Subgroups — C₁₉×#13186 #18019145

Order 4864.

310 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#365	C₂	1	2	yes	maximal
2	C₂×C₁₉×#364	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1772	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1386	C₂	1	2	yes	maximal
6	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
7	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
8	C₁₉×#427	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#106	—	2	1	no	—
10	C₂×C₁₉×#106	C₂²	1	2	yes	—
11	C₁₉×#405	—	2	1	no	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#384	—	2	1	no	—
14	C₁₉×#365	—	2	4	no	—
15	C₁₉×#364	C₄	1	4	yes	complemented
16	C₁₉×#339	—	2	1	no	—
17	C₂×M₁₆×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
20	C₁₉×#117	—	2	1	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
23	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₁₉×M₃₂	—	2	2	no	—
25	C₁₉×M₃₂	C₂×C₄	1	4	yes	—
26	C₂×C₁₆×C₁₉	—	2	2	no	—
27	C₁₉×#108	—	2	1	no	—
28	C₁₉×#108	D₄	1	2	yes	—
29	C₁₉×#107	Q₈	1	2	yes	—
30	C₁₉×#106	—	2	1	no	—
31	C₁₉×#106	—	2	2	no	—
32	C₁₉×#106	—	2	2	no	—
33	C₁₉×#106	—	4	2	no	—
34	C₁₉×#97	—	4	1	no	—
35	C₄×C₈×C₁₉	—	4	1	no	—
36	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₉	Q₈	1	2	yes	—
38	C₂²×C₄×C₁₉	—	2	1	no	—
39	C₂²×C₄×C₁₉	—	4	2	no	—
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	M₁₆×C₁₉	—	2	2	no	—
42	M₁₆×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	—	4	1	no	—
44	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
48	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
53	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	4	2	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	8	4	no	—
58	C₂²⋊C₄×C₁₉	—	4	1	no	—
59	C₄²×C₁₉	—	2	1	no	—
60	C₄²×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
62	C₁₆×C₁₉	—	2	4	no	—
63	#13186	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂×C₄×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	—	8	4	no	—
69	C₂×C₄×C₁₉	—	8	2	no	—
70	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
76	C₈×C₁₉	—	4	2	no	—
77	C₈×C₁₉	#106	1	2	yes	—
78	C₈×C₁₉	#106	1	2	yes	—
79	C₈×C₁₉	C₄×D₄	1	1	yes	characteristic
80	C₈×C₁₉	C₄×Q₈	1	1	yes	characteristic
81	C₈×C₁₉	#125	1	1	yes	characteristic
82	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
83	C₂×#365	C₂×C₁₉	1	2	yes	—
84	C₂×#364	C₂×C₁₉	1	1	yes	characteristic
85	#1844	C₂×C₁₉	1	1	yes	characteristic
86	#1772	C₂×C₁₉	1	1	yes	characteristic
87	#1386	C₂×C₁₉	1	2	yes	—
88	C₂²×C₁₉	—	2	2	no	—
89	C₂²×C₁₉	#428	1	1	yes	characteristic
90	C₂²×C₁₉	#460	1	1	yes	characteristic
91	C₂²×C₁₉	#476	1	1	yes	characteristic
92	C₄×C₁₉	—	2	4	no	—
93	C₄×C₁₉	—	8	2	no	—
94	C₄×C₁₉	—	16	2	no	—
95	C₄×C₁₉	#389	1	1	yes	characteristic
96	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
97	C₄×C₁₉	#461	1	1	yes	characteristic
98	C₄×C₁₉	#475	1	1	yes	characteristic
99	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
100	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
101	#427	C₂²×C₁₉	1	1	yes	characteristic
102	C₂×#106	—	2	1	no	—
103	C₂×#106	C₂²×C₁₉	1	2	yes	—
104	#405	—	2	1	no	—
105	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
106	#384	—	2	1	no	—
107	#365	—	2	4	no	—
108	#364	C₄×C₁₉	1	4	yes	complemented
109	#339	—	2	1	no	—
110	C₂×C₁₉	—	2	1	no	—
111	C₂×C₁₉	—	2	1	no	—
112	C₂×C₁₉	#1948	1	1	yes	characteristic
113	C₂×C₁₉	#2230	1	2	yes	—
114	C₂×M₁₆	—	2	1	no	—
115	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
116	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
117	#117	—	2	1	no	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	—	4	2	no	—
120	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
121	M₃₂	—	2	2	no	—
122	M₃₂	C₂×C₄×C₁₉	1	4	yes	—
123	C₂×C₁₆	—	2	2	no	—
124	#108	—	2	1	no	—
125	#108	D₄×C₁₉	1	2	yes	—
126	#107	Q₈×C₁₉	1	2	yes	—
127	#106	—	2	1	no	—
128	#106	—	2	2	no	—
129	#106	—	2	2	no	—
130	#106	—	4	2	no	—
131	#97	—	4	1	no	—
132	C₄×C₈	—	4	1	no	—
133	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
134	C₄×C₈	Q₈×C₁₉	1	2	yes	—
135	C₁₉	#13186	1	1	yes	characteristic, direct product factor, Sylow
136	C₂²×C₄	—	2	1	no	—
137	C₂²×C₄	—	4	2	no	—
138	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
139	M₁₆	—	2	2	no	—
140	M₁₆	—	4	1	no	—
141	C₂×C₈	—	4	1	no	—
142	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
143	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
144	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
145	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
146	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
147	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
148	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
149	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
150	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
151	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
152	C₄⋊C₄	—	2	2	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	8	4	no	—
156	C₂²⋊C₄	—	4	1	no	—
157	C₄²	—	2	1	no	—
158	C₄²	—	4	1	no	—
159	C₄²	C₄⋊C₄×C₁₉	1	2	yes	—
160	C₁₆	—	2	4	no	—
161	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	8	4	no	—
166	C₂×C₄	—	8	2	no	—
167	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
168	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
169	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
171	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
172	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
173	C₈	—	4	2	no	—
174	C₈	C₁₉×#106	1	2	yes	—
175	C₈	C₁₉×#106	1	2	yes	—
176	C₈	C₄×D₄×C₁₉	1	1	yes	characteristic
177	C₈	C₄×Q₈×C₁₉	1	1	yes	characteristic
178	C₈	C₁₉×#125	1	1	yes	characteristic
179	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
180	C₂²	—	2	2	no	—
181	C₂²	C₁₉×#428	1	1	yes	characteristic
182	C₂²	C₁₉×#460	1	1	yes	characteristic
183	C₂²	C₁₉×#476	1	1	yes	characteristic
184	C₄	—	2	4	no	—
185	C₄	—	8	2	no	—
186	C₄	—	16	2	no	—
187	C₄	C₁₉×#389	1	1	yes	characteristic
188	C₄	C₂×C₁₉×#106	1	1	yes	characteristic
189	C₄	C₁₉×#461	1	1	yes	characteristic
190	C₄	C₁₉×#475	1	1	yes	characteristic
191	C₂	—	2	1	no	—
192	C₂	—	2	1	no	—
193	C₂	C₁₉×#1948	1	1	yes	characteristic
194	C₂	C₁₉×#2230	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#476
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₉×#364	C₄	semidirect
63. #13186	C₁₉	direct (N × H)
108. #364	C₄×C₁₉	semidirect
135. C₁₉	#13186	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×#365	2
C₂×C₁₉×#364	2
C₁₉×#1844	2
C₁₉×#1772	2
C₁₉×#1386	2
#13186	19

Subgroups — C19×#13186 #18019145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13186 #18019145