Finite Group Databasebeta

← C₂×C₅×C₇×C₃₆₇ #38787484

Subgroups — C₂×C₅×C₇×C₃₆₇ #38787484

Order 25690.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₃₆₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₃₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₃₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₃₆₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₃₆₇	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₆₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₃₆₇	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₅×C₇	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇	C₂×C₃₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇	C₅×C₃₆₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅	C₇×C₃₆₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇	C₂×C₅×C₃₆₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₅	C₂×C₇×C₃₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₇×C₃₆₇	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. C₅×C₇×C₃₆₇	C₂	direct (N × H)
2. C₂×C₇×C₃₆₇	C₅	direct (N × H)
3. C₂×C₅×C₃₆₇	C₇	direct (N × H)
4. C₇×C₃₆₇	C₂×C₅	direct (N × H)
5. C₅×C₃₆₇	C₂×C₇	direct (N × H)
6. C₂×C₃₆₇	C₅×C₇	direct (N × H)
7. C₃₆₇	C₂×C₅×C₇	direct (N × H)
8. C₂×C₅×C₇	C₃₆₇	direct (N × H)
9. C₅×C₇	C₂×C₃₆₇	direct (N × H)
10. C₂×C₇	C₅×C₃₆₇	direct (N × H)
11. C₂×C₅	C₇×C₃₆₇	direct (N × H)
12. C₇	C₂×C₅×C₃₆₇	direct (N × H)
13. C₅	C₂×C₇×C₃₆₇	direct (N × H)
14. C₂	C₅×C₇×C₃₆₇	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×C₃₆₇	2
C₂×C₇×C₃₆₇	5
C₂×C₅×C₃₆₇	7
C₂×C₅×C₇	367