Subgroups — C₁₉×#2805 #14560662

Order 2432.

368 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×#400	C₂	1	2	yes	maximal
2	C₁₉×#400	C₂	1	2	yes	maximal
3	C₁₉×#395	C₂	1	2	yes	maximal
4	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#389	C₂	1	2	yes	maximal
6	C₁₉×#389	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#389	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#387	C₂	1	2	yes	maximal
9	C₁₉×#387	C₂	1	2	yes	maximal
10	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#95	C₂²	1	2	yes	—
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	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₄⋊C₄×C₁₉	—	4	2	no	—
47	C₄⋊C₄×C₁₉	—	4	1	no	—
48	C₄⋊C₄×C₁₉	—	4	1	no	—
49	C₄⋊C₄×C₁₉	—	4	1	no	—
50	C₄⋊C₄×C₁₉	—	4	2	no	—
51	C₄⋊C₄×C₁₉	Q₈	1	4	yes	complemented
52	C₄²×C₁₉	—	4	1	no	—
53	C₄²×C₁₉	—	4	2	no	—
54	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
55	Q₈×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	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	C₂×Q₈	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
81	C₂×C₄×C₁₉	#41	1	2	yes	—
82	C₂×C₄×C₁₉	#41	1	2	yes	—
83	#2805	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
86	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
87	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
88	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
89	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
90	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	—	2	2	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	2	4	no	—
95	C₄×C₁₉	—	4	2	no	—
96	C₄×C₁₉	—	4	2	no	—
97	C₄×C₁₉	—	4	2	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	—	4	2	no	—
100	#400	C₂×C₁₉	1	2	yes	—
101	#400	C₂×C₁₉	1	2	yes	—
102	#395	C₂×C₁₉	1	2	yes	—
103	#391	C₂×C₁₉	1	1	yes	characteristic
104	#389	C₂×C₁₉	1	1	yes	characteristic
105	#389	C₂×C₁₉	1	1	yes	characteristic
106	#389	C₂×C₁₉	1	2	yes	—
107	#387	C₂×C₁₉	1	2	yes	—
108	#387	C₂×C₁₉	1	2	yes	—
109	C₂×C₁₉	#538	1	1	yes	characteristic
110	C₂×C₁₉	#539	1	1	yes	characteristic
111	C₂×C₁₉	#544	1	1	yes	characteristic
112	C₂×C₁₉	#554	1	1	yes	characteristic
113	C₂×C₁₉	#556	1	1	yes	characteristic
114	C₂×C₁₉	#557	1	1	yes	characteristic
115	C₂×C₁₉	#563	1	1	yes	characteristic
116	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
117	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
118	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
119	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
121	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
122	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
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	1	yes	characteristic
126	C₂×C₄²	C₂²×C₁₉	1	2	yes	—
127	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
128	#95	C₂²×C₁₉	1	2	yes	—
129	#95	C₂²×C₁₉	1	2	yes	—
130	#95	C₂²×C₁₉	1	2	yes	—
131	#95	C₂²×C₁₉	1	2	yes	—
132	#95	C₂²×C₁₉	1	2	yes	—
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	C₁₉	#2805	1	1	yes	characteristic, direct product factor, Sylow
138	C₂×Q₈	—	2	2	no	—
139	C₂×Q₈	—	4	1	no	—
140	C₂×Q₈	—	4	1	no	—
141	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
142	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
143	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
144	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
145	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
146	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
147	C₂²×C₄	C₂³×C₁₉	1	2	yes	—
148	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
149	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	2	2	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	1	no	—
155	C₄⋊C₄	—	4	1	no	—
156	C₄⋊C₄	—	4	1	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	Q₈×C₁₉	1	4	yes	complemented
159	C₄²	—	4	1	no	—
160	C₄²	—	4	2	no	—
161	C₂³	C₂⁴×C₁₉	1	1	yes	characteristic
162	Q₈	—	4	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	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	C₂×Q₈×C₁₉	1	2	yes	—
187	C₂×C₄	C₂×Q₈×C₁₉	1	4	yes	—
188	C₂×C₄	#41×C₁₉	1	2	yes	—
189	C₂×C₄	#41×C₁₉	1	2	yes	—
190	C₂²	C₂²×Q₈×C₁₉	1	1	yes	characteristic
191	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
192	C₂²	C₂×#41×C₁₉	1	1	yes	characteristic
193	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
194	C₂²	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
195	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
196	C₂²	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
197	C₄	—	2	2	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	2	no	—
200	C₄	—	2	4	no	—
201	C₄	—	4	2	no	—
202	C₄	—	4	2	no	—
203	C₄	—	4	2	no	—
204	C₄	—	4	2	no	—
205	C₄	—	4	2	no	—
206	C₂	C₁₉×#538	1	1	yes	characteristic
207	C₂	C₁₉×#539	1	1	yes	characteristic
208	C₂	C₁₉×#544	1	1	yes	characteristic
209	C₂	C₁₉×#554	1	1	yes	characteristic
210	C₂	C₁₉×#556	1	1	yes	characteristic
211	C₂	C₁₉×#557	1	1	yes	characteristic
212	C₂	C₁₉×#563	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
51. C₄⋊C₄×C₁₉	Q₈	semidirect
83. #2805	C₁₉	direct (N × H)
137. C₁₉	#2805	direct (N × H)
158. 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×#400	2
C₁₉×#395	2
C₁₉×#391	2
C₁₉×#389	2
C₁₉×#387	2
#2805	19

Subgroups — C19×#2805 #14560662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2805 #14560662