Subgroups — C₁₃⋊H(5,𝔽₃) #15691694

Order 3159.

586 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₁₃⋊C₃)	C₃	1	12	yes	maximal, complemented
2	H(3,𝔽₃)×C₁₃⋊C₃	C₃	1	27	yes	maximal, complemented
3	C₃×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₁₃	C₃²	1	4	yes	complemented
5	C₃²×C₁₃⋊C₃	C₃²	1	36	yes	complemented
6	C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	complemented
7	C₃²⋊(C₁₃⋊C₃)	C₃²	1	72	yes	complemented
8	C₃²⋊(C₁₃⋊C₃)	C₃²	1	9	yes	complemented
9	H(5,𝔽₃)	—	13	1	no	maximal, Sylow
10	C₃²×C₁₃	—	9	4	no	—
11	C₃²×C₁₃	C₃³	1	1	yes	characteristic
12	C₃²×C₁₃	C₃³	1	12	yes	—
13	C₃×C₁₃⋊C₃	—	9	36	no	—
14	C₃×C₁₃⋊C₃	C₃³	1	27	yes	—
15	C₃×H(3,𝔽₃)	—	13	12	no	—
16	C₃×H(3,𝔽₃)	—	13	27	no	—
17	C₃×H(3,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₃×C₁₃	—	3	12	no	—
19	C₃×C₁₃	—	3	1	no	—
20	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
21	C₁₃⋊C₃	—	3	27	no	—
22	C₃³	—	13	36	no	—
23	C₃³	C₃×C₁₃⋊C₃	1	4	yes	complemented
24	H(3,𝔽₃)	—	13	9	no	—
25	H(3,𝔽₃)	—	13	72	no	—
26	H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	9	yes	complemented
27	C₁₃	H(5,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	9	4	no	—
29	C₃²	—	13	27	no	—
30	C₃²	—	117	36	no	—
31	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
32	C₃²	C₃²×C₁₃⋊C₃	1	12	yes	—
33	C₃	—	3	1	no	—
34	C₃	—	3	12	no	—
35	C₃	—	39	27	no	—
36	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.