Finite Group Databasebeta

← C₃×C₅×C₂₃×C₇₁ #37587673

Subgroups — C₃×C₅×C₂₃×C₇₁ #37587673

Order 24495.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₂₃×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₇₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅×C₇₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇₁	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅×C₂₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₃	C₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
9	C₇₁	C₃×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₂₃	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂₃	C₃×C₅×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	C₂₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₃×C₂₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₅×C₂₃×C₇₁	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×C₂₃×C₇₁	C₃	direct (N × H)
2. C₃×C₂₃×C₇₁	C₅	direct (N × H)
3. C₂₃×C₇₁	C₃×C₅	direct (N × H)
4. C₃×C₅×C₇₁	C₂₃	direct (N × H)
5. C₅×C₇₁	C₃×C₂₃	direct (N × H)
6. C₃×C₅×C₂₃	C₇₁	direct (N × H)
7. C₃×C₇₁	C₅×C₂₃	direct (N × H)
8. C₅×C₂₃	C₃×C₇₁	direct (N × H)
9. C₇₁	C₃×C₅×C₂₃	direct (N × H)
10. C₃×C₂₃	C₅×C₇₁	direct (N × H)
11. C₂₃	C₃×C₅×C₇₁	direct (N × H)
12. C₃×C₅	C₂₃×C₇₁	direct (N × H)
13. C₅	C₃×C₂₃×C₇₁	direct (N × H)
14. C₃	C₅×C₂₃×C₇₁	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×C₂₃×C₇₁	3
C₃×C₂₃×C₇₁	5
C₃×C₅×C₇₁	23
C₃×C₅×C₂₃	71