Subgroups — C₄×C₉×C₁₃×C₄₁ #34062849

Order 19188.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₃×C₄₁	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×C₄₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₃×C₄₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₄₁	C₂×C₉	1	1	yes	characteristic
9	C₂×C₉×C₄₁	C₂×C₁₃	1	1	yes	characteristic
10	C₁₃×C₄₁	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₄×C₄₁	C₃×C₁₃	1	1	yes	characteristic
12	C₄×C₉×C₁₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₉×C₄₁	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₄₁	C₂×C₃×C₁₃	1	1	yes	characteristic
15	C₂×C₉×C₁₃	C₂×C₄₁	1	1	yes	characteristic
16	C₄×C₄₁	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₄×C₁₃	C₃×C₄₁	1	1	yes	characteristic
18	C₃×C₄₁	C₃×C₄×C₁₃	1	1	yes	characteristic
19	C₉×C₁₃	C₄×C₄₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₄₁	C₂×C₉×C₁₃	1	1	yes	characteristic
21	C₂×C₃×C₁₃	C₂×C₃×C₄₁	1	1	yes	characteristic
22	C₄×C₁₃	C₉×C₄₁	1	1	yes	characteristic, direct product factor, Hall
23	C₄₁	C₄×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₁₃	C₃×C₄×C₄₁	1	1	yes	characteristic
25	C₄×C₉	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₁₃	C₂×C₉×C₄₁	1	1	yes	characteristic
27	C₂×C₉	C₂×C₁₃×C₄₁	1	1	yes	characteristic
28	C₁₃	C₄×C₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₄	C₃×C₁₃×C₄₁	1	1	yes	characteristic
30	C₉	C₄×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₃×C₄₁	1	1	yes	characteristic
32	C₄	C₉×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₃×C₄₁	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₃×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₁₃×C₄₁
socle, prime radical	C₂×C₃×C₁₃×C₄₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₄₁	C₄	direct (N × H)
5. C₄×C₁₃×C₄₁	C₉	direct (N × H)
7. C₄×C₉×C₄₁	C₁₃	direct (N × H)
10. C₁₃×C₄₁	C₄×C₉	direct (N × H)
12. C₄×C₉×C₁₃	C₄₁	direct (N × H)
13. C₉×C₄₁	C₄×C₁₃	direct (N × H)
16. C₄×C₄₁	C₉×C₁₃	direct (N × H)
19. C₉×C₁₃	C₄×C₄₁	direct (N × H)
22. C₄×C₁₃	C₉×C₄₁	direct (N × H)
23. C₄₁	C₄×C₉×C₁₃	direct (N × H)
25. C₄×C₉	C₁₃×C₄₁	direct (N × H)
28. C₁₃	C₄×C₉×C₄₁	direct (N × H)
30. C₉	C₄×C₁₃×C₄₁	direct (N × H)
32. C₄	C₉×C₁₃×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₃×C₄₁	2
C₃×C₄×C₁₃×C₄₁	3
C₄×C₉×C₄₁	13
C₄×C₉×C₁₃	41

Subgroups — C4×C9×C13×C41 #34062849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₁₃×C₄₁ #34062849