Subgroups — C₃×C₁₃×C₈₁⋊C₃ #23744983

Order 9477.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₈₁⋊C₃	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₁₃×C₈₁	C₃	1	3	yes	maximal, complemented
4	C₃²×C₉×C₁₃	C₉	1	1	yes	characteristic
5	C₃×C₁₃×C₂₇	C₉	1	2	yes	—
6	C₃×C₁₃×C₂₇	C₉	1	6	yes	—
7	C₃×C₁₃×C₂₇	C₃²	1	3	yes	—
8	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
9	C₁₃×C₈₁	C₃²	1	9	yes	complemented
10	C₃×C₈₁⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	C₂₇	1	1	yes	characteristic
12	C₃×C₉×C₁₃	C₂₇	1	6	yes	—
13	C₃×C₉×C₁₃	C₂₇	1	2	yes	—
14	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
15	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
16	C₁₃×C₂₇	C₃×C₉	1	6	yes	—
17	C₁₃×C₂₇	C₃×C₉	1	2	yes	—
18	C₁₃×C₂₇	C₃³	1	1	yes	characteristic
19	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic
20	C₈₁⋊C₃	C₃×C₁₃	1	9	yes	direct product factor
21	C₃×C₈₁	C₃×C₁₃	1	3	yes	complemented
22	C₃²×C₁₃	—	3	3	no	—
23	C₃²×C₁₃	C₃×C₂₇	1	3	yes	—
24	C₃²×C₁₃	C₃×C₂₇	1	1	yes	characteristic
25	C₉×C₁₃	C₃×C₂₇	1	6	yes	—
26	C₉×C₁₃	C₃×C₂₇	1	2	yes	—
27	C₉×C₁₃	C₃²×C₉	1	1	yes	characteristic
28	C₃²×C₉	C₉×C₁₃	1	1	yes	characteristic
29	C₃×C₂₇	C₉×C₁₃	1	2	yes	—
30	C₃×C₂₇	C₉×C₁₃	1	6	yes	—
31	C₃×C₂₇	C₃²×C₁₃	1	3	yes	—
32	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
33	C₈₁	C₃²×C₁₃	1	9	yes	complemented
34	C₃×C₁₃	—	3	3	no	—
35	C₃×C₁₃	C₈₁⋊C₃	1	3	yes	direct product factor
36	C₃×C₁₃	C₃²×C₂₇	1	1	yes	characteristic
37	C₃³	C₁₃×C₂₇	1	1	yes	characteristic
38	C₃×C₉	C₁₃×C₂₇	1	6	yes	—
39	C₃×C₉	C₁₃×C₂₇	1	2	yes	—
40	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
41	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
42	C₂₇	C₃×C₉×C₁₃	1	6	yes	—
43	C₂₇	C₃×C₉×C₁₃	1	2	yes	—
44	C₂₇	C₃³×C₁₃	1	1	yes	characteristic
45	C₁₃	C₃×C₈₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
46	C₃²	—	3	3	no	—
47	C₃²	C₃×C₁₃×C₂₇	1	3	yes	—
48	C₃²	C₃×C₁₃×C₂₇	1	1	yes	characteristic
49	C₉	C₃×C₁₃×C₂₇	1	2	yes	—
50	C₉	C₃×C₁₃×C₂₇	1	6	yes	—
51	C₉	C₃²×C₉×C₁₃	1	1	yes	characteristic
52	C₃	—	3	3	no	—
53	C₃	C₁₃×C₈₁⋊C₃	1	3	yes	direct product factor
54	C₃	C₃²×C₁₃×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₁₃×C₂₇	C₃²
commutator	C₃	C₃²×C₁₃×C₂₇
Frattini, cosocle	C₂₇	C₃³×C₁₃
socle	C₃²×C₁₃	C₃×C₂₇
prime radical	C₃³×C₁₃	C₂₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₈₁⋊C₃	C₃	direct (N × H)
3. C₃×C₁₃×C₈₁	C₃	semidirect
9. C₁₃×C₈₁	C₃²	semidirect
10. C₃×C₈₁⋊C₃	C₁₃	direct (N × H)
20. C₈₁⋊C₃	C₃×C₁₃	direct (N × H)
21. C₃×C₈₁	C₃×C₁₃	semidirect
33. C₈₁	C₃²×C₁₃	semidirect
35. C₃×C₁₃	C₈₁⋊C₃	direct (N × H)
45. C₁₃	C₃×C₈₁⋊C₃	direct (N × H)
53. C₃	C₁₃×C₈₁⋊C₃	direct (N × H)

Subgroups — C3×C13×C81⋊C3 #23744983

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×C₈₁⋊C₃ #23744983