Subgroups — #3998

Order 160.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#168	C₂	1	1	yes	maximal, characteristic
2	#674	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅	C₄	1	1	yes	characteristic
4	#168	C₄	1	1	yes	characteristic
5	#168	C₂²	1	1	yes	characteristic
6	M₃₂	—	5	1	no	maximal, Sylow
7	C₂²×C₅	C₈	1	1	yes	characteristic
8	C₄×C₅	C₈	1	1	yes	characteristic
9	C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈	—	5	1	no	—
11	C₁₆	—	5	2	no	—
12	C₂×C₅	—	2	1	no	—
13	C₂×C₅	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
15	C₈	—	5	1	no	—
16	C₈	—	5	1	no	—
17	C₅	M₃₂	1	1	yes	characteristic, complemented, Sylow
18	C₂²	#170	1	1	yes	characteristic
19	C₄	#170	1	1	yes	characteristic
20	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×#170	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #674	C₂	semidirect
17. C₅	M₃₂	semidirect

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