Subgroups — C₄×C₅×C₁₉×C₆₄ #72201607

Order 24320.

172 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₁₉×C₆₄	C₂	1	2	yes	maximal
3	C₄×C₅×C₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₂×C₅×C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₅×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
6	C₅×C₁₉×C₆₄	C₄	1	4	yes	direct product factor
7	C₄×C₅×C₈×C₁₉	C₈	1	1	yes	characteristic
8	C₂×C₅×C₁₆×C₁₉	C₈	1	1	yes	characteristic
9	C₂×C₅×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₅×C₁₉×C₃₂	C₈	1	2	yes	—
11	C₅×C₁₉×C₃₂	C₂×C₄	1	2	yes	—
12	C₄×C₁₉×C₆₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₉×C₆₄	C₂×C₅	1	2	yes	—
14	C₄×C₁₉×C₃₂	C₂×C₅	1	1	yes	characteristic
15	C₂×C₅×C₈×C₁₉	C₁₆	1	1	yes	characteristic
16	C₂×C₅×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₅×C₁₉	C₁₆	1	1	yes	characteristic
18	C₅×C₁₆×C₁₉	C₁₆	1	2	yes	—
19	C₅×C₁₆×C₁₉	C₄²	1	1	yes	characteristic
20	C₅×C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
21	C₄×C₅×C₆₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₁₉×C₃₂	C₄×C₅	1	1	yes	characteristic
23	C₂×C₁₉×C₃₂	C₂²×C₅	1	1	yes	characteristic
24	C₄×C₁₆×C₁₉	C₄×C₅	1	1	yes	characteristic
25	C₁₉×C₆₄	C₄×C₅	1	4	yes	direct product factor
26	C₂×C₄×C₅×C₁₉	C₃₂	1	2	yes	—
27	C₂×C₄×C₅×C₁₉	C₂×C₁₆	1	1	yes	characteristic
28	C₅×C₈×C₁₉	C₃₂	1	2	yes	—
29	C₅×C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
30	C₅×C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
31	C₂×C₅×C₆₄	C₂×C₁₉	1	2	yes	—
32	C₄×C₅×C₃₂	C₂×C₁₉	1	1	yes	characteristic
33	C₂×C₁₆×C₁₉	C₅×C₈	1	1	yes	characteristic
34	C₂×C₁₆×C₁₉	C₂×C₄×C₅	1	1	yes	characteristic
35	C₄×C₈×C₁₉	C₅×C₈	1	1	yes	characteristic
36	C₁₉×C₃₂	C₅×C₈	1	2	yes	—
37	C₁₉×C₃₂	C₂×C₄×C₅	1	2	yes	—
38	C₂²×C₅×C₁₉	C₂×C₃₂	1	1	yes	characteristic
39	C₄×C₅×C₁₉	C₆₄	1	4	yes	direct product factor
40	C₄×C₅×C₁₉	C₄×C₁₆	1	1	yes	characteristic
41	C₄×C₅×C₁₉	C₂×C₃₂	1	1	yes	characteristic
42	C₂×C₅×C₃₂	C₄×C₁₉	1	1	yes	characteristic
43	C₂×C₅×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
44	C₄×C₅×C₁₆	C₄×C₁₉	1	1	yes	characteristic
45	C₅×C₆₄	C₄×C₁₉	1	4	yes	direct product factor
46	C₂×C₈×C₁₉	C₅×C₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₉	C₂×C₅×C₈	1	1	yes	characteristic
48	C₄²×C₁₉	C₅×C₁₆	1	1	yes	characteristic
49	C₁₆×C₁₉	C₅×C₁₆	1	2	yes	—
50	C₁₆×C₁₉	C₄²×C₅	1	1	yes	characteristic
51	C₁₆×C₁₉	C₂×C₅×C₈	1	1	yes	characteristic
52	C₄×C₆₄	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₅×C₁₉	C₄×C₃₂	1	1	yes	characteristic
54	C₂×C₅×C₁₉	C₂×C₆₄	1	2	yes	—
55	C₂×C₅×C₁₆	C₈×C₁₉	1	1	yes	characteristic
56	C₂×C₅×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
57	C₄×C₅×C₈	C₈×C₁₉	1	1	yes	characteristic
58	C₅×C₃₂	C₈×C₁₉	1	2	yes	—
59	C₅×C₃₂	C₂×C₄×C₁₉	1	2	yes	—
60	C₂×C₄×C₁₉	C₅×C₃₂	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×C₅×C₁₆	1	1	yes	characteristic
62	C₈×C₁₉	C₅×C₃₂	1	2	yes	—
63	C₈×C₁₉	C₄×C₅×C₈	1	1	yes	characteristic
64	C₈×C₁₉	C₂×C₅×C₁₆	1	1	yes	characteristic
65	C₂×C₆₄	C₂×C₅×C₁₉	1	2	yes	—
66	C₄×C₃₂	C₂×C₅×C₁₉	1	1	yes	characteristic
