Subgroups — C₅×#126 #4112

Order 160.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊C₄	C₂	1	3	yes	maximal, complemented
2	C₅×C₂²⋊C₄	C₂	1	3	yes	maximal
3	C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅	C₂²	1	3	yes	—
6	C₂×C₄×C₅	C₂²	1	3	yes	—
7	#126	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₅	—	2	3	no	—
9	C₂²×C₅	C₂³	1	1	yes	characteristic
10	C₄×C₅	—	2	3	no	—
11	C₄×C₅	—	2	3	no	—
12	C₄⋊C₄	C₂×C₅	1	3	yes	complemented
13	C₂²⋊C₄	C₂×C₅	1	3	yes	—
14	C₄²	C₂×C₅	1	1	yes	characteristic, complemented
15	C₂×C₅	—	4	1	no	—
16	C₂×C₅	#41	1	3	yes	—
17	C₂³	C₂²×C₅	1	1	yes	characteristic
18	C₂×C₄	C₂²×C₅	1	3	yes	—
19	C₂×C₄	C₂²×C₅	1	3	yes	—
20	C₅	#126	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	—	2	3	no	—
22	C₂²	C₂³×C₅	1	1	yes	characteristic
23	C₄	—	2	3	no	—
24	C₄	—	2	3	no	—
25	C₂	—	4	1	no	—
26	C₂	C₅×#41	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₅
prime radical	C₂³×C₅	C₂²
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.