Subgroups — C₃×C₁₃×#6862 #23744737

Order 9477.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₃²⋊C₉	C₃	1	4	yes	maximal
2	C₁₃×#6862	C₃	1	9	yes	maximal, direct product factor
3	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
4	C₃²×C₉×C₁₃	—	3	4	no	—
5	C₁₃×C₃²⋊C₉	—	3	8	no	—
6	C₁₃×C₃²⋊C₉	C₃²	1	12	yes	—
7	C₃×#6862	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₃	—	3	12	no	—
9	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
10	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃³×C₁₃	C₃³	1	1	yes	characteristic
12	C₃×C₉×C₁₃	—	3	12	no	—
13	C₃×C₉×C₁₃	—	9	12	no	—
14	C₃×C₃²⋊C₉	C₃×C₁₃	1	4	yes	—
15	#6862	C₃×C₁₃	1	9	yes	direct product factor
16	C₃²×C₁₃	—	3	8	no	—
17	C₃²×C₁₃	—	3	4	no	—
18	C₃²×C₁₃	—	9	9	no	—
19	C₃²×C₁₃	#731	1	12	yes	—
20	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	C₉×C₁₃	—	9	12	no	—
22	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
23	C₃²×C₉	—	3	4	no	—
24	C₃²⋊C₉	—	3	8	no	—
25	C₃²⋊C₉	C₃²×C₁₃	1	12	yes	—
26	C₃×C₁₃	—	9	2	no	—
27	C₃×C₁₃	—	9	1	no	—
28	C₃×C₁₃	#6862	1	9	yes	direct product factor
29	C₃×C₁₃	C₃×#731	1	4	yes	—
30	C₃³	—	3	12	no	—
31	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
32	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃³	C₃³×C₁₃	1	1	yes	characteristic
34	C₃×C₉	—	3	12	no	—
35	C₃×C₉	—	9	12	no	—
36	C₁₃	C₃×#6862	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²	—	3	8	no	—
38	C₃²	—	3	4	no	—
39	C₃²	—	9	9	no	—
40	C₃²	C₁₃×#731	1	12	yes	—
41	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₉	—	9	12	no	—
43	C₃	—	9	2	no	—
44	C₃	—	9	1	no	—
45	C₃	C₁₃×#6862	1	9	yes	direct product factor
46	C₃	C₃×C₁₃×#731	1	4	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6862	C₃	direct (N × H)
7. C₃×#6862	C₁₃	direct (N × H)
15. #6862	C₃×C₁₃	direct (N × H)
28. C₃×C₁₃	#6862	direct (N × H)
36. C₁₃	C₃×#6862	direct (N × H)
45. C₃	C₁₃×#6862	direct (N × H)

Subgroups — C3×C13×#6862 #23744737

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6862 #23744737