Subgroups — C₅×#127 #4113

Order 160.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄	C₂	1	6	yes	maximal, complemented
2	C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₅	C₂²	1	4	yes	—
4	C₅×D₄	—	2	12	no	—
5	C₂×C₄×C₅	C₂²	1	3	yes	—
6	#127	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₅	—	2	12	no	—
8	C₂²×C₅	C₂³	1	1	yes	characteristic
9	C₄×C₅	D₄	1	6	yes	complemented
10	C₂×D₄	C₂×C₅	1	6	yes	complemented
11	C₄²	C₂×C₅	1	1	yes	characteristic, complemented
12	C₂×C₅	—	4	4	no	—
13	C₂×C₅	C₂×D₄	1	3	yes	—
14	C₂³	C₂²×C₅	1	4	yes	—
15	D₄	—	2	12	no	—
16	C₂×C₄	C₂²×C₅	1	3	yes	—
17	C₅	#127	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²	—	2	12	no	—
19	C₂²	C₂³×C₅	1	1	yes	characteristic
20	C₄	C₅×D₄	1	6	yes	complemented
21	C₂	—	4	4	no	—
22	C₂	C₂×C₅×D₄	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

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

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