Subgroups — C₂×D₁₅×C₅₂₁ #44530481

Order 31260.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×C₅₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₅₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₅₂₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₅₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₅₂₁	—	5	1	no	maximal, Hall
6	C₂×C₅×C₅₂₁	D₃	1	1	yes	characteristic, complemented
7	D₅×C₅₂₁	—	3	2	no	—
8	C₂×C₃×C₅₂₁	D₅	1	1	yes	characteristic, complemented
9	D₃×C₅₂₁	—	5	2	no	—
10	C₅×C₅₂₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₅₂₁	—	15	1	no	Hall
12	C₃×C₅₂₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₂₁	—	15	2	no	—
14	C₂×C₅₂₁	D₁₅	1	1	yes	characteristic, direct product factor
15	C₅₂₁	C₂×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₁₅	C₅₂₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅	C₂×C₅₂₁	1	1	yes	characteristic, complemented
18	D₁₅	C₂×C₅₂₁	1	2	yes	direct product factor
19	C₂×D₅	—	3	1	no	Hall
20	C₃×C₅	C₂²×C₅₂₁	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃	—	5	1	no	Hall
22	C₂×C₅	D₃×C₅₂₁	1	1	yes	characteristic, complemented
23	D₅	—	3	2	no	—
24	C₂×C₃	D₅×C₅₂₁	1	1	yes	characteristic, complemented
25	D₃	—	5	2	no	—
26	C₅	C₂×D₃×C₅₂₁	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	15	1	no	Sylow
28	C₃	C₂×D₅×C₅₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	15	2	no	—
30	C₂	D₁₅×C₅₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅₂₁	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₅₂₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₅₂₁	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅₂₁

Complements

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

N	H ≅ G/N	type
1. D₁₅×C₅₂₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₅₂₁	C₂	semidirect
4. C₃×C₅×C₅₂₁	C₂²	semidirect
6. C₂×C₅×C₅₂₁	D₃	semidirect
8. C₂×C₃×C₅₂₁	D₅	semidirect
10. C₅×C₅₂₁	C₂×D₃	semidirect
12. C₃×C₅₂₁	C₂×D₅	semidirect
14. C₂×C₅₂₁	D₁₅	direct (N × H)
15. C₅₂₁	C₂×D₁₅	direct (N × H)
16. C₂×D₁₅	C₅₂₁	direct (N × H)
17. C₂×C₃×C₅	C₂×C₅₂₁	semidirect
18. D₁₅	C₂×C₅₂₁	direct (N × H)
20. C₃×C₅	C₂²×C₅₂₁	semidirect
22. C₂×C₅	D₃×C₅₂₁	semidirect
24. C₂×C₃	D₅×C₅₂₁	semidirect
26. C₅	C₂×D₃×C₅₂₁	semidirect
28. C₃	C₂×D₅×C₅₂₁	semidirect
30. C₂	D₁₅×C₅₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₅×C₅₂₁	2
C₂×C₃×C₅×C₅₂₁	2
C₂×D₅×C₅₂₁	3
C₂×D₃×C₅₂₁	5
C₂×D₁₅	521

Subgroups — C2×D15×C521 #44530481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₅×C₅₂₁ #44530481