Subgroups — C₁₃²×C₉⋊AGL(1,𝔽₅) #44477751

Order 30420.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅×C₁₃²	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×ΓL(1,𝔽₁₆)	—	3	1	no	maximal
3	C₅×C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃²×Dic₉	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₃²	D₃	1	1	yes	characteristic
6	C₁₃²×AGL(1,𝔽₅)	—	9	1	no	Hall
7	C₂×C₉×C₁₃²	—	5	1	no	—
8	C₃×C₅×C₁₃²	Dic₃	1	1	yes	characteristic
9	C₁₃×C₉⋊AGL(1,𝔽₅)	C₁₃	1	14	yes	maximal, direct product factor
10	Dic₃×C₁₃²	—	15	1	no	—
11	D₅×C₁₃²	D₉	1	1	yes	characteristic
12	C₉×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
13	C₉×D₅×C₁₃	C₂×C₁₃	1	14	yes	—
14	C₂×C₃×C₁₃²	—	5	1	no	—
15	C₅×C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₁₃×ΓL(1,𝔽₁₆)	—	3	14	no	—
17	C₄×C₁₃²	—	45	1	no	Hall
18	C₅×C₉×C₁₃	C₄×C₁₃	1	14	yes	complemented
19	C₃×C₁₃²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
20	C₁₃×Dic₉	—	5	14	no	—
21	C₃×D₅×C₁₃	D₃×C₁₃	1	14	yes	—
22	C₂×C₁₃²	—	5	1	no	—
23	C₁₃×AGL(1,𝔽₅)	—	9	14	no	—
24	C₂×C₉×C₁₃	—	5	14	no	—
25	C₃×C₅×C₁₃	Dic₃×C₁₃	1	14	yes	—
26	C₉⋊AGL(1,𝔽₅)	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
27	C₁₃²	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
28	Dic₃×C₁₃	—	15	14	no	—
29	D₅×C₁₃	C₁₃×D₉	1	14	yes	—
30	C₉×C₁₃	C₁₃×AGL(1,𝔽₅)	1	14	yes	complemented
31	C₉×D₅	C₂×C₁₃²	1	1	yes	characteristic
32	C₂×C₃×C₁₃	—	5	14	no	—
33	C₅×C₁₃	C₁₃×Dic₉	1	14	yes	complemented
34	ΓL(1,𝔽₁₆)	—	3	1	no	—
35	C₄×C₁₃	—	45	14	no	—
36	C₅×C₉	C₄×C₁₃²	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₃	C₁₃×ΓL(1,𝔽₁₆)	1	14	yes	—
38	Dic₉	—	5	1	no	Hall
39	C₃×D₅	D₃×C₁₃²	1	1	yes	characteristic
40	C₂×C₁₃	—	5	14	no	—
41	AGL(1,𝔽₅)	—	9	1	no	Hall
42	C₂×C₉	—	5	1	no	—
43	C₃×C₅	Dic₃×C₁₃²	1	1	yes	characteristic
44	C₁₃	C₁₃×C₉⋊AGL(1,𝔽₅)	1	14	yes	direct product factor
45	Dic₃	—	15	1	no	—
46	D₅	C₁₃²×D₉	1	1	yes	characteristic
47	C₉	C₁₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	5	1	no	—
49	C₅	C₁₃²×Dic₉	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	45	1	no	Sylow
51	C₃	C₁₃²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
52	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃²	C₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₄×C₁₃²
Frattini	C₃	C₁₃²×ΓL(1,𝔽₁₆)
Fitting	C₅×C₉×C₁₃²	C₄
socle	C₃×C₅×C₁₃²	Dic₃
prime radical	C₃×D₅×C₁₃²	D₃
cosocle	C₉×D₅	C₂×C₁₃²
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₁₃²

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃²	C₄	semidirect
9. C₁₃×C₉⋊AGL(1,𝔽₅)	C₁₃	direct (N × H)
12. C₉×C₁₃²	AGL(1,𝔽₅)	semidirect
15. C₅×C₁₃²	Dic₉	semidirect
18. C₅×C₉×C₁₃	C₄×C₁₃	semidirect
26. C₉⋊AGL(1,𝔽₅)	C₁₃²	direct (N × H)
27. C₁₃²	C₉⋊AGL(1,𝔽₅)	direct (N × H)
30. C₉×C₁₃	C₁₃×AGL(1,𝔽₅)	semidirect
33. C₅×C₁₃	C₁₃×Dic₉	semidirect
36. C₅×C₉	C₄×C₁₃²	semidirect
44. C₁₃	C₁₃×C₉⋊AGL(1,𝔽₅)	direct (N × H)
47. C₉	C₁₃²×AGL(1,𝔽₅)	semidirect
49. C₅	C₁₃²×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×D₅×C₁₃²	2
C₁₃²×ΓL(1,𝔽₁₆)	3
C₁₃²×Dic₉	5
C₁₃×C₉⋊AGL(1,𝔽₅)	13

Subgroups — C132×C9⋊AGL(1,𝔽5) #44477751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃²×C₉⋊AGL(1,𝔽₅) #44477751