Subgroups — C₁₃×AΣL(1,𝔽₂₇) #11760413

Order 1053.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
3	C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₃	—	3	3	no	—
5	C₃²×C₁₃	—	3	1	no	—
6	C₃²×C₁₃	—	3	1	no	—
7	C₃²×C₁₃	C₃²	1	1	yes	characteristic
8	C₉×C₁₃	—	3	2	no	—
9	AΣL(1,𝔽₂₇)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃×C₁₃	—	3	3	no	—
11	C₃×C₁₃	—	3	1	no	—
12	C₃×C₁₃	—	9	1	no	—
13	C₃×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃³	C₃×C₁₃	1	1	yes	characteristic, complemented
15	3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
16	H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic, complemented
17	C₁₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic, direct product factor, Sylow
18	C₃²	—	3	3	no	—
19	C₃²	—	3	1	no	—
20	C₃²	—	3	1	no	—
21	C₃²	C₃²×C₁₃	1	1	yes	characteristic
22	C₉	—	3	2	no	—
23	C₃	—	3	1	no	—
24	C₃	—	3	3	no	—
25	C₃	—	9	1	no	—
26	C₃	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃²×C₁₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃²×C₁₃ ◁ G

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

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