Subgroups — #21419270

Order 7533.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578902	C₃	1	1	yes	maximal, characteristic, complemented
2	#14578900	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578886	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#732	C₃	1	1	yes	maximal, characteristic, complemented
5	H(3,𝔽₃)×C₃₁	—	3	1	no	—
6	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
7	C₃²⋊(C₃₁⋊C₃)	—	3	1	no	—
8	#11719689	—	3	1	no	—
9	C₃×C₃₁⋊C₉	—	3	1	no	—
10	C₃²×C₃₁	—	9	1	no	—
11	C₃²×C₃₁	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₃₁⋊C₃	—	9	1	no	—
13	C₉×C₃₁	—	3	1	no	—
14	C₃₁⋊C₉	—	9	1	no	—
15	C₃₁⋊C₉	—	9	1	no	—
16	#6881	—	31	1	no	maximal, Sylow
17	C₃×C₃₁	—	3	1	no	—
18	C₃×C₃₁	—	27	1	no	—
19	C₃×C₃₁	#732	1	1	yes	characteristic
20	C₃₁⋊C₃	—	27	1	no	—
21	#733	—	31	1	no	—
22	#732	—	31	1	no	—
23	#732	C₃₁⋊C₃	1	1	yes	characteristic, complemented
24	C₉⋊C₉	—	31	1	no	—
25	C₃₁	#6881	1	1	yes	characteristic, complemented, Sylow
26	3₋¹⁺²	—	93	1	no	—
27	H(3,𝔽₃)	—	3	1	no	—
28	H(3,𝔽₃)	—	93	1	no	—
29	C₃×C₉	—	93	1	no	—
30	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
31	C₃²	—	9	1	no	—
32	C₃²	—	279	1	no	—
33	C₃²	C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic
34	C₉	—	3	1	no	—
35	C₉	—	279	1	no	—
36	C₉	—	279	1	no	—
37	C₃	—	3	1	no	—
38	C₃	—	27	1	no	—
39	C₃	—	837	1	no	—
40	C₃	#14578899	1	1	yes	characteristic

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