Subgroups — C₃×C₁₃×#6864 #23744830

Order 9477.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₂₇	C₃	1	3	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6864	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₁₃	C₉	1	3	yes	—
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×C₂₇	C₉	1	27	yes	complemented
7	C₃×C₁₃×C₂₇	C₃²	1	9	yes	—
8	C₉²×C₁₃	C₉	1	6	yes	—
9	C₉²×C₁₃	C₃²	1	3	yes	—
10	C₃×#6864	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₁₃	—	3	9	no	—
13	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
14	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
15	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
16	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×C₂₇	C₃×C₉	1	27	yes	complemented
18	C₃²×C₂₇	C₃×C₁₃	1	3	yes	—
19	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
20	#6864	C₃×C₁₃	1	9	yes	direct product factor
21	C₃²×C₁₃	C₉²	1	3	yes	—
22	C₃²×C₁₃	C₂₇⋊C₃	1	9	yes	—
23	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
24	C₉×C₁₃	—	3	9	no	—
25	C₉×C₁₃	C₉²	1	6	yes	—
26	C₉×C₁₃	C₃²×C₉	1	3	yes	—
27	C₃²×C₉	C₉×C₁₃	1	3	yes	—
28	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
29	C₃×C₂₇	C₉×C₁₃	1	27	yes	complemented
30	C₃×C₂₇	C₃²×C₁₃	1	9	yes	—
31	C₉²	C₉×C₁₃	1	6	yes	—
32	C₉²	C₃²×C₁₃	1	3	yes	—
33	C₃×C₁₃	#6864	1	9	yes	direct product factor
34	C₃×C₁₃	C₃×C₉²	1	1	yes	characteristic
35	C₃×C₁₃	C₃×C₂₇⋊C₃	1	3	yes	—
36	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
37	C₃×C₉	—	3	9	no	—
38	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
39	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
40	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
41	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
42	C₂₇	C₃×C₉×C₁₃	1	27	yes	complemented
43	C₁₃	C₃×#6864	1	1	yes	characteristic, direct product factor, Sylow
44	C₃²	C₉²×C₁₃	1	3	yes	—
45	C₃²	C₁₃×C₂₇⋊C₃	1	9	yes	—
46	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
47	C₉	—	3	9	no	—
48	C₉	C₉²×C₁₃	1	6	yes	—
49	C₉	C₃²×C₉×C₁₃	1	3	yes	—
50	C₃	C₁₃×#6864	1	9	yes	direct product factor
51	C₃	C₃×C₉²×C₁₃	1	1	yes	characteristic
52	C₃	C₃×C₁₃×C₂₇⋊C₃	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉×C₁₃	C₃²
commutator	C₃	C₃×C₉²×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle, prime radical	C₃³×C₁₃	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6864	C₃	direct (N × H)
6. C₃×C₁₃×C₂₇	C₉	semidirect
10. C₃×#6864	C₁₃	direct (N × H)
17. C₁₃×C₂₇	C₃×C₉	semidirect
20. #6864	C₃×C₁₃	direct (N × H)
29. C₃×C₂₇	C₉×C₁₃	semidirect
33. C₃×C₁₃	#6864	direct (N × H)
42. C₂₇	C₃×C₉×C₁₃	semidirect
43. C₁₃	C₃×#6864	direct (N × H)
50. C₃	C₁₃×#6864	direct (N × H)

Subgroups — C3×C13×#6864 #23744830

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6864 #23744830