Finite Group Databasebeta

← C₂×C₅²×C₇² #14578564

Subgroups — C₂×C₅²×C₇² #14578564

Order 2450.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇²	C₅	1	6	yes	maximal, direct product factor
3	C₂×C₅²×C₇	C₇	1	8	yes	maximal, direct product factor
4	C₅×C₇²	C₂×C₅	1	6	yes	direct product factor
5	C₅²×C₇	C₂×C₇	1	8	yes	direct product factor
6	C₂×C₇²	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₇	C₅×C₇	1	48	yes	direct product factor
8	C₂×C₅²	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₇²	C₂×C₅²	1	1	yes	characteristic, direct product factor, Sylow
10	C₅×C₇	C₂×C₅×C₇	1	48	yes	direct product factor
11	C₅²	C₂×C₇²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	C₅²×C₇	1	8	yes	direct product factor
13	C₂×C₅	C₅×C₇²	1	6	yes	direct product factor
14	C₇	C₂×C₅²×C₇	1	8	yes	direct product factor
15	C₅	C₂×C₅×C₇²	1	6	yes	direct product factor
16	C₂	C₅²×C₇²	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×C₇²	C₂	direct (N × H)
2. C₂×C₅×C₇²	C₅	direct (N × H)
3. C₂×C₅²×C₇	C₇	direct (N × H)
4. C₅×C₇²	C₂×C₅	direct (N × H)
5. C₅²×C₇	C₂×C₇	direct (N × H)
6. C₂×C₇²	C₅²	direct (N × H)
7. C₂×C₅×C₇	C₅×C₇	direct (N × H)
8. C₂×C₅²	C₇²	direct (N × H)
9. C₇²	C₂×C₅²	direct (N × H)
10. C₅×C₇	C₂×C₅×C₇	direct (N × H)
11. C₅²	C₂×C₇²	direct (N × H)
12. C₂×C₇	C₅²×C₇	direct (N × H)
13. C₂×C₅	C₅×C₇²	direct (N × H)
14. C₇	C₂×C₅²×C₇	direct (N × H)
15. C₅	C₂×C₅×C₇²	direct (N × H)
16. C₂	C₅²×C₇²	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×C₇²	2
C₂×C₅×C₇²	5
C₂×C₅²×C₇	7