Subgroups — C₄²×C₅×C₃₂ #72182425

Order 2560.

708 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₃₂	C₂	1	6	yes	maximal
2	C₄²×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×C₃₂	C₂²	1	4	yes	—
4	C₂×C₄×C₅×C₁₆	C₄	1	3	yes	—
5	C₂×C₄×C₅×C₁₆	C₂²	1	3	yes	—
6	C₄²×C₅×C₈	C₄	1	1	yes	characteristic
7	C₄×C₅×C₃₂	C₄	1	24	yes	direct product factor
8	C₄²×C₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂²×C₅×C₁₆	C₂×C₄	1	3	yes	—
10	C₂²×C₅×C₁₆	C₂³	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	C₈	1	3	yes	—
12	C₂×C₄×C₅×C₈	C₂×C₄	1	3	yes	—
13	C₄³×C₅	C₈	1	1	yes	characteristic
14	C₂×C₅×C₃₂	C₂×C₄	1	24	yes	—
15	C₄×C₅×C₁₆	C₈	1	12	yes	—
16	C₄×C₅×C₁₆	C₂×C₄	1	12	yes	—
17	C₂×C₄×C₃₂	C₂×C₅	1	6	yes	—
18	C₄²×C₁₆	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₅×C₈	C₂×C₈	1	3	yes	—
20	C₂²×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₅	C₁₆	1	4	yes	—
22	C₂×C₄²×C₅	C₂×C₈	1	3	yes	—
23	C₂×C₅×C₁₆	C₄²	1	6	yes	—
24	C₂×C₅×C₁₆	C₂×C₈	1	12	yes	—
25	C₂×C₅×C₁₆	C₂²×C₄	1	6	yes	—
26	C₄×C₅×C₈	C₁₆	1	12	yes	—
27	C₄×C₅×C₈	C₄²	1	6	yes	—
28	C₄×C₅×C₈	C₂×C₈	1	6	yes	—
29	C₅×C₃₂	C₄²	1	16	yes	direct product factor
30	C₂²×C₃₂	C₂²×C₅	1	4	yes	—
31	C₂×C₄×C₁₆	C₄×C₅	1	3	yes	—
32	C₂×C₄×C₁₆	C₂²×C₅	1	3	yes	—
33	C₄²×C₈	C₄×C₅	1	1	yes	characteristic
34	C₄×C₃₂	C₄×C₅	1	24	yes	direct product factor
35	C₂²×C₄×C₅	C₂×C₁₆	1	6	yes	—
36	C₂²×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₅×C₈	C₄×C₈	1	6	yes	—
38	C₂×C₅×C₈	C₂×C₁₆	1	12	yes	—
39	C₂×C₅×C₈	C₂×C₄²	1	3	yes	—
40	C₂×C₅×C₈	C₂²×C₈	1	3	yes	—
41	C₄²×C₅	C₃₂	1	16	yes	direct product factor
42	C₄²×C₅	C₄×C₈	1	6	yes	—
43	C₄²×C₅	C₂×C₁₆	1	6	yes	—
44	C₅×C₁₆	C₄×C₈	1	12	yes	—
45	C₅×C₁₆	C₂×C₄²	1	4	yes	—
46	C₂²×C₁₆	C₂×C₄×C₅	1	3	yes	—
47	C₂²×C₁₆	C₂³×C₅	1	1	yes	characteristic
48	C₂×C₄×C₈	C₅×C₈	1	3	yes	—
49	C₂×C₄×C₈	C₂×C₄×C₅	1	3	yes	—
50	C₄³	C₅×C₈	1	1	yes	characteristic
51	C₂×C₃₂	C₂×C₄×C₅	1	24	yes	—
52	C₄×C₁₆	C₅×C₈	1	12	yes	—
53	C₄×C₁₆	C₂×C₄×C₅	1	12	yes	—
54	C₂³×C₅	C₂²×C₁₆	1	1	yes	characteristic
55	C₂×C₄×C₅	C₄×C₁₆	1	12	yes	—
56	C₂×C₄×C₅	C₂×C₃₂	1	24	yes	—
57	C₂×C₄×C₅	C₂×C₄×C₈	1	3	yes	—
58	C₂×C₄×C₅	C₂²×C₁₆	1	3	yes	—
59	C₅×C₈	C₄×C₁₆	1	12	yes	—
60	C₅×C₈	C₄³	1	1	yes	characteristic
61	C₅×C₈	C₂×C₄×C₈	1	3	yes	—
