Subgroups — AGL(1,𝔽₅)×#92788 #23778482

Order 10140.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#92788	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#92788	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×#92788	—	5	1	no	maximal, Hall
5	D₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×#92788	—	5	1	no	—
7	C₅×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₁₃⋊C₃	—	13	14	no	maximal
9	C₄×C₁₃²	—	5	1	no	Hall
10	#92788	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
11	D₅×C₁₃⋊C₃	—	13	14	no	—
12	C₂×C₁₃²	—	5	1	no	—
13	C₁₃×AGL(1,𝔽₅)	C₁₃⋊C₃	1	14	yes	complemented
14	C₅×C₁₃⋊C₃	—	13	14	no	—
15	C₁₃²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₁₃⋊C₃	—	65	14	no	—
17	D₅×C₁₃	C₂×C₁₃⋊C₃	1	14	yes	—
18	C₂×C₁₃⋊C₃	—	65	14	no	—
19	C₅×C₁₃	C₄×C₁₃⋊C₃	1	14	yes	complemented
20	C₃×AGL(1,𝔽₅)	—	169	1	no	Hall
21	C₄×C₁₃	—	5	14	no	—
22	C₁₃⋊C₃	—	13	14	no	—
23	C₃×D₅	—	169	1	no	—
24	C₂×C₁₃	—	5	14	no	—
25	AGL(1,𝔽₅)	#92788	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅	—	169	1	no	Hall
27	C₁₃	AGL(1,𝔽₅)×C₁₃⋊C₃	1	14	yes	complemented
28	C₃×C₄	—	845	1	no	Hall
29	D₅	C₂×#92788	1	1	yes	characteristic
30	C₂×C₃	—	845	1	no	—
31	C₅	C₄×#92788	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	5	1	no	Sylow
33	C₃	—	169	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃²	C₃×C₄
prime radical	D₅×#92788	C₂
cosocle	D₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.