Subgroups — D₁₃×D₅₀₁ #39907539

Order 26052.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₅₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₅₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₆₇	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁₇₁	—	3	1	no	—
7	C₁₃×D₁₆₇	—	3	1	no	—
8	D₁₃×C₁₆₇	D₃	1	1	yes	characteristic, complemented
9	C₁₃×C₁₆₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₅₀₁	—	13	1	no	maximal, Hall
11	C₂×C₃×C₁₆₇	—	13	1	no	—
12	D₅₀₁	—	13	1	no	—
13	D₅₀₁	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂×D₁₆₇	—	39	1	no	Hall
15	C₃×C₁₆₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₆₇	—	13	1	no	—
17	D₁₆₇	—	3	1	no	—
18	D₁₆₇	—	39	1	no	—
19	C₁₆₇	D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₁₃	—	167	1	no	maximal, Hall
21	D₃₉	—	167	1	no	—
22	C₃×D₁₃	D₁₆₇	1	1	yes	characteristic, complemented
23	D₃×C₁₃	—	167	1	no	—
24	C₂×D₁₃	—	501	1	no	Hall
25	C₃×C₁₃	C₂×D₁₆₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	501	1	no	—
27	D₁₃	—	501	1	no	—
28	D₁₃	D₅₀₁	1	1	yes	characteristic, direct product factor
29	C₁₃	C₂×D₅₀₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2171	1	no	Hall
31	C₂×C₃	—	13	1	no	—
32	D₃	—	2171	1	no	—
33	D₃	—	167	1	no	—
34	C₂²	—	6513	1	no	Sylow
35	C₃	D₁₃×D₁₆₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	13	1	no	—
37	C₂	—	6513	1	no	—
38	C₂	—	501	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₆₅₁₃	C₂	semidirect
2. C₁₃×D₅₀₁	C₂	semidirect
3. C₃×D₁₃×C₁₆₇	C₂	semidirect
5. C₃×C₁₃×C₁₆₇	C₂²	semidirect
8. D₁₃×C₁₆₇	D₃	semidirect
9. C₁₃×C₁₆₇	C₂×D₃	semidirect
13. D₅₀₁	D₁₃	direct (N × H)
15. C₃×C₁₆₇	C₂×D₁₃	semidirect
19. C₁₆₇	D₃×D₁₃	semidirect
22. C₃×D₁₃	D₁₆₇	semidirect
25. C₃×C₁₃	C₂×D₁₆₇	semidirect
28. D₁₃	D₅₀₁	direct (N × H)
29. C₁₃	C₂×D₅₀₁	semidirect
35. C₃	D₁₃×D₁₆₇	semidirect

Maximal subgroups

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

subgroup	index
D₆₅₁₃	2
C₁₃×D₅₀₁	2
C₃×D₁₃×C₁₆₇	2
D₁₃×D₁₆₇	3
C₂×D₅₀₁	13
D₃×D₁₃	167

Subgroups — D13×D501 #39907539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₅₀₁ #39907539