Subgroups — C₅×#106 #3981

Order 160.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄×C₅	—	2	2	no	—
4	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₅×C₈	C₄	1	2	yes	complemented
6	#106	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₅	D₄	1	1	yes	characteristic
8	C₄×C₅	—	4	2	no	—
9	C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₄×C₅	Q₈	1	1	yes	characteristic
11	C₂×C₈	C₂×C₅	1	1	yes	characteristic
12	C₄⋊C₄	C₂×C₅	1	2	yes	—
13	C₂×C₅	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₅	SD₁₆	1	2	yes	—
15	C₂×C₄	—	2	2	no	—
16	C₂×C₄	C₂²×C₅	1	1	yes	characteristic
17	C₈	C₄×C₅	1	2	yes	complemented
18	C₅	#106	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₅×D₄	1	1	yes	characteristic
20	C₄	—	4	2	no	—
21	C₄	C₂×C₄×C₅	1	1	yes	characteristic
22	C₄	C₅×Q₈	1	1	yes	characteristic
23	C₂	C₅×C₄⋊C₄	1	1	yes	characteristic
24	C₂	C₅×SD₁₆	1	2	yes	—

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.