Finite Group Databasebeta

← C₃²×C₂₅×C₇₃ #30656017

Subgroups — C₃²×C₂₅×C₇₃ #30656017

Order 16425.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×C₇₃	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₅×C₇₃	C₅	1	1	yes	maximal, characteristic
3	C₂₅×C₇₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅×C₇₃	C₃×C₅	1	4	yes	—
5	C₃²×C₇₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₇₃	C₃²×C₅	1	1	yes	characteristic
7	C₃²×C₂₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₇₃	C₃×C₂₅	1	4	yes	direct product factor
9	C₃×C₂₅	C₃×C₇₃	1	4	yes	direct product factor
10	C₇₃	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
11	C₃²×C₅	C₅×C₇₃	1	1	yes	characteristic
12	C₂₅	C₃²×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₅	C₃×C₅×C₇₃	1	4	yes	—
14	C₃²	C₂₅×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₅	C₃²×C₅×C₇₃	1	1	yes	characteristic
16	C₃	C₃×C₂₅×C₇₃	1	4	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃²×C₅×C₇₃
socle, prime radical	C₃²×C₅×C₇₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₅×C₇₃	C₃	direct (N × H)
3. C₂₅×C₇₃	C₃²	direct (N × H)
5. C₃²×C₇₃	C₂₅	direct (N × H)
7. C₃²×C₂₅	C₇₃	direct (N × H)
8. C₃×C₇₃	C₃×C₂₅	direct (N × H)
9. C₃×C₂₅	C₃×C₇₃	direct (N × H)
10. C₇₃	C₃²×C₂₅	direct (N × H)
12. C₂₅	C₃²×C₇₃	direct (N × H)
14. C₃²	C₂₅×C₇₃	direct (N × H)
16. C₃	C₃×C₂₅×C₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂₅×C₇₃	3
C₃²×C₅×C₇₃	5
C₃²×C₂₅	73