67	C₅×C₁₉	C₄×C₆₄	1	1	yes	characteristic, direct product factor, Hall
68	C₂×C₅×C₈	C₁₆×C₁₉	1	1	yes	characteristic
69	C₂×C₅×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
70	C₄²×C₅	C₁₆×C₁₉	1	1	yes	characteristic
71	C₅×C₁₆	C₁₆×C₁₉	1	2	yes	—
72	C₅×C₁₆	C₄²×C₁₉	1	1	yes	characteristic
73	C₅×C₁₆	C₂×C₈×C₁₉	1	1	yes	characteristic
74	C₂²×C₁₉	C₂×C₅×C₃₂	1	1	yes	characteristic
75	C₄×C₁₉	C₅×C₆₄	1	4	yes	direct product factor
76	C₄×C₁₉	C₄×C₅×C₁₆	1	1	yes	characteristic
77	C₄×C₁₉	C₂×C₅×C₃₂	1	1	yes	characteristic
78	C₂×C₃₂	C₄×C₅×C₁₉	1	1	yes	characteristic
79	C₂×C₃₂	C₂²×C₅×C₁₉	1	1	yes	characteristic
80	C₄×C₁₆	C₄×C₅×C₁₉	1	1	yes	characteristic
81	C₆₄	C₄×C₅×C₁₉	1	4	yes	direct product factor
82	C₂×C₄×C₅	C₁₉×C₃₂	1	2	yes	—
83	C₂×C₄×C₅	C₂×C₁₆×C₁₉	1	1	yes	characteristic
84	C₅×C₈	C₁₉×C₃₂	1	2	yes	—
85	C₅×C₈	C₄×C₈×C₁₉	1	1	yes	characteristic
86	C₅×C₈	C₂×C₁₆×C₁₉	1	1	yes	characteristic
87	C₂×C₁₉	C₄×C₅×C₃₂	1	1	yes	characteristic
88	C₂×C₁₉	C₂×C₅×C₆₄	1	2	yes	—
89	C₂×C₁₆	C₅×C₈×C₁₉	1	1	yes	characteristic
90	C₂×C₁₆	C₂×C₄×C₅×C₁₉	1	1	yes	characteristic
91	C₄×C₈	C₅×C₈×C₁₉	1	1	yes	characteristic
92	C₃₂	C₅×C₈×C₁₉	1	2	yes	—
93	C₃₂	C₂×C₄×C₅×C₁₉	1	2	yes	—
94	C₂²×C₅	C₂×C₁₉×C₃₂	1	1	yes	characteristic
95	C₄×C₅	C₁₉×C₆₄	1	4	yes	direct product factor
96	C₄×C₅	C₄×C₁₆×C₁₉	1	1	yes	characteristic
97	C₄×C₅	C₂×C₁₉×C₃₂	1	1	yes	characteristic
98	C₁₉	C₄×C₅×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
99	C₂×C₈	C₅×C₁₆×C₁₉	1	1	yes	characteristic
100	C₂×C₈	C₂×C₅×C₈×C₁₉	1	1	yes	characteristic
101	C₄²	C₅×C₁₆×C₁₉	1	1	yes	characteristic
102	C₁₆	C₅×C₁₆×C₁₉	1	2	yes	—
103	C₁₆	C₄²×C₅×C₁₉	1	1	yes	characteristic
104	C₁₆	C₂×C₅×C₈×C₁₉	1	1	yes	characteristic
105	C₂×C₅	C₄×C₁₉×C₃₂	1	1	yes	characteristic
106	C₂×C₅	C₂×C₁₉×C₆₄	1	2	yes	—
107	C₂×C₄	C₅×C₁₉×C₃₂	1	2	yes	—
108	C₂×C₄	C₂×C₅×C₁₆×C₁₉	1	1	yes	characteristic
109	C₈	C₅×C₁₉×C₃₂	1	2	yes	—
110	C₈	C₂×C₅×C₁₆×C₁₉	1	1	yes	characteristic
111	C₈	C₄×C₅×C₈×C₁₉	1	1	yes	characteristic
112	C₅	C₄×C₁₉×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
113	C₂²	C₂×C₅×C₁₉×C₃₂	1	1	yes	characteristic
114	C₄	C₅×C₁₉×C₆₄	1	4	yes	direct product factor
115	C₄	C₂×C₅×C₁₉×C₃₂	1	1	yes	characteristic
116	C₄	C₄×C₅×C₁₆×C₁₉	1	1	yes	characteristic
117	C₂	C₂×C₅×C₁₉×C₆₄	1	2	yes	—
118	C₂	C₄×C₅×C₁₉×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃₂	C₂²×C₅×C₁₉
socle, prime radical	C₂²×C₅×C₁₉	C₂×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×C₁₉×C₆₄	C₄	direct (N × H)
12. C₄×C₁₉×C₆₄	C₅	direct (N × H)
21. C₄×C₅×C₆₄	C₁₉	direct (N × H)
25. C₁₉×C₆₄	C₄×C₅	direct (N × H)
39. C₄×C₅×C₁₉	C₆₄	direct (N × H)
45. C₅×C₆₄	C₄×C₁₉	direct (N × H)
52. C₄×C₆₄	C₅×C₁₉	direct (N × H)
67. C₅×C₁₉	C₄×C₆₄	direct (N × H)
75. C₄×C₁₉	C₅×C₆₄	direct (N × H)
81. C₆₄	C₄×C₅×C₁₉	direct (N × H)
95. C₄×C₅	C₁₉×C₆₄	direct (N × H)
98. C₁₉	C₄×C₅×C₆₄	direct (N × H)
112. C₅	C₄×C₁₉×C₆₄	direct (N × H)
114. C₄	C₅×C₁₉×C₆₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₁₉×C₃₂	2
C₂×C₅×C₁₉×C₆₄	2
C₄×C₁₉×C₆₄	5
C₄×C₅×C₆₄	19

Subgroups — C4×C5×C19×C64 #72201607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₁₉×C₆₄ #72201607