Subgroups — #4133

Order 160.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#713	C₂	1	1	yes	maximal, characteristic
2	#700	C₂	1	3	yes	maximal, complemented
3	D₅⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₅×Q₈	C₄	1	1	yes	characteristic
5	D₂₀	C₄	1	3	yes	—
6	C₄×D₅	C₂²	1	3	yes	—
7	#170	C₂²	1	1	yes	characteristic
8	#170	C₂²	1	3	yes	—
9	#131	—	5	1	no	maximal, Sylow
10	C₂×D₅	C₂×C₄	1	3	yes	—
11	C₄×C₅	C₂×C₄	1	3	yes	—
12	Dic₅	C₂³	1	1	yes	characteristic
13	#41	—	5	1	no	—
14	M₁₆	—	5	3	no	—
15	C₂×C₈	—	5	3	no	—
16	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
17	D₅	—	2	3	no	—
18	Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
19	D₄	—	5	3	no	—
20	C₂×C₄	—	5	3	no	—
21	C₈	—	5	1	no	—
22	C₈	—	5	3	no	—
23	C₅	#131	1	1	yes	characteristic, complemented, Sylow
24	C₂²	—	5	3	no	—
25	C₄	—	5	1	no	—
26	C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
27	C₂	—	10	3	no	—
28	C₂	C₂²×AGL(1,𝔽₅)	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.