Subgroups — C₃×#14578911 #21419431

Order 7533.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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