Subgroups — Q₈×AGL(1,𝔽₅) #4134

Order 160.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊AGL(1,𝔽₅)	C₂	1	3	yes	maximal
3	C₄×AGL(1,𝔽₅)	C₂	1	3	yes	maximal
4	C₂×AGL(1,𝔽₅)	C₂²	1	3	yes	—
5	C₂×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
6	C₅×Q₈	C₄	1	1	yes	characteristic, complemented
7	C₄×D₅	C₂²	1	3	yes	—
8	Dic₁₀	C₄	1	3	yes	complemented
9	C₄×Q₈	—	5	1	no	maximal, Sylow
10	C₂×D₅	C₂³	1	1	yes	characteristic
11	AGL(1,𝔽₅)	—	2	3	no	—
12	AGL(1,𝔽₅)	Q₈	1	2	yes	direct product factor
13	C₄×C₅	C₂×C₄	1	3	yes	—
14	Dic₅	C₂×C₄	1	3	yes	—
15	C₂×Q₈	—	5	1	no	—
16	C₄⋊C₄	—	5	3	no	—
17	C₄²	—	5	3	no	—
18	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
19	D₅	C₂×Q₈	1	1	yes	characteristic
20	D₅	#41	1	1	yes	characteristic
21	Q₈	—	5	3	no	—
22	Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
23	C₂×C₄	—	5	1	no	—
24	C₂×C₄	—	5	3	no	—
25	C₂×C₄	—	5	3	no	—
26	C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	5	1	no	—
28	C₄	—	5	2	no	—
29	C₄	—	5	3	no	—
30	C₄	—	10	3	no	—
31	C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
32	C₂	—	5	1	no	—
33	C₂	—	5	1	no	—
34	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.