Subgroups — #21419438

Order 7533.

460 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578911	C₃	1	27	yes	maximal, complemented
2	C₃×#11719689	C₃	1	12	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₃₁	C₃²	1	4	yes	—
5	H(3,𝔽₃)×C₃₁	C₃²	1	9	yes	—
6	#11719689	C₃²	1	9	yes	—
7	#11719689	C₃²	1	72	yes	complemented
8	C₃×C₃₁⋊C₉	C₃²	1	36	yes	complemented
9	C₃²×C₃₁	—	9	4	no	—
10	C₃²×C₃₁	C₃³	1	12	yes	—
11	C₃²×C₃₁	C₃³	1	1	yes	characteristic
12	C₃₁⋊C₉	C₃³	1	27	yes	—
13	3₋¹⁺⁴	—	31	1	no	maximal, Sylow
14	C₃×C₃₁	—	3	1	no	—
15	C₃×C₃₁	—	3	12	no	—
16	C₃×C₃₁	C₃⁴	1	1	yes	characteristic
17	#737	—	31	27	no	—
18	C₃×3₋¹⁺²	—	31	12	no	—
19	C₃×H(3,𝔽₃)	C₃₁⋊C₃	1	1	yes	characteristic
20	C₃₁	3₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
21	C₃³	C₃×C₃₁⋊C₃	1	4	yes	—
22	3₋¹⁺²	—	31	9	no	—
23	3₋¹⁺²	—	31	72	no	—
24	H(3,𝔽₃)	C₃×C₃₁⋊C₃	1	9	yes	—
25	C₃×C₉	—	31	36	no	—
26	C₃²	—	9	4	no	—
27	C₃²	C₃²×C₃₁⋊C₃	1	12	yes	—
28	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
29	C₉	—	31	27	no	—
30	C₃	—	3	1	no	—
31	C₃	—	3	12	no	—
32	C₃	C₃³×C₃₁⋊C₃	1	1	yes	characteristic

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