Subgroups — C₁₉×#34639 #18040598

Order 4864.

1738 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2645	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2644	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2643	C₂	1	8	yes	maximal, complemented
4	C₁₉×#2401	C₂	1	8	yes	maximal, complemented
5	C₁₉×#2297	C₂	1	3	yes	maximal
6	C₁₉×#2296	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#117	C₂²	1	3	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
11	C₁₉×#401	C₂²	1	8	yes	—
12	C₁₉×#400	C₂²	1	24	yes	—
13	C₁₉×#397	C₂²	1	24	yes	—
14	C₁₉×#396	C₂²	1	8	yes	—
15	C₁₉×#391	C₂²	1	6	yes	—
16	C₁₉×#390	C₂²	1	6	yes	—
17	C₁₉×#389	C₂²	1	12	yes	—
18	C₁₉×#386	C₂²	1	12	yes	—
19	C₁₉×#385	C₂²	1	12	yes	—
20	C₄×C₄⋊C₄×C₁₉	C₂²	1	12	yes	—
21	C₄×C₂²⋊C₄×C₁₉	C₂²	1	12	yes	—
22	C₁₉×#376	C₂²	1	4	yes	—
23	C₁₉×#376	C₂²	1	4	yes	—
24	C₂×C₁₉×#95	C₂²	1	4	yes	—
25	C₂×#41×C₁₉	—	2	12	no	—
26	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×#117	—	2	12	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
34	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
35	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
36	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
37	C₂×C₄²×C₁₉	—	2	12	no	—
38	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
39	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
40	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
41	C₁₉×#95	C₂³	1	4	yes	—
42	C₁₉×#95	C₂³	1	12	yes	—
43	C₁₉×#95	C₂³	1	24	yes	—
44	C₁₉×#95	C₂³	1	24	yes	—
45	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
46	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
47	#41×C₁₉	—	4	16	no	—
48	C₂×Q₈×C₁₉	—	2	6	no	—
49	C₂×D₄×C₁₉	—	2	12	no	—
50	C₂×D₄×C₁₉	—	2	6	no	—
51	C₂²×C₄×C₁₉	—	2	12	no	—
52	C₂²×C₄×C₁₉	—	2	12	no	—
53	C₂²×C₄×C₁₉	—	4	12	no	—
54	C₂²×C₄×C₁₉	#41	1	12	yes	—
55	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
56	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
57	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	12	no	—
61	C₄⋊C₄×C₁₉	—	4	24	no	—
62	C₂²⋊C₄×C₁₉	—	2	12	no	—
63	C₂²⋊C₄×C₁₉	—	4	24	no	—
64	C₄²×C₁₉	—	2	12	no	—
65	C₄²×C₁₉	—	2	12	no	—
66	C₄²×C₁₉	—	2	12	no	—
67	#34639	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂³×C₁₉	—	2	4	no	—
69	C₂³×C₁₉	—	2	6	no	—
70	C₂³×C₁₉	—	2	8	no	—
71	C₂³×C₁₉	C₂×#41	1	6	yes	—
72	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	4	no	—
74	D₄×C₁₉	—	4	8	no	—
75	D₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	2	12	no	—
77	C₂×C₄×C₁₉	—	2	12	no	—
78	C₂×C₄×C₁₉	—	2	6	no	—
79	C₂×C₄×C₁₉	—	2	12	no	—
80	C₂×C₄×C₁₉	—	2	24	no	—
81	C₂×C₄×C₁₉	—	2	12	no	—
82	C₂×C₄×C₁₉	—	4	24	no	—
83	C₂×C₄×C₁₉	—	4	8	no	—
84	C₂×C₄×C₁₉	#126	1	16	yes	—
85	C₂×C₄×C₁₉	C₂×#41	1	6	yes	—
86	C₂×C₄×C₁₉	C₂×#41	1	6	yes	—
87	#2645	C₂×C₁₉	1	4	yes	complemented
88	#2644	C₂×C₁₉	1	4	yes	complemented
89	#2643	C₂×C₁₉	1	8	yes	complemented
90	#2401	C₂×C₁₉	1	8	yes	complemented
91	#2297	C₂×C₁₉	1	3	yes	—
92	#2296	C₂×C₁₉	1	3	yes	complemented
93	C₂×#376	C₂×C₁₉	1	1	yes	characteristic, complemented
94	C₂²×C₁₉	—	2	12	no	—
95	C₂²×C₁₉	—	4	2	no	—
96	C₂²×C₁₉	—	4	12	no	—
97	C₂²×C₁₉	C₂×#126	1	4	yes	—
98	C₂²×C₁₉	C₂²×#41	1	3	yes	—
99	C₂²×C₁₉	#585	1	4	yes	—
100	C₄×C₁₉	—	4	2	no	—
101	C₄×C₁₉	—	4	12	no	—
102	C₄×C₁₉	—	4	12	no	—
103	C₄×C₁₉	C₂×#126	1	4	yes	—
104	C₄×C₁₉	C₂×#126	1	4	yes	—
105	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
106	C₂×#117	C₂²×C₁₉	1	3	yes	—
107	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
108	#401	C₂²×C₁₉	1	8	yes	—
109	#400	C₂²×C₁₉	1	24	yes	—
110	#397	C₂²×C₁₉	1	24	yes	—
111	#396	C₂²×C₁₉	1	8	yes	—
112	#391	C₂²×C₁₉	1	6	yes	—
113	#390	C₂²×C₁₉	1	6	yes	—
114	#389	C₂²×C₁₉	1	12	yes	—
