Subgroups — C₂×C₅×C₉×C₅₃ #18012002

Order 4770.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₅₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅×C₅₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₅₃	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₅₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₅₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₅₃	C₃×C₅	1	1	yes	characteristic
8	C₅×C₅₃	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅₃	C₂×C₃×C₅	1	1	yes	characteristic
10	C₂×C₅₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅₃	C₂×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₅×C₉	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅	C₃×C₅₃	1	1	yes	characteristic
15	C₂×C₉	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅	C₂×C₃×C₅₃	1	1	yes	characteristic
17	C₂×C₅	C₉×C₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₉	C₂×C₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₃×C₅×C₅₃	1	1	yes	characteristic
20	C₅	C₂×C₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂×C₃×C₅×C₅₃	1	1	yes	characteristic
22	C₂	C₅×C₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₅₃
socle, prime radical	C₂×C₃×C₅×C₅₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₅₃	C₂	direct (N × H)
3. C₂×C₉×C₅₃	C₅	direct (N × H)
5. C₂×C₅×C₅₃	C₉	direct (N × H)
6. C₉×C₅₃	C₂×C₅	direct (N × H)
8. C₅×C₅₃	C₂×C₉	direct (N × H)
10. C₂×C₅₃	C₅×C₉	direct (N × H)
11. C₂×C₅×C₉	C₅₃	direct (N × H)
12. C₅₃	C₂×C₅×C₉	direct (N × H)
13. C₅×C₉	C₂×C₅₃	direct (N × H)
15. C₂×C₉	C₅×C₅₃	direct (N × H)
17. C₂×C₅	C₉×C₅₃	direct (N × H)
18. C₉	C₂×C₅×C₅₃	direct (N × H)
20. C₅	C₂×C₉×C₅₃	direct (N × H)
22. C₂	C₅×C₉×C₅₃	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×C₉×C₅₃	2
C₂×C₃×C₅×C₅₃	3
C₂×C₉×C₅₃	5
C₂×C₅×C₉	53

Subgroups — C2×C5×C9×C53 #18012002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×C₅₃ #18012002