Finite Group Databasebeta

← C₂×C₇₃×C₁₂₅ #72196002

Subgroups — C₂×C₇₃×C₁₂₅ #72196002

Order 18250.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×C₁₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₅×C₇₃	C₅	1	1	yes	maximal, characteristic
3	C₂₅×C₇₃	C₂×C₅	1	1	yes	characteristic
4	C₂×C₅×C₇₃	C₂₅	1	1	yes	characteristic
5	C₅×C₇₃	C₂×C₂₅	1	1	yes	characteristic
6	C₂×C₁₂₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇₃	C₁₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₁₂₅	C₂×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₇₃	C₂×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₂₅	C₅×C₇₃	1	1	yes	characteristic
11	C₂₅	C₂×C₅×C₇₃	1	1	yes	characteristic
12	C₂×C₅	C₂₅×C₇₃	1	1	yes	characteristic
13	C₅	C₂×C₂₅×C₇₃	1	1	yes	characteristic
14	C₂	C₇₃×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅	C₂×C₅×C₇₃
socle, prime radical	C₂×C₅×C₇₃	C₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×C₁₂₅	C₂	direct (N × H)
6. C₂×C₁₂₅	C₇₃	direct (N × H)
7. C₂×C₇₃	C₁₂₅	direct (N × H)
8. C₁₂₅	C₂×C₇₃	direct (N × H)
9. C₇₃	C₂×C₁₂₅	direct (N × H)
14. C₂	C₇₃×C₁₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×C₁₂₅	2
C₂×C₂₅×C₇₃	5
C₂×C₁₂₅	73