Subgroups — C₂×D₅×C₃₁×C₅₃ #45659596

Order 32860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃₁×C₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₃₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₁×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₃₁×C₅₃	—	5	1	no	maximal, Hall
5	C₂×C₃₁×C₅₃	—	5	2	no	—
6	C₂×C₃₁×C₅₃	D₅	1	1	yes	characteristic, direct product factor
7	C₃₁×C₅₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₅×C₅₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₅×C₃₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₅₃	C₂×C₃₁	1	1	yes	characteristic, complemented
11	D₅×C₅₃	C₂×C₃₁	1	2	yes	direct product factor
12	C₂×C₅×C₃₁	C₂×C₅₃	1	1	yes	characteristic, complemented
13	D₅×C₃₁	C₂×C₅₃	1	2	yes	direct product factor
14	C₅×C₅₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₅₃	—	5	1	no	Hall
16	C₅×C₃₁	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₃₁	—	5	1	no	Hall
18	C₂×C₅₃	—	5	2	no	—
19	C₂×C₅₃	D₅×C₃₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	—	5	2	no	—
21	C₂×C₃₁	D₅×C₅₃	1	1	yes	characteristic, direct product factor
22	C₅₃	C₂×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₁	C₂×D₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₅	C₃₁×C₅₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅	C₂×C₃₁×C₅₃	1	1	yes	characteristic, complemented
26	D₅	C₂×C₃₁×C₅₃	1	2	yes	direct product factor
27	C₅	C₂²×C₃₁×C₅₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	5	1	no	Sylow
29	C₂	—	5	2	no	—
30	C₂	D₅×C₃₁×C₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁×C₅₃	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃₁×C₅₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₁×C₅₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃₁×C₅₃

Complements

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

N	H ≅ G/N	type
1. D₅×C₃₁×C₅₃	C₂	direct (N × H)
2. C₂×C₅×C₃₁×C₅₃	C₂	semidirect
3. C₅×C₃₁×C₅₃	C₂²	semidirect
6. C₂×C₃₁×C₅₃	D₅	direct (N × H)
7. C₃₁×C₅₃	C₂×D₅	direct (N × H)
8. C₂×D₅×C₅₃	C₃₁	direct (N × H)
9. C₂×D₅×C₃₁	C₅₃	direct (N × H)
10. C₂×C₅×C₅₃	C₂×C₃₁	semidirect
11. D₅×C₅₃	C₂×C₃₁	direct (N × H)
12. C₂×C₅×C₃₁	C₂×C₅₃	semidirect
13. D₅×C₃₁	C₂×C₅₃	direct (N × H)
14. C₅×C₅₃	C₂²×C₃₁	semidirect
16. C₅×C₃₁	C₂²×C₅₃	semidirect
19. C₂×C₅₃	D₅×C₃₁	direct (N × H)
21. C₂×C₃₁	D₅×C₅₃	direct (N × H)
22. C₅₃	C₂×D₅×C₃₁	direct (N × H)
23. C₃₁	C₂×D₅×C₅₃	direct (N × H)
24. C₂×D₅	C₃₁×C₅₃	direct (N × H)
25. C₂×C₅	C₂×C₃₁×C₅₃	semidirect
26. D₅	C₂×C₃₁×C₅₃	direct (N × H)
27. C₅	C₂²×C₃₁×C₅₃	semidirect
30. C₂	D₅×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
D₅×C₃₁×C₅₃	2
C₂×C₅×C₃₁×C₅₃	2
C₂²×C₃₁×C₅₃	5
C₂×D₅×C₅₃	31
C₂×D₅×C₃₁	53

Subgroups — C2×D5×C31×C53 #45659596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₃₁×C₅₃ #45659596