Subgroups — C₃⁵×C₁₃⋊C₃ #23748624

Order 9477.

113264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₁₃⋊C₃	C₃	1	363	yes	maximal, direct product factor
2	C₃⁵×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₁₃⋊C₃	C₃²	1	10890	yes	direct product factor
4	C₃⁴×C₁₃	C₃²	1	121	yes	complemented
5	C₃⁶	—	13	1	no	maximal, Sylow
6	C₃³×C₁₃	C₃³	1	1210	yes	complemented
7	C₃²×C₁₃⋊C₃	C₃³	1	32670	yes	direct product factor
8	C₃⁵	—	13	363	no	—
9	C₃⁵	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
10	C₃²×C₁₃	C₃⁴	1	1210	yes	complemented
11	C₃×C₁₃⋊C₃	C₃⁴	1	9801	yes	direct product factor
12	C₃⁴	—	13	10890	no	—
13	C₃⁴	C₃×C₁₃⋊C₃	1	121	yes	direct product factor
14	C₃×C₁₃	C₃⁵	1	121	yes	complemented
15	C₁₃⋊C₃	C₃⁵	1	243	yes	direct product factor
16	C₃³	—	13	32670	no	—
17	C₃³	C₃²×C₁₃⋊C₃	1	1210	yes	direct product factor
18	C₁₃	C₃⁶	1	1	yes	characteristic, complemented, Sylow
19	C₃²	—	13	9801	no	—
20	C₃²	C₃³×C₁₃⋊C₃	1	1210	yes	direct product factor
21	C₃	—	13	243	no	—
22	C₃	C₃⁴×C₁₃⋊C₃	1	121	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃⁵	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃⁶
Frattini	C₁	G
Fitting, socle	C₃⁵×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃⁵

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