Finite Group Databasebeta

← C₄×C₉×C₅₆₃ #35202425

Subgroups — C₄×C₉×C₅₆₃ #35202425

Order 20268.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₅₆₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅₆₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₅₆₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₅₆₃	C₂×C₃	1	1	yes	characteristic
5	C₄×C₅₆₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅₆₃	C₃×C₄	1	1	yes	characteristic
7	C₂×C₅₆₃	C₂×C₉	1	1	yes	characteristic
8	C₅₆₃	C₄×C₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₄×C₉	C₅₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₉	C₂×C₅₆₃	1	1	yes	characteristic
11	C₃×C₄	C₃×C₅₆₃	1	1	yes	characteristic
12	C₉	C₄×C₅₆₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃	C₂×C₃×C₅₆₃	1	1	yes	characteristic
14	C₄	C₉×C₅₆₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₃×C₄×C₅₆₃	1	1	yes	characteristic
16	C₂	C₂×C₉×C₅₆₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₅₆₃
socle, prime radical	C₂×C₃×C₅₆₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₅₆₃	C₄	direct (N × H)
5. C₄×C₅₆₃	C₉	direct (N × H)
8. C₅₆₃	C₄×C₉	direct (N × H)
9. C₄×C₉	C₅₆₃	direct (N × H)
12. C₉	C₄×C₅₆₃	direct (N × H)
14. C₄	C₉×C₅₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₅₆₃	2
C₃×C₄×C₅₆₃	3
C₄×C₉	563