Subgroups — C₃×C₁₃×C₉⋊C₂₇ #23744856

Order 9477.

284 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×C₉⋊C₂₇	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₁₃	C₉	1	2	yes	—
5	C₃²×C₉×C₁₃	C₉	1	1	yes	characteristic
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×C₂₇	—	3	9	no	—
8	C₃×C₁₃×C₂₇	C₃²	1	9	yes	—
9	C₉²×C₁₃	C₉	1	6	yes	—
10	C₉²×C₁₃	C₃²	1	3	yes	—
11	C₃×C₉⋊C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₁₃	—	3	6	no	—
14	C₃×C₉×C₁₃	C₂₇	1	9	yes	complemented
15	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
16	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
17	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	—
19	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×C₂₇	—	3	9	no	—
21	C₃²×C₂₇	C₃×C₁₃	1	3	yes	—
22	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
23	C₉⋊C₂₇	C₃×C₁₃	1	9	yes	direct product factor
24	C₃²×C₁₃	C₉⋊C₉	1	3	yes	—
25	C₃²×C₁₃	C₃×C₂₇	1	3	yes	—
26	C₃²×C₁₃	C₂₇⋊C₃	1	6	yes	—
27	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
28	C₉×C₁₃	—	3	6	no	—
29	C₉×C₁₃	C₉⋊C₉	1	6	yes	—
30	C₉×C₁₃	C₃×C₂₇	1	9	yes	complemented
31	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
32	C₃²×C₉	C₉×C₁₃	1	2	yes	—
33	C₃²×C₉	C₉×C₁₃	1	1	yes	characteristic
34	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
35	C₃×C₂₇	—	3	9	no	—
36	C₃×C₂₇	C₃²×C₁₃	1	9	yes	—
37	C₉²	C₉×C₁₃	1	6	yes	—
38	C₉²	C₃²×C₁₃	1	3	yes	—
39	C₃×C₁₃	C₉⋊C₂₇	1	9	yes	direct product factor
40	C₃×C₁₃	C₃×C₉⋊C₉	1	1	yes	characteristic
41	C₃×C₁₃	C₃²×C₂₇	1	1	yes	characteristic
42	C₃×C₁₃	C₃×C₂₇⋊C₃	1	2	yes	—
43	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
44	C₃×C₉	—	3	6	no	—
45	C₃×C₉	C₁₃×C₂₇	1	9	yes	complemented
46	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
47	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
48	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
49	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	—
50	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
51	C₂₇	—	3	9	no	—
52	C₁₃	C₃×C₉⋊C₂₇	1	1	yes	characteristic, direct product factor, Sylow
53	C₃²	C₁₃×C₉⋊C₉	1	3	yes	—
54	C₃²	C₃×C₁₃×C₂₇	1	3	yes	—
55	C₃²	C₁₃×C₂₇⋊C₃	1	6	yes	—
56	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
57	C₉	—	3	6	no	—
58	C₉	C₁₃×C₉⋊C₉	1	6	yes	—
59	C₉	C₃×C₁₃×C₂₇	1	9	yes	complemented
60	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
61	C₃	C₁₃×C₉⋊C₂₇	1	9	yes	direct product factor
62	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic
63	C₃	C₃²×C₁₃×C₂₇	1	1	yes	characteristic
64	C₃	C₃×C₁₃×C₂₇⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₃²×C₉×C₁₃	C₃²
commutator	C₃	C₃²×C₁₃×C₂₇
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×C₉⋊C₂₇	C₃	direct (N × H)
11. C₃×C₉⋊C₂₇	C₁₃	direct (N × H)
14. C₃×C₉×C₁₃	C₂₇	semidirect
23. C₉⋊C₂₇	C₃×C₁₃	direct (N × H)
30. C₉×C₁₃	C₃×C₂₇	semidirect
39. C₃×C₁₃	C₉⋊C₂₇	direct (N × H)
45. C₃×C₉	C₁₃×C₂₇	semidirect
52. C₁₃	C₃×C₉⋊C₂₇	direct (N × H)
59. C₉	C₃×C₁₃×C₂₇	semidirect
61. C₃	C₁₃×C₉⋊C₂₇	direct (N × H)

Subgroups — C3×C13×C9⋊C27 #23744856

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×C₉⋊C₂₇ #23744856