Subgroups — C₈×AGL(1,𝔽₅) #3991

Order 160.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	C₂×AGL(1,𝔽₅)	C₄	1	2	yes	—
5	C₄×D₅	C₂²	1	1	yes	characteristic
6	#170	C₄	1	2	yes	complemented
7	C₅×C₈	C₄	1	1	yes	characteristic, complemented
8	#168	C₄	1	1	yes	characteristic, complemented
9	C₄×C₈	—	5	1	no	maximal, Sylow
10	C₂×D₅	C₂×C₄	1	1	yes	characteristic
11	AGL(1,𝔽₅)	C₈	1	4	yes	direct product factor
12	C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	Dic₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈	—	5	1	no	—
15	C₂×C₈	—	5	1	no	—
16	C₄²	—	5	1	no	—
17	C₂×C₅	C₄²	1	1	yes	characteristic
18	D₅	C₂×C₈	1	2	yes	—
19	C₂×C₄	—	5	2	no	—
20	C₂×C₄	—	5	1	no	—
21	C₈	—	5	2	no	—
22	C₈	—	5	1	no	—
23	C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
24	C₅	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	5	1	no	—
26	C₄	—	5	4	no	—
27	C₄	—	5	1	no	—
28	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₂	—	5	2	no	—
30	C₂	C₄×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.