Subgroups — AGL(1,𝔽₅)×C₃₇×C₄₉ #49136367

Order 36260.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃₇×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₇×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₃₇×C₄₉	—	5	1	no	maximal, Hall
4	C₇×AGL(1,𝔽₅)×C₃₇	C₇	1	1	yes	maximal, characteristic
5	C₂×C₃₇×C₄₉	—	5	1	no	—
6	C₇×D₅×C₃₇	C₂×C₇	1	1	yes	characteristic
7	C₃₇×C₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇×C₃₇	C₄×C₇	1	1	yes	characteristic
9	C₄×C₇×C₃₇	—	5	1	no	—
10	AGL(1,𝔽₅)×C₄₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	AGL(1,𝔽₅)×C₃₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₃₇	—	5	1	no	—
13	D₅×C₄₉	C₂×C₃₇	1	1	yes	characteristic
14	D₅×C₃₇	C₂×C₄₉	1	1	yes	characteristic
15	C₇×C₃₇	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic
16	C₅×C₄₉	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
17	C₄×C₄₉	—	5	1	no	Hall
18	C₅×C₃₇	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
19	C₄×C₃₇	—	5	1	no	Hall
20	C₇×AGL(1,𝔽₅)	C₇×C₃₇	1	1	yes	characteristic
21	C₂×C₄₉	—	5	1	no	—
22	C₂×C₃₇	—	5	1	no	—
23	C₇×D₅	C₂×C₇×C₃₇	1	1	yes	characteristic
24	C₄₉	AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃₇	AGL(1,𝔽₅)×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₅×C₇	C₄×C₇×C₃₇	1	1	yes	characteristic
27	C₄×C₇	—	5	1	no	—
28	AGL(1,𝔽₅)	C₃₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	—	5	1	no	—
30	D₅	C₂×C₃₇×C₄₉	1	1	yes	characteristic
31	C₇	C₇×AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic
32	C₅	C₄×C₃₇×C₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	5	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇×C₄₉	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₃₇×C₄₉
Frattini	C₇	C₇×AGL(1,𝔽₅)×C₃₇
Fitting	C₅×C₃₇×C₄₉	C₄
socle	C₅×C₇×C₃₇	C₄×C₇
prime radical	C₇×D₅×C₃₇	C₂×C₇
cosocle	C₇×D₅	C₂×C₇×C₃₇
LCS	G ▷ C₅
UCS	C₁ ◁ C₃₇×C₄₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₇×C₄₉	C₄	semidirect
7. C₃₇×C₄₉	AGL(1,𝔽₅)	direct (N × H)
10. AGL(1,𝔽₅)×C₄₉	C₃₇	direct (N × H)
11. AGL(1,𝔽₅)×C₃₇	C₄₉	direct (N × H)
16. C₅×C₄₉	C₄×C₃₇	semidirect
18. C₅×C₃₇	C₄×C₄₉	semidirect
24. C₄₉	AGL(1,𝔽₅)×C₃₇	direct (N × H)
25. C₃₇	AGL(1,𝔽₅)×C₄₉	direct (N × H)
28. AGL(1,𝔽₅)	C₃₇×C₄₉	direct (N × H)
32. C₅	C₄×C₃₇×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃₇×C₄₉	2
C₄×C₃₇×C₄₉	5
C₇×AGL(1,𝔽₅)×C₃₇	7
AGL(1,𝔽₅)×C₄₉	37

Subgroups — AGL(1,𝔽5)×C37×C49 #49136367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×C₃₇×C₄₉ #49136367