Subgroups — C₃×C₄×C₁₃×C₆₁ #23748892

Order 9516.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₆₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₆₁	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₄×C₆₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₆₁	C₂×C₁₃	1	1	yes	characteristic
8	C₄×C₆₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₆₁	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₄×C₁₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₆₁	C₂×C₃×C₁₃	1	1	yes	characteristic
12	C₂×C₃×C₁₃	C₂×C₆₁	1	1	yes	characteristic
13	C₆₁	C₃×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₄×C₁₃	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃	C₄×C₆₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	C₂×C₃×C₆₁	1	1	yes	characteristic
17	C₁₃	C₃×C₄×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₃×C₆₁	1	1	yes	characteristic
20	C₄	C₃×C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₁₃×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₁₃×C₆₁
socle, prime radical	C₂×C₃×C₁₃×C₆₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₆₁	C₃	direct (N × H)
3. C₃×C₁₃×C₆₁	C₄	direct (N × H)
5. C₁₃×C₆₁	C₃×C₄	direct (N × H)
6. C₃×C₄×C₆₁	C₁₃	direct (N × H)
8. C₄×C₆₁	C₃×C₁₃	direct (N × H)
9. C₃×C₆₁	C₄×C₁₃	direct (N × H)
10. C₃×C₄×C₁₃	C₆₁	direct (N × H)
13. C₆₁	C₃×C₄×C₁₃	direct (N × H)
14. C₄×C₁₃	C₃×C₆₁	direct (N × H)
15. C₃×C₁₃	C₄×C₆₁	direct (N × H)
17. C₁₃	C₃×C₄×C₆₁	direct (N × H)
18. C₃×C₄	C₁₃×C₆₁	direct (N × H)
20. C₄	C₃×C₁₃×C₆₁	direct (N × H)
21. C₃	C₄×C₁₃×C₆₁	direct (N × H)

Subgroups — C3×C4×C13×C61 #23748892

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₄×C₁₃×C₆₁ #23748892