Subgroups — C₅×Q₆₄ #64840

Order 320.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₃₂	C₂	1	2	yes	maximal
2	C₅×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₅×Q₁₆	—	2	2	no	—
4	C₅×C₁₆	C₂²	1	1	yes	characteristic
5	Q₆₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₅×Q₈	—	4	2	no	—
7	C₅×C₈	D₄	1	1	yes	characteristic
8	Q₃₂	C₂×C₅	1	2	yes	—
9	C₃₂	C₂×C₅	1	1	yes	characteristic
10	C₄×C₅	—	8	2	no	—
11	C₄×C₅	D₈	1	1	yes	characteristic
12	Q₁₆	—	2	2	no	—
13	C₁₆	C₂²×C₅	1	1	yes	characteristic
14	C₂×C₅	D₁₆	1	1	yes	characteristic
15	Q₈	—	4	2	no	—
16	C₈	C₅×D₄	1	1	yes	characteristic
17	C₅	Q₆₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₄	—	8	2	no	—
19	C₄	C₅×D₈	1	1	yes	characteristic
20	C₂	C₅×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₅	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₅
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆ ◁ G

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

N	H ≅ G/N	type
5. Q₆₄	C₅	direct (N × H)
17. C₅	Q₆₄	direct (N × H)

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