Subgroups — #15691698

Order 3159.

460 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11760452	C₃	1	27	yes	maximal, complemented
2	C₃×#66851	C₃	1	12	yes	maximal, complemented
3	C₃×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₁₃	C₃²	1	4	yes	—
5	C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
6	#66851	C₃²	1	9	yes	—
7	#66851	C₃²	1	72	yes	complemented
8	C₃×C₁₃⋊C₉	C₃²	1	36	yes	complemented
9	3₋¹⁺⁴	—	13	1	no	maximal, Sylow
10	C₃²×C₁₃	—	9	4	no	—
11	C₃²×C₁₃	C₃³	1	12	yes	—
12	C₃²×C₁₃	C₃³	1	1	yes	characteristic
13	C₁₃⋊C₉	C₃³	1	27	yes	—
14	#737	—	13	27	no	—
15	C₃×3₋¹⁺²	—	13	12	no	—
16	C₃×H(3,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic
17	C₃×C₁₃	—	3	1	no	—
18	C₃×C₁₃	—	3	12	no	—
19	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
20	C₃³	C₃×C₁₃⋊C₃	1	4	yes	—
21	3₋¹⁺²	—	13	9	no	—
22	3₋¹⁺²	—	13	72	no	—
23	H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	9	yes	—
24	C₃×C₉	—	13	36	no	—
25	C₁₃	3₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
26	C₃²	—	9	4	no	—
27	C₃²	C₃²×C₁₃⋊C₃	1	12	yes	—
28	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
29	C₉	—	13	27	no	—
30	C₃	—	3	1	no	—
31	C₃	—	3	12	no	—
32	C₃	C₃³×C₁₃⋊C₃	1	1	yes	characteristic

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.