Finite Group Databasebeta

← C₂×C₅×C₅₃×C₅₉ #44530780

Subgroups — C₂×C₅×C₅₃×C₅₉ #44530780

Order 31270.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₅₃×C₅₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅₃×C₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅₃×C₅₉	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅×C₅₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₅₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₅₉	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₅₃	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₅₉	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅₃	C₅×C₅₉	1	1	yes	characteristic, direct product factor, Hall
10	C₅₉	C₂×C₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₅₃	C₂×C₅×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	C₅₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₅₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₅₃×C₅₉	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×C₅₃×C₅₉	C₂	direct (N × H)
2. C₂×C₅₃×C₅₉	C₅	direct (N × H)
3. C₅₃×C₅₉	C₂×C₅	direct (N × H)
4. C₂×C₅×C₅₉	C₅₃	direct (N × H)
5. C₂×C₅×C₅₃	C₅₉	direct (N × H)
6. C₅×C₅₉	C₂×C₅₃	direct (N × H)
7. C₅×C₅₃	C₂×C₅₉	direct (N × H)
8. C₂×C₅₉	C₅×C₅₃	direct (N × H)
9. C₂×C₅₃	C₅×C₅₉	direct (N × H)
10. C₅₉	C₂×C₅×C₅₃	direct (N × H)
11. C₅₃	C₂×C₅×C₅₉	direct (N × H)
12. C₂×C₅	C₅₃×C₅₉	direct (N × H)
13. C₅	C₂×C₅₃×C₅₉	direct (N × H)
14. C₂	C₅×C₅₃×C₅₉	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×C₅₃×C₅₉	2
C₂×C₅₃×C₅₉	5
C₂×C₅×C₅₉	53
C₂×C₅×C₅₃	59