Subgroups — C₅×C₉×C₁₃×C₅₃ #44526513

Order 31005.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₅₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₃×C₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₃×C₅₃	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₅×C₉×C₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃×C₅₃	C₃×C₅	1	1	yes	characteristic
6	C₃×C₅×C₅₃	C₃×C₁₃	1	1	yes	characteristic
7	C₁₃×C₅₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₉×C₁₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₉×C₅₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₅₃	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₁₃	C₃×C₅₃	1	1	yes	characteristic
12	C₃×C₅₃	C₃×C₅×C₁₃	1	1	yes	characteristic
13	C₉×C₁₃	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₃	C₉×C₅₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅₃	C₅×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₉	C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₁₃	C₃×C₅×C₅₃	1	1	yes	characteristic
18	C₃×C₅	C₃×C₁₃×C₅₃	1	1	yes	characteristic
19	C₁₃	C₅×C₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₉	C₅×C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₉×C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₅×C₁₃×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₁₃×C₅₃
socle, prime radical	C₃×C₅×C₁₃×C₅₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₃×C₅₃	C₅	direct (N × H)
3. C₅×C₁₃×C₅₃	C₉	direct (N × H)
4. C₅×C₉×C₅₃	C₁₃	direct (N × H)
7. C₁₃×C₅₃	C₅×C₉	direct (N × H)
8. C₅×C₉×C₁₃	C₅₃	direct (N × H)
9. C₉×C₅₃	C₅×C₁₃	direct (N × H)
10. C₅×C₅₃	C₉×C₁₃	direct (N × H)
13. C₉×C₁₃	C₅×C₅₃	direct (N × H)
14. C₅×C₁₃	C₉×C₅₃	direct (N × H)
15. C₅₃	C₅×C₉×C₁₃	direct (N × H)
16. C₅×C₉	C₁₃×C₅₃	direct (N × H)
19. C₁₃	C₅×C₉×C₅₃	direct (N × H)
20. C₉	C₅×C₁₃×C₅₃	direct (N × H)
21. C₅	C₉×C₁₃×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
C₃×C₅×C₁₃×C₅₃	3
C₉×C₁₃×C₅₃	5
C₅×C₉×C₅₃	13
C₅×C₉×C₁₃	53

Subgroups — C5×C9×C13×C53 #44526513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₃×C₅₃ #44526513