Subgroups — C₁₉×#2806 #14560663

Order 2432.

392 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#398	C₂	1	2	yes	maximal
2	C₁₉×#398	C₂	1	2	yes	maximal
3	C₁₉×#395	C₂	1	2	yes	maximal
4	C₁₉×#391	C₂	1	2	yes	maximal
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#389	C₂	1	2	yes	maximal
8	C₁₉×#389	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#387	C₂	1	2	yes	maximal
10	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
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	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#95	C₂²	1	2	yes	—
24	C₁₉×#95	C₂²	1	2	yes	—
25	C₁₉×#95	C₂²	1	2	yes	—
26	C₁₉×#95	C₂²	1	2	yes	—
27	C₁₉×#95	C₂²	1	2	yes	—
28	C₁₉×#95	C₂²	1	2	yes	—
29	C₁₉×#95	C₂²	1	2	yes	—
30	C₁₉×#95	C₂²	1	2	yes	—
31	C₂×Q₈×C₁₉	—	2	2	no	—
32	C₂×Q₈×C₁₉	—	4	1	no	—
33	C₂×Q₈×C₁₉	—	4	1	no	—
34	C₂×Q₈×C₁₉	—	4	1	no	—
35	C₂×Q₈×C₁₉	—	4	1	no	—
36	C₂×Q₈×C₁₉	Q₈	1	4	yes	complemented
37	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₄⋊C₄×C₁₉	—	2	4	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	1	no	—
49	C₄⋊C₄×C₁₉	—	4	1	no	—
50	C₄⋊C₄×C₁₉	—	4	1	no	—
51	C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	4	2	no	—
53	C₄⋊C₄×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	Q₈	1	4	yes	complemented
55	C₄²×C₁₉	—	4	1	no	—
56	C₄²×C₁₉	—	4	2	no	—
57	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
58	Q₈×C₁₉	—	4	4	no	—
59	Q₈×C₁₉	—	4	4	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	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	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
84	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
85	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
86	C₂×C₄×C₁₉	#41	1	2	yes	—
87	#2806	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
89	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
90	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
91	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
92	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
93	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
94	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	2	4	no	—
100	C₄×C₁₉	—	4	2	no	—
101	C₄×C₁₉	—	4	2	no	—
102	C₄×C₁₉	—	4	2	no	—
103	C₄×C₁₉	—	4	2	no	—
104	#398	C₂×C₁₉	1	2	yes	—
105	#398	C₂×C₁₉	1	2	yes	—
106	#395	C₂×C₁₉	1	2	yes	—
107	#391	C₂×C₁₉	1	2	yes	—
108	#391	C₂×C₁₉	1	1	yes	characteristic
109	#391	C₂×C₁₉	1	1	yes	characteristic
110	#389	C₂×C₁₉	1	2	yes	—
111	#389	C₂×C₁₉	1	1	yes	characteristic
112	#387	C₂×C₁₉	1	2	yes	—
113	C₂×C₁₉	#538	1	1	yes	characteristic
114	C₂×C₁₉	#543	1	1	yes	characteristic
115	C₂×C₁₉	#544	1	1	yes	characteristic
116	C₂×C₁₉	#554	1	1	yes	characteristic
117	C₂×C₁₉	#557	1	1	yes	characteristic
118	C₂×C₁₉	Q₈²	1	1	yes	characteristic
119	C₂×C₁₉	#562	1	1	yes	characteristic
120	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
121	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
122	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
123	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
124	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
125	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
126	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
127	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
128	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
129	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
130	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
131	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
132	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
133	#95	C₂²×C₁₉	1	2	yes	—
134	#95	C₂²×C₁₉	1	2	yes	—
135	#95	C₂²×C₁₉	1	2	yes	—
136	#95	C₂²×C₁₉	1	2	yes	—
137	#95	C₂²×C₁₉	1	2	yes	—
138	#95	C₂²×C₁₉	1	2	yes	—
139	#95	C₂²×C₁₉	1	2	yes	—
140	#95	C₂²×C₁₉	1	2	yes	—
141	C₁₉	#2806	1	1	yes	characteristic, direct product factor, Sylow
142	C₂×Q₈	—	2	2	no	—
143	C₂×Q₈	—	4	1	no	—
144	C₂×Q₈	—	4	1	no	—
145	C₂×Q₈	—	4	1	no	—
146	C₂×Q₈	—	4	1	no	—
147	C₂×Q₈	Q₈×C₁₉	1	4	yes	complemented
148	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
149	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
150	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
151	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
152	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
153	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
154	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
156	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
157	C₄⋊C₄	—	2	4	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	4	1	no	—
160	C₄⋊C₄	—	4	1	no	—
161	C₄⋊C₄	—	4	1	no	—
162	C₄⋊C₄	—	4	2	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	Q₈×C₁₉	1	4	yes	complemented
166	C₄²	—	4	1	no	—
167	C₄²	—	4	2	no	—
168	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
169	Q₈	—	4	4	no	—
170	Q₈	—	4	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	1	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	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
194	C₂×C₄	C₂×Q₈×C₁₉	1	4	yes	—
195	C₂×C₄	C₂×Q₈×C₁₉	1	4	yes	—
196	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
197	C₂×C₄	#41×C₁₉	1	2	yes	—
198	C₂²	C₂²×Q₈×C₁₉	1	1	yes	characteristic
199	C₂²	C₂²×Q₈×C₁₉	1	1	yes	characteristic
200	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
201	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
203	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
205	C₄	—	2	2	no	—
206	C₄	—	2	2	no	—
207	C₄	—	2	4	no	—
208	C₄	—	2	2	no	—
209	C₄	—	2	4	no	—
210	C₄	—	4	2	no	—
211	C₄	—	4	2	no	—
212	C₄	—	4	2	no	—
213	C₄	—	4	2	no	—
214	C₂	C₁₉×#538	1	1	yes	characteristic
215	C₂	C₁₉×#543	1	1	yes	characteristic
216	C₂	C₁₉×#544	1	1	yes	characteristic
217	C₂	C₁₉×#554	1	1	yes	characteristic
218	C₂	C₁₉×#557	1	1	yes	characteristic
219	C₂	Q₈²×C₁₉	1	1	yes	characteristic
220	C₂	C₁₉×#562	1	1	yes	characteristic

	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
36. C₂×Q₈×C₁₉	Q₈	semidirect
54. C₄⋊C₄×C₁₉	Q₈	semidirect
87. #2806	C₁₉	direct (N × H)
141. C₁₉	#2806	direct (N × H)
147. C₂×Q₈	Q₈×C₁₉	semidirect
165. C₄⋊C₄	Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#398	2
C₁₉×#395	2
C₁₉×#391	2
C₁₉×#389	2
C₁₉×#387	2
#2806	19

Subgroups — C19×#2806 #14560663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2806 #14560663