Finite Group Databasebeta

← C₅×C₇×C₂₃×C₃₇ #44446874

Subgroups — C₅×C₇×C₂₃×C₃₇ #44446874

Order 29785.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₂₃×C₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₇×C₃₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂₃×C₃₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₇×C₂₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₃₇	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₃₇	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₂₃	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₂₃	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃₇	C₅×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₅×C₇	C₂₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂₃	C₅×C₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₅×C₂₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₅	C₇×C₂₃×C₃₇	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. C₇×C₂₃×C₃₇	C₅	direct (N × H)
2. C₅×C₂₃×C₃₇	C₇	direct (N × H)
3. C₅×C₇×C₃₇	C₂₃	direct (N × H)
4. C₂₃×C₃₇	C₅×C₇	direct (N × H)
5. C₅×C₇×C₂₃	C₃₇	direct (N × H)
6. C₇×C₃₇	C₅×C₂₃	direct (N × H)
7. C₅×C₃₇	C₇×C₂₃	direct (N × H)
8. C₇×C₂₃	C₅×C₃₇	direct (N × H)
9. C₅×C₂₃	C₇×C₃₇	direct (N × H)
10. C₃₇	C₅×C₇×C₂₃	direct (N × H)
11. C₅×C₇	C₂₃×C₃₇	direct (N × H)
12. C₂₃	C₅×C₇×C₃₇	direct (N × H)
13. C₇	C₅×C₂₃×C₃₇	direct (N × H)
14. C₅	C₇×C₂₃×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₃×C₃₇	5
C₅×C₂₃×C₃₇	7
C₅×C₇×C₃₇	23
C₅×C₇×C₂₃	37