115	#386	C₂²×C₁₉	1	12	yes	—
116	#385	C₂²×C₁₉	1	12	yes	—
117	C₄×C₄⋊C₄	C₂²×C₁₉	1	12	yes	—
118	C₄×C₂²⋊C₄	C₂²×C₁₉	1	12	yes	—
119	#376	C₂²×C₁₉	1	4	yes	—
120	#376	C₂²×C₁₉	1	4	yes	—
121	C₂×#95	C₂²×C₁₉	1	4	yes	—
122	C₂×C₁₉	—	2	4	no	—
123	C₂×C₁₉	—	8	2	no	—
124	C₂×C₁₉	C₂²×#126	1	1	yes	characteristic
125	C₂×C₁₉	#3455	1	6	yes	—
126	C₂×#41	—	2	12	no	—
127	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
128	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
129	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
130	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
131	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
132	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
133	#117	—	2	12	no	—
134	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
135	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
136	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
137	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
138	C₂×C₄²	—	2	12	no	—
139	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
140	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
141	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
142	#95	C₂³×C₁₉	1	4	yes	—
143	#95	C₂³×C₁₉	1	12	yes	—
144	#95	C₂³×C₁₉	1	24	yes	—
145	#95	C₂³×C₁₉	1	24	yes	—
146	C₁₉	#34639	1	1	yes	characteristic, direct product factor, Sylow
147	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
148	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
149	#41	—	4	16	no	—
150	C₂×Q₈	—	2	6	no	—
151	C₂×D₄	—	2	12	no	—
152	C₂×D₄	—	2	6	no	—
153	C₂²×C₄	—	2	12	no	—
154	C₂²×C₄	—	2	12	no	—
155	C₂²×C₄	—	4	12	no	—
156	C₂²×C₄	#41×C₁₉	1	12	yes	—
157	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
158	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
159	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
160	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
161	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
162	C₄⋊C₄	—	2	12	no	—
163	C₄⋊C₄	—	4	24	no	—
164	C₂²⋊C₄	—	2	12	no	—
165	C₂²⋊C₄	—	4	24	no	—
166	C₄²	—	2	12	no	—
167	C₄²	—	2	12	no	—
168	C₄²	—	2	12	no	—
169	C₂³	—	2	4	no	—
170	C₂³	—	2	6	no	—
171	C₂³	—	2	8	no	—
172	C₂³	C₂×#41×C₁₉	1	6	yes	—
173	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
174	Q₈	—	4	4	no	—
175	D₄	—	4	8	no	—
176	D₄	—	4	4	no	—
177	C₂×C₄	—	2	12	no	—
178	C₂×C₄	—	2	12	no	—
179	C₂×C₄	—	2	6	no	—
180	C₂×C₄	—	2	12	no	—
181	C₂×C₄	—	2	24	no	—
182	C₂×C₄	—	2	12	no	—
183	C₂×C₄	—	4	24	no	—
184	C₂×C₄	—	4	8	no	—
185	C₂×C₄	C₁₉×#126	1	16	yes	—
186	C₂×C₄	C₂×#41×C₁₉	1	6	yes	—
187	C₂×C₄	C₂×#41×C₁₉	1	6	yes	—
188	C₂²	—	2	12	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	12	no	—
191	C₂²	C₂×C₁₉×#126	1	4	yes	—
192	C₂²	C₂²×#41×C₁₉	1	3	yes	—
193	C₂²	C₁₉×#585	1	4	yes	—
194	C₄	—	4	2	no	—
195	C₄	—	4	12	no	—
196	C₄	—	4	12	no	—
197	C₄	C₂×C₁₉×#126	1	4	yes	—
198	C₄	C₂×C₁₉×#126	1	4	yes	—
199	C₂	—	2	4	no	—
200	C₂	—	8	2	no	—
201	C₂	C₂²×C₁₉×#126	1	1	yes	characteristic
202	C₂	C₁₉×#3455	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2645	C₂	semidirect
2. C₁₉×#2644	C₂	semidirect
3. C₁₉×#2643	C₂	semidirect
4. C₁₉×#2401	C₂	semidirect
6. C₁₉×#2296	C₂	semidirect
7. C₂×C₁₉×#376	C₂	semidirect
67. #34639	C₁₉	direct (N × H)
87. #2645	C₂×C₁₉	semidirect
88. #2644	C₂×C₁₉	semidirect
89. #2643	C₂×C₁₉	semidirect
90. #2401	C₂×C₁₉	semidirect
92. #2296	C₂×C₁₉	semidirect
93. C₂×#376	C₂×C₁₉	semidirect
146. C₁₉	#34639	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×#2645	2
C₁₉×#2644	2
C₁₉×#2643	2
C₁₉×#2401	2
C₁₉×#2297	2
C₁₉×#2296	2
C₂×C₁₉×#376	2
#34639	19

Subgroups — C19×#34639 #18040598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34639 #18040598