Finite Group Databasebeta

← C₂×C₅×C₄₄₉⋊C₇ #44537574

Subgroups — C₂×C₅×C₄₄₉⋊C₇ #44537574

Order 31430.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₄₉⋊C₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₄₄₉⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₄₄₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₄₉⋊C₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₄₄₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₄₄₉	C₅×C₇	1	1	yes	characteristic, complemented, Hall
7	C₄₄₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×C₇	—	449	1	no	maximal, Hall
9	C₅×C₇	—	449	1	no	Hall
10	C₂×C₇	—	449	1	no	Hall
11	C₂×C₅	C₄₄₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇	—	449	1	no	Sylow
13	C₅	C₂×C₄₄₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₄₄₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₄₉⋊C₇	C₂	direct (N × H)
2. C₂×C₄₄₉⋊C₇	C₅	direct (N × H)
3. C₂×C₅×C₄₄₉	C₇	semidirect
4. C₄₄₉⋊C₇	C₂×C₅	direct (N × H)
5. C₅×C₄₄₉	C₂×C₇	semidirect
6. C₂×C₄₄₉	C₅×C₇	semidirect
7. C₄₄₉	C₂×C₅×C₇	semidirect
11. C₂×C₅	C₄₄₉⋊C₇	direct (N × H)
13. C₅	C₂×C₄₄₉⋊C₇	direct (N × H)
14. C₂	C₅×C₄₄₉⋊C₇	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×C₄₄₉⋊C₇	2
C₂×C₄₄₉⋊C₇	5
C₂×C₅×C₄₄₉	7
C₂×C₅×C₇	449