Subgroups — C₂×C₃×D₁₃×C₆₁ #23748990

Order 9516.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₃×C₆₁	C₂×C₃	1	2	yes	direct product factor
7	C₁₃×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₆₁	—	13	1	no	maximal, Hall
9	C₂×C₃×C₆₁	—	13	2	no	—
10	C₂×C₃×C₆₁	D₁₃	1	1	yes	characteristic, direct product factor
11	C₂²×C₆₁	—	13	1	no	Hall
12	C₃×C₆₁	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×D₁₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₆₁	—	13	2	no	—
15	C₂×C₆₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₁₃	C₂×C₆₁	1	1	yes	characteristic, complemented
17	C₃×D₁₃	C₂×C₆₁	1	2	yes	direct product factor
18	C₆₁	C₂×C₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×D₁₃	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₃	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented
22	D₁₃	C₂×C₃×C₆₁	1	2	yes	direct product factor
23	C₁₃	C₂²×C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	13	1	no	Hall
25	C₂×C₃	—	13	2	no	—
26	C₂×C₃	D₁₃×C₆₁	1	1	yes	characteristic, direct product factor
27	C₂²	—	13	1	no	Sylow
28	C₃	C₂×D₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	13	2	no	—
30	C₂	C₃×D₁₃×C₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₆₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₆₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃×C₆₁	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₆₁	C₂	semidirect
3. C₂×D₁₃×C₆₁	C₃	direct (N × H)
4. C₃×C₁₃×C₆₁	C₂²	semidirect
5. C₂×C₁₃×C₆₁	C₂×C₃	semidirect
6. D₁₃×C₆₁	C₂×C₃	direct (N × H)
7. C₁₃×C₆₁	C₂²×C₃	semidirect
10. C₂×C₃×C₆₁	D₁₃	direct (N × H)
12. C₃×C₆₁	C₂×D₁₃	direct (N × H)
13. C₂×C₃×D₁₃	C₆₁	direct (N × H)
15. C₂×C₆₁	C₃×D₁₃	direct (N × H)
16. C₂×C₃×C₁₃	C₂×C₆₁	semidirect
17. C₃×D₁₃	C₂×C₆₁	direct (N × H)
18. C₆₁	C₂×C₃×D₁₃	direct (N × H)
19. C₂×D₁₃	C₃×C₆₁	direct (N × H)
20. C₃×C₁₃	C₂²×C₆₁	semidirect
21. C₂×C₁₃	C₂×C₃×C₆₁	semidirect
22. D₁₃	C₂×C₃×C₆₁	direct (N × H)
23. C₁₃	C₂²×C₃×C₆₁	semidirect
26. C₂×C₃	D₁₃×C₆₁	direct (N × H)
28. C₃	C₂×D₁₃×C₆₁	direct (N × H)
30. C₂	C₃×D₁₃×C₆₁	direct (N × H)

Subgroups — C2×C3×D13×C61 #23748990

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₁₃×C₆₁ #23748990