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#529	C₂	semidirect
2. C₁₉×#479	C₂	semidirect
3. C₁₉×#478	C₂	semidirect
4. C₁₉×#467	C₂	semidirect
6. C₁₉×#465	C₂	semidirect
7. C₁₉×#464	C₂	semidirect
8. C₁₉×#463	C₂	semidirect
9. C₂×C₁₉×C₄⋊C₈	C₂	semidirect
86. #3250	C₁₉	direct (N × H)
102. #529	C₂×C₁₉	semidirect
103. #479	C₂×C₁₉	semidirect
104. #478	C₂×C₁₉	semidirect
105. #467	C₂×C₁₉	semidirect
107. #465	C₂×C₁₉	semidirect
108. #464	C₂×C₁₉	semidirect
109. #463	C₂×C₁₉	semidirect
110. C₂×C₄⋊C₈	C₂×C₁₉	semidirect
141. C₁₉	#3250	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#529	2
C₁₉×#479	2
C₁₉×#478	2
C₁₉×#467	2
C₁₉×#466	2
C₁₉×#465	2
C₁₉×#464	2
C₁₉×#463	2
C₂×C₁₉×C₄⋊C₈	2
#3250	19

Subgroups — C19×#3250 #14561107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3250 #14561107