Subgroups — C₃³×C₁₃×C₂₇ #23745066

Order 9477.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₂₇	C₃	1	39	yes	maximal, direct product factor
3	C₃⁴×C₁₃	C₉	1	1	yes	characteristic
4	C₃²×C₉×C₁₃	C₉	1	26	yes	—
5	C₃²×C₉×C₁₃	C₃²	1	13	yes	—
6	C₃×C₁₃×C₂₇	C₃²	1	117	yes	direct product factor
7	C₃³×C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₃	C₂₇	1	27	yes	direct product factor
9	C₃³×C₁₃	C₃×C₉	1	13	yes	—
10	C₃×C₉×C₁₃	C₃×C₉	1	104	yes	—
11	C₃×C₉×C₁₃	C₃³	1	13	yes	—
12	C₁₃×C₂₇	C₃³	1	27	yes	direct product factor
13	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
14	C₃²×C₂₇	C₃×C₁₃	1	39	yes	direct product factor
15	C₃²×C₁₃	C₃×C₂₇	1	117	yes	direct product factor
16	C₃²×C₁₃	C₃²×C₉	1	13	yes	—
17	C₉×C₁₃	C₃²×C₉	1	26	yes	—
18	C₉×C₁₃	C₃⁴	1	1	yes	characteristic
19	C₃⁴	C₉×C₁₃	1	1	yes	characteristic
20	C₃²×C₉	C₉×C₁₃	1	26	yes	—
21	C₃²×C₉	C₃²×C₁₃	1	13	yes	—
22	C₃×C₂₇	C₃²×C₁₃	1	117	yes	direct product factor
23	C₃×C₁₃	C₃²×C₂₇	1	39	yes	direct product factor
24	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
25	C₃³	C₁₃×C₂₇	1	27	yes	direct product factor
26	C₃³	C₃×C₉×C₁₃	1	13	yes	—
27	C₃×C₉	C₃×C₉×C₁₃	1	104	yes	—
28	C₃×C₉	C₃³×C₁₃	1	13	yes	—
29	C₂₇	C₃³×C₁₃	1	27	yes	direct product factor
30	C₁₃	C₃³×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	C₃×C₁₃×C₂₇	1	117	yes	direct product factor
32	C₃²	C₃²×C₉×C₁₃	1	13	yes	—
33	C₉	C₃²×C₉×C₁₃	1	26	yes	—
34	C₉	C₃⁴×C₁₃	1	1	yes	characteristic
35	C₃	C₃²×C₁₃×C₂₇	1	39	yes	direct product factor
36	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃⁴×C₁₃
socle, prime radical	C₃⁴×C₁₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₃×C₂₇	C₃	direct (N × H)
6. C₃×C₁₃×C₂₇	C₃²	direct (N × H)
7. C₃³×C₂₇	C₁₃	direct (N × H)
8. C₃³×C₁₃	C₂₇	direct (N × H)
12. C₁₃×C₂₇	C₃³	direct (N × H)
14. C₃²×C₂₇	C₃×C₁₃	direct (N × H)
15. C₃²×C₁₃	C₃×C₂₇	direct (N × H)
22. C₃×C₂₇	C₃²×C₁₃	direct (N × H)
23. C₃×C₁₃	C₃²×C₂₇	direct (N × H)
25. C₃³	C₁₃×C₂₇	direct (N × H)
29. C₂₇	C₃³×C₁₃	direct (N × H)
30. C₁₃	C₃³×C₂₇	direct (N × H)
31. C₃²	C₃×C₁₃×C₂₇	direct (N × H)
35. C₃	C₃²×C₁₃×C₂₇	direct (N × H)

Subgroups — C33×C13×C27 #23745066

Conjugacy classes of subgroups

Complements

Subgroups — C₃³×C₁₃×C₂₇ #23745066