Subgroups — C₂³×AGL(1,𝔽₅) #4161

Order 160.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×AGL(1,𝔽₅)	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₅	C₄	1	1	yes	characteristic, complemented
4	C₂²×D₅	C₄	1	7	yes	complemented
5	C₂²×D₅	C₂²	1	7	yes	—
6	C₂×AGL(1,𝔽₅)	C₂²	1	28	yes	direct product factor
7	C₂³×C₄	—	5	1	no	maximal, Sylow
8	C₂²×C₅	C₂×C₄	1	7	yes	complemented
9	C₂×D₅	C₂×C₄	1	21	yes	complemented
10	C₂×D₅	C₂³	1	7	yes	—
11	AGL(1,𝔽₅)	C₂³	1	8	yes	direct product factor
12	C₂⁴	—	5	1	no	—
13	C₂²×C₄	—	5	14	no	—
14	C₂×C₅	C₂²×C₄	1	7	yes	complemented
15	D₅	C₂²×C₄	1	7	yes	complemented
16	D₅	C₂⁴	1	1	yes	characteristic
17	C₂³	—	5	7	no	—
18	C₂³	—	5	7	no	—
19	C₂³	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
20	C₂×C₄	—	5	28	no	—
21	C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
22	C₂²	—	5	7	no	—
23	C₂²	—	5	21	no	—
24	C₂²	C₂×AGL(1,𝔽₅)	1	7	yes	direct product factor
25	C₄	—	5	8	no	—
26	C₂	—	5	1	no	—
27	C₂	—	5	7	no	—
28	C₂	C₂²×AGL(1,𝔽₅)	1	7	yes	direct product factor

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.