Subgroups — C₁₉×#13266 #18019225

Order 4864.

342 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2150	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1379	C₂	1	4	yes	maximal
5	C₁₉×#533	C₄	1	1	yes	characteristic
6	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
8	C₁₉×#446	—	2	2	no	—
9	C₈×Q₈×C₁₉	—	2	2	no	—
10	C₁₉×#424	C₄	1	2	yes	—
11	C₁₉×#423	C₄	1	1	yes	characteristic
12	C₁₉×#405	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×C₄⋊C₁₆	—	2	2	no	—
15	C₄×C₁₆×C₁₉	—	2	2	no	—
16	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	C₈	1	2	yes	—
20	C₁₉×#125	C₈	1	2	yes	—
21	C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₁₉×#117	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₁₉×M₃₂	—	2	4	no	—
26	C₂×C₁₆×C₁₉	—	2	2	no	—
27	C₂×C₁₆×C₁₉	—	2	2	no	—
28	C₂×C₁₆×C₁₉	—	2	2	no	—
29	C₂×C₁₆×C₁₉	Q₈	1	4	yes	complemented
30	C₁₉×C₄⋊C₈	—	2	4	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×#97	—	2	2	no	—
33	C₄×C₈×C₁₉	—	2	2	no	—
34	C₄×C₈×C₁₉	D₄	1	2	yes	—
35	C₄×C₈×C₁₉	D₄	1	2	yes	—
36	C₂×Q₈×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	M₁₆×C₁₉	—	2	4	no	—
40	C₂×C₈×C₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	—	2	2	no	—
42	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
46	C₂×C₈×C₁₉	#41	1	2	yes	—
47	C₄⋊C₄×C₁₉	—	2	4	no	—
48	C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₄⋊C₄×C₁₉	C₂×C₈	1	4	yes	—
50	C₂²⋊C₄×C₁₉	—	2	2	no	—
51	C₄²×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
55	C₁₆×C₁₉	—	2	4	no	—
56	C₁₆×C₁₉	—	4	2	no	—
57	#13266	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
59	Q₈×C₁₉	—	4	4	no	—
60	C₂×C₄×C₁₉	—	2	4	no	—
61	C₂×C₄×C₁₉	—	2	4	no	—
62	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
63	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
64	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
66	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#131	1	2	yes	—
68	C₈×C₁₉	—	2	2	no	—
69	C₈×C₁₉	—	4	2	no	—
70	C₈×C₁₉	C₂²⋊Q₈	1	2	yes	—
71	C₈×C₁₉	#124	1	1	yes	characteristic
72	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
73	#2960	C₂×C₁₉	1	1	yes	characteristic
74	#2150	C₂×C₁₉	1	1	yes	characteristic
75	C₂×C₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic
76	#1379	C₂×C₁₉	1	4	yes	—
77	C₂²×C₁₉	—	2	2	no	—
78	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
79	C₂²×C₁₉	#446	1	2	yes	—
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	4	4	no	—
82	C₄×C₁₉	#350	1	4	yes	—
83	C₄×C₁₉	#391	1	1	yes	characteristic
84	C₄×C₁₉	#408	1	1	yes	characteristic
85	C₄×C₁₉	C₈×Q₈	1	2	yes	—
86	#533	C₄×C₁₉	1	1	yes	characteristic
87	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
88	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
89	#446	—	2	2	no	—
90	C₈×Q₈	—	2	2	no	—
91	#424	C₄×C₁₉	1	2	yes	—
92	#423	C₄×C₁₉	1	1	yes	characteristic
93	#405	C₂²×C₁₉	1	2	yes	—
94	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
95	C₄⋊C₁₆	—	2	2	no	—
96	C₄×C₁₆	—	2	2	no	—
97	C₂×C₁₉	—	2	2	no	—
98	C₂×C₁₉	#1984	1	1	yes	characteristic
99	C₂×C₁₉	C₂×#350	1	2	yes	—
100	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
101	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
102	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
103	C₄⋊Q₈	C₈×C₁₉	1	2	yes	—
104	#125	C₈×C₁₉	1	2	yes	—
105	C₂²⋊Q₈	—	2	2	no	—
106	C₄×Q₈	—	2	2	no	—
107	#117	C₂×C₄×C₁₉	1	2	yes	—
108	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
109	M₃₂	—	2	4	no	—
110	C₂×C₁₆	—	2	2	no	—
111	C₂×C₁₆	—	2	2	no	—
112	C₂×C₁₆	—	2	2	no	—
113	C₂×C₁₆	Q₈×C₁₉	1	4	yes	complemented
114	C₄⋊C₈	—	2	4	no	—
115	C₄⋊C₈	—	2	2	no	—
116	#97	—	2	2	no	—
117	C₄×C₈	—	2	2	no	—
118	C₄×C₈	D₄×C₁₉	1	2	yes	—
119	C₄×C₈	D₄×C₁₉	1	2	yes	—
120	C₁₉	#13266	1	1	yes	characteristic, direct product factor, Sylow
121	C₂×Q₈	—	2	2	no	—
122	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
123	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
124	M₁₆	—	2	4	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
128	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
129	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
130	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
131	C₂×C₈	#41×C₁₉	1	2	yes	—
132	C₄⋊C₄	—	2	4	no	—
133	C₄⋊C₄	—	2	2	no	—
134	C₄⋊C₄	C₂×C₈×C₁₉	1	4	yes	—
135	C₂²⋊C₄	—	2	2	no	—
136	C₄²	—	2	2	no	—
137	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
138	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
139	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
140	C₁₆	—	2	4	no	—
141	C₁₆	—	4	2	no	—
142	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
143	Q₈	—	4	4	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
147	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
148	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
149	C₂×C₄	C₄×Q₈×C₁₉	1	2	yes	—
150	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
151	C₂×C₄	C₁₉×#131	1	2	yes	—
152	C₈	—	2	2	no	—
153	C₈	—	4	2	no	—
154	C₈	C₁₉×C₂²⋊Q₈	1	2	yes	—
155	C₈	C₁₉×#124	1	1	yes	characteristic
156	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
157	C₂²	—	2	2	no	—
158	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
159	C₂²	C₁₉×#446	1	2	yes	—
160	C₄	—	2	2	no	—
161	C₄	—	4	4	no	—
162	C₄	C₁₉×#350	1	4	yes	—
163	C₄	C₁₉×#391	1	1	yes	characteristic
164	C₄	C₁₉×#408	1	1	yes	characteristic
165	C₄	C₈×Q₈×C₁₉	1	2	yes	—
166	C₂	—	2	2	no	—
167	C₂	C₁₉×#1984	1	1	yes	characteristic
168	C₂	C₂×C₁₉×#350	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₉	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
29. C₂×C₁₆×C₁₉	Q₈	semidirect
57. #13266	C₁₉	direct (N × H)
113. C₂×C₁₆	Q₈×C₁₉	semidirect
120. C₁₉	#13266	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×#2960	2
C₁₉×#2150	2
C₂×C₄×C₁₆×C₁₉	2
C₁₉×#1379	2
#13266	19

Subgroups — C19×#13266 #18019225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13266 #18019225