Subgroups — C₃³×C₃³⋊C₁₃ #23748631

Order 9477.

4464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃³⋊C₁₃	C₃	1	13	yes	maximal, direct product factor
2	C₃×C₃³⋊C₁₃	C₃²	1	13	yes	direct product factor
3	C₃⁶	C₁₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₃³×C₁₃	—	27	1	no	maximal
5	C₃³⋊C₁₃	C₃³	1	1	yes	characteristic, direct product factor
6	C₃⁵	—	13	26	no	—
7	C₃⁵	—	13	1	no	—
8	C₃⁵	C₃×C₁₃	1	13	yes	complemented
9	C₃²×C₁₃	—	27	13	no	—
10	C₃⁴	—	13	104	no	—
11	C₃⁴	—	13	13	no	—
12	C₃⁴	—	13	26	no	—
13	C₃⁴	—	13	78	no	—
14	C₃⁴	—	13	624	no	—
15	C₃⁴	—	13	1	no	—
16	C₃⁴	C₃²×C₁₃	1	13	yes	complemented
17	C₃×C₁₃	—	27	13	no	—
18	C₃³	—	13	26	no	—
19	C₃³	—	13	13	no	—
20	C₃³	—	13	104	no	—
21	C₃³	—	13	312	no	—
22	C₃³	—	13	624	no	—
23	C₃³	—	13	864	no	—
24	C₃³	—	13	624	no	—
25	C₃³	—	13	26	no	—
26	C₃³	—	13	13	no	—
27	C₃³	C₃³⋊C₁₃	1	1	yes	characteristic, direct product factor
28	C₃³	C₃³×C₁₃	1	1	yes	characteristic, complemented
29	C₁₃	—	27	1	no	Sylow
30	C₃²	—	13	1	no	—
31	C₃²	—	13	26	no	—
32	C₃²	—	13	78	no	—
33	C₃²	—	13	624	no	—
34	C₃²	—	13	104	no	—
35	C₃²	—	13	13	no	—
36	C₃²	C₃×C₃³⋊C₁₃	1	13	yes	direct product factor
37	C₃	—	13	26	no	—
38	C₃	—	13	1	no	—
39	C₃	C₃²×C₃³⋊C₁₃	1	13	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃³	C₃³⋊C₁₃
commutator, cosocle, hypocenter	C₃³	C₃³×C₁₃
Frattini	C₁	G
Fitting, socle	C₃⁶	C₁₃
LCS	G ▷ C₃³
UCS	C₁ ◁ C₃³

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