62	C₂²×C₈	C₂×C₅×C₈	1	3	yes	—
63	C₂²×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
64	C₂×C₄²	C₅×C₁₆	1	4	yes	—
65	C₂×C₄²	C₂×C₅×C₈	1	3	yes	—
66	C₂×C₁₆	C₄²×C₅	1	6	yes	—
67	C₂×C₁₆	C₂×C₅×C₈	1	12	yes	—
68	C₂×C₁₆	C₂²×C₄×C₅	1	6	yes	—
69	C₄×C₈	C₅×C₁₆	1	12	yes	—
70	C₄×C₈	C₄²×C₅	1	6	yes	—
71	C₄×C₈	C₂×C₅×C₈	1	6	yes	—
72	C₃₂	C₄²×C₅	1	16	yes	direct product factor
73	C₂²×C₅	C₂×C₄×C₁₆	1	3	yes	—
74	C₂²×C₅	C₂²×C₃₂	1	4	yes	—
75	C₄×C₅	C₄×C₃₂	1	24	yes	direct product factor
76	C₄×C₅	C₄²×C₈	1	1	yes	characteristic
77	C₄×C₅	C₂×C₄×C₁₆	1	3	yes	—
78	C₂²×C₄	C₂×C₅×C₁₆	1	6	yes	—
79	C₂²×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
80	C₂×C₈	C₄×C₅×C₈	1	6	yes	—
81	C₂×C₈	C₂×C₅×C₁₆	1	12	yes	—
82	C₂×C₈	C₂×C₄²×C₅	1	3	yes	—
83	C₂×C₈	C₂²×C₅×C₈	1	3	yes	—
84	C₄²	C₅×C₃₂	1	16	yes	direct product factor
85	C₄²	C₄×C₅×C₈	1	6	yes	—
86	C₄²	C₂×C₅×C₁₆	1	6	yes	—
87	C₁₆	C₄×C₅×C₈	1	12	yes	—
88	C₁₆	C₂×C₄²×C₅	1	4	yes	—
89	C₂×C₅	C₄²×C₁₆	1	1	yes	characteristic
90	C₂×C₅	C₂×C₄×C₃₂	1	6	yes	—
91	C₂³	C₂²×C₅×C₁₆	1	1	yes	characteristic
92	C₂×C₄	C₄×C₅×C₁₆	1	12	yes	—
93	C₂×C₄	C₂×C₅×C₃₂	1	24	yes	—
94	C₂×C₄	C₂×C₄×C₅×C₈	1	3	yes	—
95	C₂×C₄	C₂²×C₅×C₁₆	1	3	yes	—
96	C₈	C₄×C₅×C₁₆	1	12	yes	—
97	C₈	C₄³×C₅	1	1	yes	characteristic
98	C₈	C₂×C₄×C₅×C₈	1	3	yes	—
99	C₅	C₄²×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
100	C₂²	C₂×C₄×C₅×C₁₆	1	3	yes	—
101	C₂²	C₂²×C₅×C₃₂	1	4	yes	—
102	C₄	C₄×C₅×C₃₂	1	24	yes	direct product factor
103	C₄	C₄²×C₅×C₈	1	1	yes	characteristic
104	C₄	C₂×C₄×C₅×C₁₆	1	3	yes	—
105	C₂	C₄²×C₅×C₁₆	1	1	yes	characteristic
106	C₂	C₂×C₄×C₅×C₃₂	1	6	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₆	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂²×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₄×C₅×C₃₂	C₄	direct (N × H)
8. C₄²×C₃₂	C₅	direct (N × H)
29. C₅×C₃₂	C₄²	direct (N × H)
34. C₄×C₃₂	C₄×C₅	direct (N × H)
41. C₄²×C₅	C₃₂	direct (N × H)
72. C₃₂	C₄²×C₅	direct (N × H)
75. C₄×C₅	C₄×C₃₂	direct (N × H)
84. C₄²	C₅×C₃₂	direct (N × H)
99. C₅	C₄²×C₃₂	direct (N × H)
102. C₄	C₄×C₅×C₃₂	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×C₄×C₅×C₃₂	2
C₄²×C₅×C₁₆	2
C₄²×C₃₂	5

Subgroups — C42×C5×C32 #72182425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅×C₃₂ #72182425