Subgroups — C₃₁×C₄₉⋊AGL(1,𝔽₅) #44477113

Order 30380.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₄₉	—	5	1	no	maximal, Hall
4	C₃₁×C₇⋊AGL(1,𝔽₅)	—	7	1	no	maximal
5	C₂×C₃₁×C₄₉	—	5	1	no	—
6	C₇×D₅×C₃₁	D₇	1	1	yes	characteristic
7	C₃₁×C₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₃₁	Dic₇	1	1	yes	characteristic
9	C₄₉⋊AGL(1,𝔽₅)	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	Dic₇×C₃₁	—	35	1	no	—
11	AGL(1,𝔽₅)×C₃₁	—	49	1	no	Hall
12	D₅×C₄₉	C₂×C₃₁	1	1	yes	characteristic
13	C₂×C₇×C₃₁	—	5	1	no	—
14	D₅×C₃₁	D₄₉	1	1	yes	characteristic
15	C₅×C₄₉	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₇×C₃₁	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
17	Dic₄₉	—	5	1	no	Hall
18	C₅×C₃₁	Dic₄₉	1	1	yes	characteristic, complemented, Hall
19	C₇⋊AGL(1,𝔽₅)	—	7	1	no	—
20	C₄×C₃₁	—	245	1	no	Hall
21	C₂×C₄₉	—	5	1	no	—
22	C₇×D₅	D₇×C₃₁	1	1	yes	characteristic
23	C₂×C₃₁	—	5	1	no	—
24	C₄₉	AGL(1,𝔽₅)×C₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	Dic₇×C₃₁	1	1	yes	characteristic
26	C₃₁	C₄₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
27	Dic₇	—	35	1	no	—
28	AGL(1,𝔽₅)	—	49	1	no	Hall
29	C₂×C₇	—	5	1	no	—
30	D₅	C₃₁×D₄₉	1	1	yes	characteristic
31	C₇	C₃₁×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₅	C₃₁×Dic₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	245	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	C₄₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₄₉	C₄×C₃₁
Frattini	C₇	C₃₁×C₇⋊AGL(1,𝔽₅)
Fitting	C₅×C₃₁×C₄₉	C₄
socle	C₅×C₇×C₃₁	Dic₇
prime radical	C₇×D₅×C₃₁	D₇
cosocle	D₅×C₄₉	C₂×C₃₁
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₁×C₄₉	C₄	semidirect
7. C₃₁×C₄₉	AGL(1,𝔽₅)	semidirect
9. C₄₉⋊AGL(1,𝔽₅)	C₃₁	direct (N × H)
15. C₅×C₄₉	C₄×C₃₁	semidirect
18. C₅×C₃₁	Dic₄₉	semidirect
24. C₄₉	AGL(1,𝔽₅)×C₃₁	semidirect
26. C₃₁	C₄₉⋊AGL(1,𝔽₅)	direct (N × H)
32. C₅	C₃₁×Dic₄₉	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃₁×C₄₉	2
C₃₁×Dic₄₉	5
C₃₁×C₇⋊AGL(1,𝔽₅)	7
C₄₉⋊AGL(1,𝔽₅)	31

Subgroups — C31×C49⋊AGL(1,𝔽5) #44477113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×C₄₉⋊AGL(1,𝔽₅) #44477113