Subgroups — AGL(1,𝔽₅)×AGL(1,𝔽₈) #11765472

Order 1120.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×AGL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
2	C₅×AGL(1,𝔽₈)	C₄	1	1	yes	characteristic, complemented
3	C₄×AGL(1,𝔽₈)	—	5	1	no	maximal, Hall
4	C₂³×AGL(1,𝔽₅)	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×AGL(1,𝔽₅)	—	8	1	no	maximal
6	C₂×AGL(1,𝔽₈)	—	5	1	no	—
7	C₂³×D₅	C₂×C₇	1	1	yes	characteristic
8	C₂²×AGL(1,𝔽₅)	—	7	1	no	—
9	C₂²×AGL(1,𝔽₅)	—	7	1	no	—
10	C₇×D₅	—	8	1	no	—
11	AGL(1,𝔽₈)	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
12	C₂³×C₅	C₄×C₇	1	1	yes	characteristic, complemented
13	C₂²×D₅	—	7	1	no	—
14	C₂²×D₅	—	7	1	no	—
15	C₂×AGL(1,𝔽₅)	—	7	1	no	—
16	C₂×AGL(1,𝔽₅)	—	7	3	no	—
17	C₅×C₇	—	8	1	no	Hall
18	C₂³×C₄	—	5	1	no	Sylow
19	C₄×C₇	—	40	1	no	—
20	C₂²×C₅	—	7	1	no	—
21	C₂×D₅	—	7	1	no	—
22	C₂×D₅	—	7	3	no	—
23	AGL(1,𝔽₅)	—	7	1	no	—
24	AGL(1,𝔽₅)	AGL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
25	C₂⁴	—	5	1	no	—
26	C₂²×C₄	—	35	1	no	—
27	C₂²×C₄	—	35	1	no	—
28	C₂×C₇	—	40	1	no	—
29	C₂×C₅	—	7	1	no	—
30	D₅	—	7	1	no	—
31	D₅	C₂×AGL(1,𝔽₈)	1	1	yes	characteristic
32	C₂³	—	35	1	no	—
33	C₂³	—	35	1	no	—
34	C₂³	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
35	C₂×C₄	—	35	1	no	—
36	C₂×C₄	—	35	3	no	—
37	C₇	—	8	1	no	Sylow
38	C₅	C₄×AGL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	7	1	no	—
40	C₂²	—	35	1	no	—
41	C₂²	—	35	3	no	—
42	C₄	—	5	1	no	—
43	C₄	—	35	1	no	—
44	C₂	—	5	1	no	—
45	C₂	—	7	1	no	—
46	C₂	—	35	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂³×C₅	C₄×C₇
prime radical	D₅×AGL(1,𝔽₈)	C₂
cosocle	C₂³×D₅	C₂×C₇
LCS	G ▷ C₂³×C₅
UCS	C₁

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.