Subgroups — C₂×C₁₃×D₅₀₁ #39907549

Order 26052.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₅₀₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₆₇	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₁₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₆₇	D₃	1	1	yes	characteristic, complemented
6	C₁₃×D₁₆₇	—	3	2	no	—
7	C₁₃×C₁₆₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅₀₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₆₇	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₅₀₁	C₂×C₁₃	1	2	yes	direct product factor
11	C₂×D₁₆₇	—	3	1	no	Hall
12	C₃×C₁₆₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₆₇	D₃×C₁₃	1	1	yes	characteristic, complemented
14	D₁₆₇	—	3	2	no	—
15	C₁₆₇	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₃×C₁₃	—	167	1	no	maximal, Hall
17	C₂×C₃×C₁₃	D₁₆₇	1	1	yes	characteristic, complemented
18	D₃×C₁₃	—	167	2	no	—
19	C₂²×C₁₃	—	501	1	no	Hall
20	C₃×C₁₃	C₂×D₁₆₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	—	501	2	no	—
22	C₂×C₁₃	D₅₀₁	1	1	yes	characteristic, direct product factor
23	C₁₃	C₂×D₅₀₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	—	167	1	no	Hall
25	C₂×C₃	C₁₃×D₁₆₇	1	1	yes	characteristic, complemented
26	D₃	—	167	2	no	—
27	C₂²	—	501	1	no	Sylow
28	C₃	C₂×C₁₃×D₁₆₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	501	2	no	—
30	C₂	C₁₃×D₅₀₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₅₀₁
commutator, cosocle, hypocenter	C₃×C₁₆₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₆₇	C₂
LCS	G ▷ C₃×C₁₆₇
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₅₀₁	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₆₇	C₂	semidirect
4. C₃×C₁₃×C₁₆₇	C₂²	semidirect
5. C₂×C₁₃×C₁₆₇	D₃	semidirect
7. C₁₃×C₁₆₇	C₂×D₃	semidirect
8. C₂×D₅₀₁	C₁₃	direct (N × H)
9. C₂×C₃×C₁₆₇	C₂×C₁₃	semidirect
10. D₅₀₁	C₂×C₁₃	direct (N × H)
12. C₃×C₁₆₇	C₂²×C₁₃	semidirect
13. C₂×C₁₆₇	D₃×C₁₃	semidirect
15. C₁₆₇	C₂×D₃×C₁₃	semidirect
17. C₂×C₃×C₁₃	D₁₆₇	semidirect
20. C₃×C₁₃	C₂×D₁₆₇	semidirect
22. C₂×C₁₃	D₅₀₁	direct (N × H)
23. C₁₃	C₂×D₅₀₁	direct (N × H)
25. C₂×C₃	C₁₃×D₁₆₇	semidirect
28. C₃	C₂×C₁₃×D₁₆₇	semidirect
30. C₂	C₁₃×D₅₀₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₅₀₁	2
C₂×C₃×C₁₃×C₁₆₇	2
C₂×C₁₃×D₁₆₇	3
C₂×D₅₀₁	13
C₂×D₃×C₁₃	167

Subgroups — C2×C13×D501 #39907549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₅₀₁ #39907549