Subgroups — D₅×C₃₁×D₆₁ #49180708

Order 37820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₃₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₁×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₃₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×D₆₁	—	5	1	no	maximal, Hall
6	C₂×C₃₁×C₆₁	—	5	1	no	—
7	C₃₁×D₆₁	—	5	1	no	—
8	C₃₁×D₆₁	D₅	1	1	yes	characteristic, direct product factor
9	C₃₁×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×D₆₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×D₅×C₃₁	—	61	1	no	maximal, Hall
12	D₃₀₅	C₂×C₃₁	1	1	yes	characteristic, complemented
13	C₅×D₆₁	C₂×C₃₁	1	1	yes	characteristic, complemented
14	D₅×C₆₁	C₂×C₃₁	1	1	yes	characteristic, complemented
15	C₂×C₅×C₃₁	—	61	1	no	—
16	D₅×C₃₁	—	61	1	no	—
17	D₅×C₃₁	D₆₁	1	1	yes	characteristic, direct product factor
18	C₅×C₆₁	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
19	C₂×D₆₁	—	5	1	no	Hall
20	C₅×C₃₁	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃₁	—	305	1	no	Hall
22	C₂×C₆₁	—	5	1	no	—
23	D₆₁	—	5	1	no	—
24	D₆₁	D₅×C₃₁	1	1	yes	characteristic, direct product factor
25	C₂×C₃₁	—	5	1	no	—
26	C₂×C₃₁	—	305	1	no	—
27	C₂×C₃₁	—	61	1	no	—
28	C₆₁	C₂×D₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
29	C₃₁	D₅×D₆₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₅	—	61	1	no	Hall
31	C₂×C₅	—	61	1	no	—
32	D₅	—	61	1	no	—
33	D₅	C₃₁×D₆₁	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₃₁×D₆₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	305	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	305	1	no	—
38	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₅×D₆₁
commutator, cosocle, hypocenter	C₅×C₆₁	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₆₁	C₂²
LCS	G ▷ C₅×C₆₁
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₃₀₅	C₂	semidirect
2. D₅×C₃₁×C₆₁	C₂	semidirect
3. C₅×C₃₁×D₆₁	C₂	semidirect
4. C₅×C₃₁×C₆₁	C₂²	semidirect
8. C₃₁×D₆₁	D₅	direct (N × H)
9. C₃₁×C₆₁	C₂×D₅	semidirect
10. D₅×D₆₁	C₃₁	direct (N × H)
12. D₃₀₅	C₂×C₃₁	semidirect
13. C₅×D₆₁	C₂×C₃₁	semidirect
14. D₅×C₆₁	C₂×C₃₁	semidirect
17. D₅×C₃₁	D₆₁	direct (N × H)
18. C₅×C₆₁	C₂²×C₃₁	semidirect
20. C₅×C₃₁	C₂×D₆₁	semidirect
24. D₆₁	D₅×C₃₁	direct (N × H)
28. C₆₁	C₂×D₅×C₃₁	semidirect
29. C₃₁	D₅×D₆₁	direct (N × H)
33. D₅	C₃₁×D₆₁	direct (N × H)
34. C₅	C₂×C₃₁×D₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×D₃₀₅	2
D₅×C₃₁×C₆₁	2
C₅×C₃₁×D₆₁	2
C₂×C₃₁×D₆₁	5
D₅×D₆₁	31
C₂×D₅×C₃₁	61

Subgroups — D5×C31×D61 #49180708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃₁×D₆₁ #49180708