Subgroups — C₅×#131 #4117

Order 160.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×M₁₆	C₂	1	3	yes	maximal, complemented
3	C₂×C₅×C₈	C₂	1	3	yes	maximal, complemented
4	C₅×Q₈	C₄	1	1	yes	characteristic
5	C₅×D₄	C₄	1	3	yes	—
6	C₂×C₄×C₅	C₂²	1	3	yes	—
7	C₅×C₈	C₂²	1	3	yes	—
8	C₅×C₈	C₂²	1	1	yes	characteristic
9	#131	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅	C₂×C₄	1	3	yes	—
11	C₄×C₅	C₂×C₄	1	3	yes	—
12	C₄×C₅	C₂³	1	1	yes	characteristic
13	#41	C₂×C₅	1	1	yes	characteristic
14	M₁₆	C₂×C₅	1	3	yes	complemented
15	C₂×C₈	C₂×C₅	1	3	yes	complemented
16	C₂×C₅	—	2	3	no	—
17	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
18	Q₈	C₄×C₅	1	1	yes	characteristic
19	D₄	C₄×C₅	1	3	yes	—
20	C₂×C₄	C₂²×C₅	1	3	yes	—
21	C₈	C₂²×C₅	1	1	yes	characteristic
22	C₈	C₂²×C₅	1	3	yes	—
23	C₅	#131	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²	C₂×C₄×C₅	1	3	yes	—
25	C₄	C₂×C₄×C₅	1	3	yes	—
26	C₄	C₂³×C₅	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×C₄×C₅	1	1	yes	characteristic

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.