Subgroups — C₃⁵×C₉×C₁₃ #72205402

Order 28431.

221200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁶×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃⁴×C₉×C₁₃	C₃	1	363	yes	maximal, direct product factor
3	C₃⁵×C₁₃	C₉	1	243	yes	direct product factor
4	C₃⁵×C₁₃	C₃²	1	121	yes	—
5	C₃³×C₉×C₁₃	C₃²	1	10890	yes	direct product factor
6	C₃⁵×C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃⁴×C₁₃	C₃×C₉	1	9801	yes	direct product factor
8	C₃⁴×C₁₃	C₃³	1	1210	yes	—
9	C₃²×C₉×C₁₃	C₃³	1	32670	yes	direct product factor
10	C₃⁶	C₃×C₁₃	1	1	yes	characteristic
11	C₃⁴×C₉	C₃×C₁₃	1	363	yes	direct product factor
12	C₃³×C₁₃	C₃²×C₉	1	32670	yes	direct product factor
13	C₃³×C₁₃	C₃⁴	1	1210	yes	—
14	C₃×C₉×C₁₃	C₃⁴	1	9801	yes	direct product factor
15	C₃⁵	C₉×C₁₃	1	243	yes	direct product factor
16	C₃⁵	C₃²×C₁₃	1	121	yes	—
17	C₃³×C₉	C₃²×C₁₃	1	10890	yes	direct product factor
18	C₃²×C₁₃	C₃³×C₉	1	10890	yes	direct product factor
19	C₃²×C₁₃	C₃⁵	1	121	yes	—
20	C₉×C₁₃	C₃⁵	1	243	yes	direct product factor
21	C₃⁴	C₃×C₉×C₁₃	1	9801	yes	direct product factor
22	C₃⁴	C₃³×C₁₃	1	1210	yes	—
23	C₃²×C₉	C₃³×C₁₃	1	32670	yes	direct product factor
24	C₃×C₁₃	C₃⁴×C₉	1	363	yes	direct product factor
25	C₃×C₁₃	C₃⁶	1	1	yes	characteristic
26	C₃³	C₃²×C₉×C₁₃	1	32670	yes	direct product factor
27	C₃³	C₃⁴×C₁₃	1	1210	yes	—
28	C₃×C₉	C₃⁴×C₁₃	1	9801	yes	direct product factor
29	C₁₃	C₃⁵×C₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₃²	C₃³×C₉×C₁₃	1	10890	yes	direct product factor
31	C₃²	C₃⁵×C₁₃	1	121	yes	—
32	C₉	C₃⁵×C₁₃	1	243	yes	direct product factor
33	C₃	C₃⁴×C₉×C₁₃	1	363	yes	direct product factor
34	C₃	C₃⁶×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃⁶×C₁₃
socle, prime radical	C₃⁶×C₁₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃⁴×C₉×C₁₃	C₃	direct (N × H)
3. C₃⁵×C₁₃	C₉	direct (N × H)
5. C₃³×C₉×C₁₃	C₃²	direct (N × H)
6. C₃⁵×C₉	C₁₃	direct (N × H)
7. C₃⁴×C₁₃	C₃×C₉	direct (N × H)
9. C₃²×C₉×C₁₃	C₃³	direct (N × H)
11. C₃⁴×C₉	C₃×C₁₃	direct (N × H)
12. C₃³×C₁₃	C₃²×C₉	direct (N × H)
14. C₃×C₉×C₁₃	C₃⁴	direct (N × H)
15. C₃⁵	C₉×C₁₃	direct (N × H)
17. C₃³×C₉	C₃²×C₁₃	direct (N × H)
18. C₃²×C₁₃	C₃³×C₉	direct (N × H)
20. C₉×C₁₃	C₃⁵	direct (N × H)
21. C₃⁴	C₃×C₉×C₁₃	direct (N × H)
23. C₃²×C₉	C₃³×C₁₃	direct (N × H)
24. C₃×C₁₃	C₃⁴×C₉	direct (N × H)
26. C₃³	C₃²×C₉×C₁₃	direct (N × H)
28. C₃×C₉	C₃⁴×C₁₃	direct (N × H)
29. C₁₃	C₃⁵×C₉	direct (N × H)
30. C₃²	C₃³×C₉×C₁₃	direct (N × H)
32. C₉	C₃⁵×C₁₃	direct (N × H)
33. C₃	C₃⁴×C₉×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁶×C₁₃	3
C₃⁴×C₉×C₁₃	3
C₃⁵×C₉	13

Subgroups — C35×C9×C13 #72205402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⁵×C₉×C₁₃ #72205402