Subgroups — #3995

Order 160.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#700	C₂	1	2	yes	maximal
2	C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₄×D₅	C₂²	1	1	yes	characteristic
4	#170	—	2	2	no	—
5	C₅×C₈	C₄	1	1	yes	characteristic
6	#168	C₄	1	1	yes	characteristic
7	#108	—	5	1	no	maximal, Sylow
8	C₂×D₅	Q₈	1	1	yes	characteristic
9	C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	Dic₅	D₄	1	1	yes	characteristic
11	M₁₆	—	5	2	no	—
12	C₂×C₈	—	5	1	no	—
13	C₂×C₅	C₄⋊C₄	1	1	yes	characteristic
14	D₅	—	2	1	no	—
15	C₂×C₄	—	5	1	no	—
16	C₈	—	5	1	no	—
17	C₈	—	10	2	no	—
18	C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
19	C₅	#108	1	1	yes	characteristic, complemented, Sylow
20	C₂²	—	5	1	no	—
21	C₄	—	5	1	no	—
22	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
23	C₂	—	10	1	no	—
24	C₂	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₅	#108	semidirect

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