Subgroups — C₂³×Dic₄₀ #13005782

Order 1280.

2078 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₂₀	C₂	1	2	yes	maximal
2	C₂³×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₄₀	C₂	1	28	yes	maximal, direct product factor
4	C₂³×Dic₁₀	—	2	2	no	—
5	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₀	—	2	14	no	—
7	C₂²×Dic₂₀	C₂²	1	28	yes	—
8	C₂²×C₅×C₁₆	C₂²	1	14	yes	—
9	C₂×Dic₄₀	C₂²	1	112	yes	direct product factor
10	C₂³×Q₃₂	—	5	1	no	maximal, Sylow
11	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
12	C₂³×Dic₅	—	4	2	no	—
13	C₂²×Dic₁₀	—	2	28	no	—
14	C₂²×Dic₁₀	—	4	14	no	—
15	C₂²×C₅×C₈	D₄	1	7	yes	—
16	C₂²×C₅×C₈	C₂³	1	7	yes	—
17	C₂×Dic₂₀	—	2	84	no	—
18	C₂×Dic₂₀	C₂³	1	56	yes	—
19	C₂×C₅×C₁₆	C₂³	1	28	yes	—
20	Dic₄₀	C₂³	1	64	yes	direct product factor
21	C₂³×Q₁₆	—	5	2	no	—
22	C₂²×Q₃₂	—	5	28	no	—
23	C₂³×C₁₆	D₅	1	1	yes	characteristic
24	C₂⁴×C₅	D₈	1	1	yes	characteristic
25	C₂²×C₄×C₅	D₈	1	7	yes	—
26	C₂²×C₄×C₅	C₂×D₄	1	7	yes	—
27	C₂²×Dic₅	—	4	28	no	—
28	C₂×Dic₁₀	—	2	56	no	—
29	C₂×Dic₁₀	—	4	84	no	—
30	C₂×C₅×C₈	C₂×D₄	1	21	yes	—
31	C₂×C₅×C₈	C₂⁴	1	7	yes	—
32	Dic₂₀	—	2	56	no	—
33	Dic₂₀	C₂⁴	1	16	yes	—
34	C₅×C₁₆	C₂⁴	1	8	yes	—
35	C₂³×Q₈	—	10	2	no	—
36	C₂²×Q₁₆	—	5	28	no	—
37	C₂²×Q₁₆	—	10	14	no	—
38	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
39	C₂×Q₃₂	—	5	112	no	—
40	C₂²×C₁₆	C₂×D₅	1	14	yes	—
41	C₂³×C₅	Q₃₂	1	8	yes	complemented
42	C₂³×C₅	C₂×D₈	1	7	yes	—
43	C₂×C₄×C₅	C₂×D₈	1	21	yes	—
44	C₂×C₄×C₅	C₂²×D₄	1	7	yes	—
45	C₂×Dic₅	—	4	56	no	—
46	Dic₁₀	—	2	16	no	—
47	Dic₁₀	—	4	56	no	—
48	C₅×C₈	C₂²×D₄	1	7	yes	—
49	C₅×C₈	C₂⁵	1	1	yes	characteristic
50	C₂²×Q₈	—	10	28	no	—
51	C₂²×Q₈	—	20	14	no	—
52	C₂³×C₄	—	20	2	no	—
53	C₂³×C₄	D₂₀	1	1	yes	characteristic
54	C₂×Q₁₆	—	5	56	no	—
55	C₂×Q₁₆	—	10	84	no	—
56	C₂²×C₈	D₂₀	1	7	yes	—
57	C₂²×C₈	C₂²×D₅	1	7	yes	—
58	Q₃₂	—	5	64	no	—
59	C₂×C₁₆	C₂²×D₅	1	28	yes	—
60	C₂²×C₅	C₂×Q₃₂	1	28	yes	complemented
61	C₂²×C₅	C₂²×D₈	1	7	yes	—
62	C₄×C₅	C₂²×D₈	1	7	yes	—
63	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
64	Dic₅	—	4	16	no	—
65	C₂⁴	D₄₀	1	1	yes	characteristic
66	C₂×Q₈	—	10	56	no	—
67	C₂×Q₈	—	20	84	no	—
68	C₂²×C₄	—	20	28	no	—
69	C₂²×C₄	D₄₀	1	7	yes	—
70	C₂²×C₄	C₂×D₂₀	1	7	yes	—
71	Q₁₆	—	5	16	no	—
72	Q₁₆	—	10	56	no	—
73	C₂×C₈	C₂×D₂₀	1	21	yes	—
74	C₂×C₈	C₂³×D₅	1	7	yes	—
75	C₁₆	C₂³×D₅	1	8	yes	—
76	C₂×C₅	C₂²×Q₃₂	1	14	yes	complemented
77	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
78	C₂³	Dic₄₀	1	8	yes	direct product factor
79	C₂³	C₂×D₄₀	1	7	yes	—
80	Q₈	—	10	16	no	—
81	Q₈	—	20	56	no	—
82	C₂×C₄	—	20	56	no	—
83	C₂×C₄	C₂×D₄₀	1	21	yes	—
84	C₂×C₄	C₂²×D₂₀	1	7	yes	—
85	C₈	C₂²×D₂₀	1	7	yes	—
86	C₈	C₂⁴×D₅	1	1	yes	characteristic
87	C₅	C₂³×Q₃₂	1	1	yes	characteristic, complemented, Sylow
88	C₂²	C₂×Dic₄₀	1	28	yes	direct product factor
89	C₂²	C₂²×D₄₀	1	7	yes	—
90	C₄	—	20	16	no	—
91	C₄	C₂²×D₄₀	1	7	yes	—
92	C₄	C₂³×D₂₀	1	1	yes	characteristic
93	C₂	C₂²×Dic₄₀	1	14	yes	direct product factor
94	C₂	C₂³×D₄₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄₀
commutator, cosocle	C₅×C₈	C₂⁵
Frattini	C₈	C₂⁴×D₅
Fitting	C₂³×C₅×C₁₆	C₂
socle, prime radical	C₂⁴×C₅	D₈
hypercenter	C₂³×C₁₆	D₅
hypocenter	C₅	C₂³×Q₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₂²×Dic₄₀	C₂	direct (N × H)
9. C₂×Dic₄₀	C₂²	direct (N × H)
20. Dic₄₀	C₂³	direct (N × H)
41. C₂³×C₅	Q₃₂	semidirect
60. C₂²×C₅	C₂×Q₃₂	semidirect
76. C₂×C₅	C₂²×Q₃₂	semidirect
78. C₂³	Dic₄₀	direct (N × H)
87. C₅	C₂³×Q₃₂	semidirect
88. C₂²	C₂×Dic₄₀	direct (N × H)
93. C₂	C₂²×Dic₄₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Dic₂₀	2
C₂³×C₅×C₁₆	2
C₂²×Dic₄₀	2
C₂³×Q₃₂	5

Subgroups — C23×Dic40 #13005782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₄₀ #13005782