Subgroups — C₂×#3932 #65192

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄₀	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#3932	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₂₀	—	2	1	no	—
6	C₂×Dic₁₀	—	2	1	no	—
7	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
8	Dic₂₀	—	2	1	no	—
9	Dic₂₀	C₂²	1	2	yes	complemented
10	D₄₀	—	2	1	no	—
11	D₄₀	C₂²	1	2	yes	—
12	C₅×C₁₆	C₂²	1	2	yes	complemented
13	C₂×SD₃₂	—	5	1	no	maximal, Sylow
14	C₂²×D₅	—	4	1	no	—
15	C₂×C₄×C₅	D₄	1	1	yes	characteristic
16	C₂×Dic₅	—	4	1	no	—
17	D₂₀	—	2	2	no	—
18	D₂₀	—	4	1	no	—
19	Dic₁₀	—	2	2	no	—
20	Dic₁₀	—	4	1	no	—
21	C₅×C₈	D₄	1	1	yes	characteristic
22	C₅×C₈	C₂³	1	1	yes	characteristic
23	C₂×Q₁₆	—	5	1	no	—
24	C₂×D₈	—	5	1	no	—
25	SD₃₂	—	5	4	no	—
26	C₂×C₁₆	D₅	1	1	yes	characteristic, complemented
27	C₂²×C₅	D₈	1	1	yes	characteristic
28	C₂×D₅	—	4	2	no	—
29	C₂×D₅	—	8	2	no	—
30	C₄×C₅	D₈	1	1	yes	characteristic
31	C₄×C₅	C₂×D₄	1	1	yes	characteristic
32	Dic₅	—	4	2	no	—
33	C₂×Q₈	—	10	1	no	—
34	C₂×D₄	—	10	1	no	—
35	Q₁₆	—	5	2	no	—
36	Q₁₆	—	10	1	no	—
37	D₈	—	5	2	no	—
38	D₈	—	10	1	no	—
39	C₂×C₈	C₂×D₅	1	1	yes	characteristic
40	C₁₆	C₂×D₅	1	2	yes	complemented
41	C₂×C₅	SD₃₂	1	2	yes	complemented
42	C₂×C₅	C₂×D₈	1	1	yes	characteristic
43	D₅	—	8	2	no	—
44	C₂³	—	20	1	no	—
45	Q₈	—	10	2	no	—
46	Q₈	—	20	1	no	—
47	D₄	—	10	2	no	—
48	D₄	—	20	1	no	—
49	C₂×C₄	—	20	1	no	—
50	C₂×C₄	D₂₀	1	1	yes	characteristic
51	C₈	D₂₀	1	1	yes	characteristic
52	C₈	C₂²×D₅	1	1	yes	characteristic
53	C₅	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	20	2	no	—
55	C₂²	—	40	2	no	—
56	C₂²	D₄₀	1	1	yes	characteristic
57	C₄	—	20	2	no	—
58	C₄	D₄₀	1	1	yes	characteristic
59	C₄	C₂×D₂₀	1	1	yes	characteristic
60	C₂	—	40	2	no	—
61	C₂	#3932	1	2	yes	direct product factor
62	C₂	C₂×D₄₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₀
commutator, cosocle	C₅×C₈	C₂³
Frattini	C₈	C₂²×D₅
Fitting	C₂×C₅×C₁₆	C₂
socle	C₂²×C₅	D₈
prime radical	C₂×D₄₀	C₂
hypercenter	C₂×C₁₆	D₅
hypocenter	C₅	C₂×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₂₀	C₂	semidirect
3. C₂×C₅×C₁₆	C₂	semidirect
4. #3932	C₂	direct (N × H)
9. Dic₂₀	C₂²	semidirect
12. C₅×C₁₆	C₂²	semidirect
26. C₂×C₁₆	D₅	semidirect
40. C₁₆	C₂×D₅	semidirect
41. C₂×C₅	SD₃₂	semidirect
53. C₅	C₂×SD₃₂	semidirect
61. C₂	#3932	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×Dic₂₀	2
C₂×D₄₀	2
C₂×C₅×C₁₆	2
#3932	2
C₂×SD₃₂	5

Subgroups — C2×#3932 #65192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3932 #65192