Subgroups — C₁₉×#13627 #18019586

Order 4864.

218 conjugacy classes of subgroups.

The subgroup lattice has 124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×M₆₄	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×C₄⋊C₃₂	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×M₆₄	—	2	4	no	—
8	C₂×C₁₉×C₃₂	C₂²	1	4	yes	—
9	C₄×C₁₆×C₁₉	C₄	1	2	yes	—
10	C₄×C₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₉	C₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₈	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	—	2	2	no	—
15	C₂×C₁₆×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
18	C₂×C₁₆×C₁₉	Q₈	1	2	yes	—
19	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₁₉	C₈	1	2	yes	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₁₉×C₃₂	—	2	4	no	—
23	C₂²×C₄×C₁₉	C₁₆	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
28	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
30	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₄²×C₁₉	C₁₆	1	1	yes	characteristic
32	C₄²×C₁₉	C₁₆	1	1	yes	characteristic
33	C₄²×C₁₉	C₂×C₈	1	2	yes	—
34	C₁₆×C₁₉	—	2	2	no	—
35	C₁₆×C₁₉	C₄⋊C₄	1	2	yes	—
36	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₁₆×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	#13627	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×C₁₆	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×C₁₆	1	2	yes	—
45	C₂×C₄×C₁₉	M₃₂	1	2	yes	—
46	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
47	C₈×C₁₉	—	2	2	no	—
48	C₈×C₁₉	C₄⋊C₈	1	2	yes	—
49	C₈×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₈×C₁₉	C₂×M₁₆	1	1	yes	characteristic
51	C₂×M₆₄	C₂×C₁₉	1	2	yes	—
52	C₂×C₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic
53	C₄⋊C₃₂	C₂×C₁₉	1	4	yes	complemented
54	C₂²×C₁₉	—	2	2	no	—
55	C₂²×C₁₉	C₄⋊C₁₆	1	2	yes	—
56	C₂²×C₁₉	C₂²×C₁₆	1	1	yes	characteristic
57	C₄×C₁₉	—	2	2	no	—
58	C₄×C₁₉	C₄⋊C₁₆	1	2	yes	—
59	C₄×C₁₉	M₆₄	1	4	yes	complemented
60	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
61	C₄×C₁₉	C₂×M₃₂	1	1	yes	characteristic
62	C₂²×C₁₆	C₄×C₁₉	1	1	yes	characteristic
63	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
64	C₂×C₄×C₈	C₄×C₁₉	1	1	yes	characteristic
65	M₆₄	—	2	4	no	—
66	C₂×C₃₂	C₂²×C₁₉	1	4	yes	—
67	C₄×C₁₆	C₄×C₁₉	1	2	yes	—
68	C₄×C₁₆	C₂²×C₁₉	1	2	yes	—
69	C₂×C₁₉	—	2	2	no	—
70	C₂×C₁₉	C₂×C₄⋊C₁₆	1	1	yes	characteristic
71	C₂×C₁₉	C₂×M₆₄	1	2	yes	—
72	C₂²×C₈	C₈×C₁₉	1	1	yes	characteristic
73	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
74	C₂×C₄²	C₈×C₁₉	1	1	yes	characteristic
75	C₂×C₁₆	—	2	2	no	—
76	C₂×C₁₆	C₂×C₄×C₁₉	1	2	yes	—
77	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
78	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
79	C₂×C₁₆	Q₈×C₁₉	1	2	yes	—
80	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
81	C₄×C₈	C₈×C₁₉	1	2	yes	—
82	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
83	C₃₂	—	2	4	no	—
84	C₁₉	#13627	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²×C₄	C₁₆×C₁₉	1	2	yes	—
86	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
89	C₂×C₈	C₂×C₈×C₁₉	1	2	yes	—
90	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
91	C₂×C₈	M₁₆×C₁₉	1	2	yes	—
92	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
93	C₄²	C₁₆×C₁₉	1	1	yes	characteristic
94	C₄²	C₁₆×C₁₉	1	1	yes	characteristic
95	C₄²	C₂×C₈×C₁₉	1	2	yes	—
96	C₁₆	—	2	2	no	—
97	C₁₆	C₄⋊C₄×C₁₉	1	2	yes	—
98	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
99	C₁₆	C₂×Q₈×C₁₉	1	1	yes	characteristic
100	C₂³	C₂×C₁₆×C₁₉	1	1	yes	characteristic
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	C₁₉×C₄⋊C₈	1	2	yes	—
103	C₂×C₄	C₂×C₁₆×C₁₉	1	2	yes	—
104	C₂×C₄	C₂×C₁₆×C₁₉	1	1	yes	characteristic
105	C₂×C₄	C₂×C₁₆×C₁₉	1	2	yes	—
106	C₂×C₄	C₁₉×M₃₂	1	2	yes	—
107	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	C₁₉×C₄⋊C₈	1	2	yes	—
110	C₈	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
111	C₈	C₂×M₁₆×C₁₉	1	1	yes	characteristic
112	C₂²	—	2	2	no	—
113	C₂²	C₁₉×C₄⋊C₁₆	1	2	yes	—
114	C₂²	C₂²×C₁₆×C₁₉	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	C₁₉×C₄⋊C₁₆	1	2	yes	—
117	C₄	C₁₉×M₆₄	1	4	yes	complemented
118	C₄	C₂×C₁₉×C₄⋊C₈	1	1	yes	characteristic
119	C₄	C₂×C₁₉×M₃₂	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×C₁₉×C₄⋊C₁₆	1	1	yes	characteristic
122	C₂	C₂×C₁₉×M₆₄	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆×C₁₉	C₂³
commutator	C₂²	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂²×C₁₉	C₂²×C₁₆
prime radical	C₂³×C₁₉	C₂×C₁₆
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×C₄⋊C₃₂	C₂	semidirect
38. #13627	C₁₉	direct (N × H)
53. C₄⋊C₃₂	C₂×C₁₉	semidirect
59. C₄×C₁₉	M₆₄	semidirect
84. C₁₉	#13627	direct (N × H)
117. C₄	C₁₉×M₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×M₆₄	2
C₂×C₄×C₁₆×C₁₉	2
C₁₉×C₄⋊C₃₂	2
#13627	19

Subgroups — C19×#13627 #18019586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13627 #18019586