Subgroups — C₉×AGL(1,𝔽₅)×C₁₃₁ #37556045

Order 23580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃×AGL(1,𝔽₅)×C₁₃₁	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×C₁₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×C₉×C₁₃₁	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₃₁	C₂×C₃	1	1	yes	characteristic
6	AGL(1,𝔽₅)×C₁₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₃₁	—	5	1	no	—
8	C₃×C₅×C₁₃₁	C₃×C₄	1	1	yes	characteristic
9	C₃×C₄×C₁₃₁	—	5	1	no	—
10	D₅×C₁₃₁	C₂×C₉	1	1	yes	characteristic
11	C₉×C₁₃₁	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₁₃₁	—	5	1	no	—
13	C₅×C₁₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₄×C₁₃₁	—	5	1	no	Hall
15	C₃×C₁₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
16	C₂×C₁₃₁	—	5	1	no	—
17	C₉×AGL(1,𝔽₅)	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₃₁	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
19	C₉×D₅	C₂×C₁₃₁	1	1	yes	characteristic
20	C₃×AGL(1,𝔽₅)	C₃×C₁₃₁	1	1	yes	characteristic
21	C₅×C₉	C₄×C₁₃₁	1	1	yes	characteristic, complemented, Hall
22	C₄×C₉	—	5	1	no	Hall
23	C₃×D₅	C₂×C₃×C₁₃₁	1	1	yes	characteristic
24	AGL(1,𝔽₅)	C₉×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₉	—	5	1	no	—
26	C₃×C₅	C₃×C₄×C₁₃₁	1	1	yes	characteristic
27	C₃×C₄	—	5	1	no	—
28	D₅	C₂×C₉×C₁₃₁	1	1	yes	characteristic
29	C₉	AGL(1,𝔽₅)×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	5	1	no	—
31	C₅	C₄×C₉×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	5	1	no	Sylow
33	C₃	C₃×AGL(1,𝔽₅)×C₁₃₁	1	1	yes	characteristic
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₃₁	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₉×C₁₃₁
Frattini	C₃	C₃×AGL(1,𝔽₅)×C₁₃₁
Fitting	C₅×C₉×C₁₃₁	C₄
socle	C₃×C₅×C₁₃₁	C₃×C₄
prime radical	C₃×D₅×C₁₃₁	C₂×C₃
cosocle	C₃×D₅	C₂×C₃×C₁₃₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₁₃₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃₁	C₄	semidirect
6. AGL(1,𝔽₅)×C₁₃₁	C₉	direct (N × H)
11. C₉×C₁₃₁	AGL(1,𝔽₅)	direct (N × H)
13. C₅×C₁₃₁	C₄×C₉	semidirect
17. C₉×AGL(1,𝔽₅)	C₁₃₁	direct (N × H)
18. C₁₃₁	C₉×AGL(1,𝔽₅)	direct (N × H)
21. C₅×C₉	C₄×C₁₃₁	semidirect
24. AGL(1,𝔽₅)	C₉×C₁₃₁	direct (N × H)
29. C₉	AGL(1,𝔽₅)×C₁₃₁	direct (N × H)
31. C₅	C₄×C₉×C₁₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×D₅×C₁₃₁	2
C₃×AGL(1,𝔽₅)×C₁₃₁	3
C₄×C₉×C₁₃₁	5
C₉×AGL(1,𝔽₅)	131

Subgroups — C9×AGL(1,𝔽5)×C131 #37556045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×AGL(1,𝔽₅)×C₁₃₁ #37556045