Subgroups — C₄×#170 #4000

Order 160.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#170	C₂	1	2	yes	maximal
2	C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅	C₄	1	1	yes	characteristic
4	C₂×Dic₅	C₄	1	1	yes	characteristic
5	C₂×Dic₅	C₂²	1	1	yes	characteristic
6	#170	C₄	1	4	yes	direct product factor
7	C₄×C₈	—	5	1	no	maximal, Sylow
8	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
9	C₄×C₅	C₈	1	2	yes	complemented
10	Dic₅	C₈	1	2	yes	complemented
11	Dic₅	C₂×C₄	1	2	yes	—
12	C₂×C₈	—	5	2	no	—
13	C₄²	—	5	1	no	—
14	C₂×C₅	C₄²	1	1	yes	characteristic
15	C₂×C₅	C₂×C₈	1	1	yes	characteristic
16	C₂×C₅	C₂×C₈	1	1	yes	characteristic
17	C₂×C₄	—	5	1	no	—
18	C₂×C₄	—	5	1	no	—
19	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₈	—	5	4	no	—
21	C₅	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
23	C₄	—	5	2	no	—
24	C₄	—	5	2	no	—
25	C₄	#170	1	2	yes	direct product factor
26	C₂	D₅⋊C₈	1	1	yes	characteristic
27	C₂	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₂	C₂×#170	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.