Subgroups — C₂×C₅×Dic₁₀ #87887

Order 400.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₅	C₂	1	2	yes	maximal
3	C₅×Dic₁₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅²	C₂²	1	1	yes	characteristic
5	C₄×C₅²	C₂²	1	2	yes	—
6	C₅×Dic₅	C₂²	1	4	yes	—
7	C₂×C₅×Q₈	—	5	1	no	maximal
8	C₂×Dic₁₀	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	Q₈	1	2	yes	complemented
10	C₂×C₅²	C₂³	1	1	yes	characteristic
11	C₅×Q₈	—	5	4	no	—
12	C₂×C₄×C₅	—	2	2	no	—
13	C₂×C₄×C₅	—	5	2	no	—
14	C₂×C₄×C₅	D₅	1	1	yes	characteristic
15	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic
16	C₂×Dic₅	C₂×C₅	1	2	yes	—
17	Dic₁₀	C₂×C₅	1	4	yes	direct product factor
18	C₅²	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	2	2	no	—
20	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
21	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
22	C₄×C₅	—	2	4	no	—
23	C₄×C₅	—	5	4	no	—
24	C₄×C₅	C₂×D₅	1	2	yes	—
25	C₄×C₅	C₂²×C₅	1	2	yes	—
26	Dic₅	C₂²×C₅	1	4	yes	—
27	C₂×Q₈	—	5	1	no	Sylow
28	C₂×C₅	—	2	4	no	—
29	C₂×C₅	—	2	2	no	—
30	C₂×C₅	Dic₁₀	1	2	yes	direct product factor
31	C₂×C₅	C₅×Q₈	1	2	yes	complemented
32	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
33	C₂×C₅	C₂³×C₅	1	1	yes	characteristic
34	Q₈	—	5	4	no	—
35	C₂×C₄	—	5	2	no	—
36	C₂×C₄	C₅×D₅	1	1	yes	characteristic
37	C₅	—	2	2	no	—
38	C₅	C₂×Dic₁₀	1	1	yes	characteristic, direct product factor
39	C₅	C₂×C₅×Q₈	1	1	yes	characteristic, complemented
40	C₂²	C₂×C₅×D₅	1	1	yes	characteristic
41	C₄	—	5	4	no	—
42	C₄	C₂×C₅×D₅	1	2	yes	—
43	C₂	C₅×Dic₁₀	1	2	yes	direct product factor
44	C₂	C₂²×C₅×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₅
commutator, cosocle	C₂×C₅	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₅
Fitting	C₂×C₄×C₅²	C₂
socle, prime radical	C₂²×C₅²	C₂²
hypercenter	C₂×C₄×C₅	D₅
hypocenter	C₅	C₂×C₅×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×Dic₁₀	C₂	direct (N × H)
8. C₂×Dic₁₀	C₅	direct (N × H)
9. C₂×C₅²	Q₈	semidirect
17. Dic₁₀	C₂×C₅	direct (N × H)
18. C₅²	C₂×Q₈	semidirect
30. C₂×C₅	Dic₁₀	direct (N × H)
31. C₂×C₅	C₅×Q₈	semidirect
38. C₅	C₂×Dic₁₀	direct (N × H)
39. C₅	C₂×C₅×Q₈	semidirect
43. C₂	C₅×Dic₁₀	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×C₅²	2
C₂×C₅×Dic₅	2
C₅×Dic₁₀	2
C₂×C₅×Q₈	5
C₂×Dic₁₀	5

Subgroups — C2×C5×Dic10 #87887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Dic₁₀ #87887