Subgroups — #21419406

Order 7533.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₃₁⋊C₃)	C₃	1	3	yes	maximal, complemented
2	#14578900	C₃	1	9	yes	maximal, complemented
3	C₃×3₋¹⁺²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₃₁	C₃²	1	1	yes	characteristic
5	C₃²×C₃₁⋊C₃	—	3	3	no	—
6	3₋¹⁺²×C₃₁	—	3	3	no	—
7	C₃×C₉×C₃₁	C₃²	1	3	yes	complemented
8	C₃²⋊(C₃₁⋊C₃)	—	3	6	no	—
9	C₃²⋊(C₃₁⋊C₃)	C₃²	1	9	yes	complemented
10	C₃²×C₃₁	—	9	1	no	—
11	C₃²×C₃₁	H(3,𝔽₃)	1	3	yes	—
12	C₃²×C₃₁	C₃³	1	1	yes	characteristic
13	C₃×C₃₁⋊C₃	—	3	9	no	—
14	C₃×C₃₁⋊C₃	—	9	9	no	—
15	C₉×C₃₁	—	3	3	no	—
16	#6911	—	31	1	no	maximal, Sylow
17	C₃×C₃₁	—	3	3	no	—
18	C₃×C₃₁	—	3	1	no	—
19	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
20	C₃₁⋊C₃	—	9	9	no	—
21	C₃×3₋¹⁺²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
22	C₃×H(3,𝔽₃)	—	31	3	no	—
23	#732	—	31	9	no	—
24	C₃₁	#6911	1	1	yes	characteristic, complemented, Sylow
25	C₃³	—	93	3	no	—
26	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
27	3₋¹⁺²	—	3	3	no	—
28	H(3,𝔽₃)	—	31	9	no	—
29	H(3,𝔽₃)	—	93	6	no	—
30	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	complemented
31	C₃²	—	9	1	no	—
32	C₃²	—	279	9	no	—
33	C₃²	—	93	9	no	—
34	C₃²	C₃²⋊(C₃₁⋊C₃)	1	3	yes	—
35	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
36	C₉	—	3	3	no	—
37	C₃	—	3	3	no	—
38	C₃	—	3	1	no	—
39	C₃	—	279	9	no	—
40	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

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