Finite Group Databasebeta

← C₅×Q₃₂ #3988

Subgroups — C₅×Q₃₂ #3988

Order 160.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₁₆	C₂	1	2	yes	maximal
2	C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×Q₈	—	2	2	no	—
4	C₅×C₈	C₂²	1	1	yes	characteristic
5	Q₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₄×C₅	—	4	2	no	—
7	C₄×C₅	D₄	1	1	yes	characteristic
8	Q₁₆	C₂×C₅	1	2	yes	—
9	C₁₆	C₂×C₅	1	1	yes	characteristic
10	C₂×C₅	D₈	1	1	yes	characteristic
11	Q₈	—	2	2	no	—
12	C₈	C₂²×C₅	1	1	yes	characteristic
13	C₅	Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
14	C₄	—	4	2	no	—
15	C₄	C₅×D₄	1	1	yes	characteristic
16	C₂	C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
5. Q₃₂	C₅	direct (N × H)
13. C₅	Q₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×Q₁₆	2
C₅×C₁₆	2
Q₃₂	5