Subgroups — C₄×C₅×C₃₁×C₅₃ #45659554

Order 32860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×C₅₃	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₃₁×C₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃₁×C₅₃	C₂×C₅	1	1	yes	characteristic
5	C₃₁×C₅₃	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₅×C₅₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₅×C₃₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₅₃	C₂×C₃₁	1	1	yes	characteristic
9	C₂×C₅×C₃₁	C₂×C₅₃	1	1	yes	characteristic
10	C₅×C₅₃	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₅₃	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₃₁	C₄×C₅₃	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₃₁	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅₃	C₂×C₅×C₃₁	1	1	yes	characteristic
15	C₂×C₃₁	C₂×C₅×C₅₃	1	1	yes	characteristic
16	C₅₃	C₄×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₁	C₄×C₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₅	C₃₁×C₅₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₂×C₃₁×C₅₃	1	1	yes	characteristic
20	C₅	C₄×C₃₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₅×C₃₁×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₃₁×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₃₁×C₅₃
socle, prime radical	C₂×C₅×C₃₁×C₅₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₁×C₅₃	C₄	direct (N × H)
3. C₄×C₃₁×C₅₃	C₅	direct (N × H)
5. C₃₁×C₅₃	C₄×C₅	direct (N × H)
6. C₄×C₅×C₅₃	C₃₁	direct (N × H)
7. C₄×C₅×C₃₁	C₅₃	direct (N × H)
10. C₅×C₅₃	C₄×C₃₁	direct (N × H)
11. C₄×C₅₃	C₅×C₃₁	direct (N × H)
12. C₅×C₃₁	C₄×C₅₃	direct (N × H)
13. C₄×C₃₁	C₅×C₅₃	direct (N × H)
16. C₅₃	C₄×C₅×C₃₁	direct (N × H)
17. C₃₁	C₄×C₅×C₅₃	direct (N × H)
18. C₄×C₅	C₃₁×C₅₃	direct (N × H)
20. C₅	C₄×C₃₁×C₅₃	direct (N × H)
21. C₄	C₅×C₃₁×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
C₂×C₅×C₃₁×C₅₃	2
C₄×C₃₁×C₅₃	5
C₄×C₅×C₅₃	31
C₄×C₅×C₃₁	53

Subgroups — C4×C5×C31×C53 #45659554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₃₁×C₅₃ #45659554