Finite Group Databasebeta

← C₂×C₅²×C₆₄₇ #44568977

Subgroups — C₂×C₅²×C₆₄₇ #44568977

Order 32350.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₆₄₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₆₄₇	C₅	1	6	yes	maximal, direct product factor
3	C₅×C₆₄₇	C₂×C₅	1	6	yes	direct product factor
4	C₂×C₆₄₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
5	C₆₄₇	C₂×C₅²	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₅²	C₆₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅²	C₂×C₆₄₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₅	C₅×C₆₄₇	1	6	yes	direct product factor
9	C₅	C₂×C₅×C₆₄₇	1	6	yes	direct product factor
10	C₂	C₅²×C₆₄₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅²×C₆₄₇	C₂	direct (N × H)
2. C₂×C₅×C₆₄₇	C₅	direct (N × H)
3. C₅×C₆₄₇	C₂×C₅	direct (N × H)
4. C₂×C₆₄₇	C₅²	direct (N × H)
5. C₆₄₇	C₂×C₅²	direct (N × H)
6. C₂×C₅²	C₆₄₇	direct (N × H)
7. C₅²	C₂×C₆₄₇	direct (N × H)
8. C₂×C₅	C₅×C₆₄₇	direct (N × H)
9. C₅	C₂×C₅×C₆₄₇	direct (N × H)
10. C₂	C₅²×C₆₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₆₄₇	2
C₂×C₅×C₆₄₇	5
C₂×C₅²	647