Finite Group Databasebeta

← C₅×D₇×C₄₄₉ #44537576

Subgroups — C₅×D₇×C₄₄₉ #44537576

Order 31430.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₄₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₄₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₄₄₉	—	7	1	no	maximal, Hall
4	C₇×C₄₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₄₄₉	D₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄₄₉	—	7	1	no	Hall
7	C₄₄₉	C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×D₇	C₄₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇	C₂×C₄₄₉	1	1	yes	characteristic, complemented, Hall
10	D₇	C₅×C₄₄₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅	—	7	1	no	Hall
12	C₇	C₂×C₅×C₄₄₉	1	1	yes	characteristic, complemented, Sylow
13	C₅	D₇×C₄₄₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₄₄₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₄₄₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₄₄₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₄₄₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₄₄₉	C₂	semidirect
2. D₇×C₄₄₉	C₅	direct (N × H)
4. C₇×C₄₄₉	C₂×C₅	semidirect
5. C₅×C₄₄₉	D₇	direct (N × H)
7. C₄₄₉	C₅×D₇	direct (N × H)
8. C₅×D₇	C₄₄₉	direct (N × H)
9. C₅×C₇	C₂×C₄₄₉	semidirect
10. D₇	C₅×C₄₄₉	direct (N × H)
12. C₇	C₂×C₅×C₄₄₉	semidirect
13. C₅	D₇×C₄₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₄₄₉	2
D₇×C₄₄₉	5
C₂×C₅×C₄₄₉	7
C₅×D₇	449