Subgroups — 3₋¹⁺²×C₃³⋊C₁₃ #23748630

Order 9477.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₃³⋊C₁₃	C₃	1	3	yes	maximal, complemented
3	C₃×C₃³⋊C₁₃	—	3	1	no	—
4	C₃×C₃³⋊C₁₃	C₃²	1	1	yes	characteristic
5	C₃³×3₋¹⁺²	C₁₃	1	1	yes	maximal, characteristic, complemented, Sylow
6	C₃³⋊C₁₃	3₋¹⁺²	1	1	yes	characteristic, direct product factor
7	C₁₃×3₋¹⁺²	—	27	1	no	maximal
8	C₃⁵	C₃×C₁₃	1	1	yes	characteristic
9	C₃²×3₋¹⁺²	—	13	1	no	—
10	C₃²×3₋¹⁺²	—	13	6	no	—
11	C₃²×3₋¹⁺²	—	13	2	no	—
12	C₃³×C₉	C₃×C₁₃	1	3	yes	complemented
13	C₃²×C₁₃	—	27	1	no	—
14	C₉×C₁₃	—	27	3	no	—
15	C₃⁴	—	3	1	no	—
16	C₃⁴	—	13	1	no	—
17	C₃⁴	—	13	2	no	—
18	C₃⁴	—	39	2	no	—
19	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
20	C₃×3₋¹⁺²	—	13	12	no	—
21	C₃×3₋¹⁺²	—	13	36	no	—
22	C₃×3₋¹⁺²	—	13	1	no	—
23	C₃×3₋¹⁺²	—	13	18	no	—
24	C₃×3₋¹⁺²	—	13	6	no	—
25	C₃×3₋¹⁺²	—	13	6	no	—
26	C₃×3₋¹⁺²	—	13	2	no	—
27	C₃²×C₉	—	13	3	no	—
28	C₃²×C₉	—	13	6	no	—
29	C₃×C₁₃	—	27	1	no	—
30	C₃×C₁₃	—	81	1	no	—
31	C₃³	—	13	2	no	—
32	C₃³	—	13	1	no	—
33	C₃³	—	13	6	no	—
34	C₃³	—	13	1	no	—
35	C₃³	—	13	2	no	—
36	C₃³	—	39	2	no	—
37	C₃³	—	39	1	no	—
38	C₃³	—	39	2	no	—
39	C₃³	—	39	4	no	—
40	C₃³	—	39	6	no	—
41	C₃³	—	39	12	no	—
42	C₃³	C₁₃×3₋¹⁺²	1	1	yes	characteristic, complemented
43	3₋¹⁺²	—	13	12	no	—
44	3₋¹⁺²	—	13	36	no	—
45	3₋¹⁺²	—	13	2	no	—
46	3₋¹⁺²	—	13	6	no	—
47	3₋¹⁺²	C₃³⋊C₁₃	1	1	yes	characteristic, direct product factor
48	C₃×C₉	—	13	3	no	—
49	C₃×C₉	—	13	18	no	—
50	C₃×C₉	—	13	6	no	—
51	C₁₃	—	27	1	no	Sylow
52	C₃²	—	13	1	no	—
53	C₃²	—	13	2	no	—
54	C₃²	—	13	6	no	—
55	C₃²	—	13	1	no	—
56	C₃²	—	13	2	no	—
57	C₃²	—	39	2	no	—
58	C₃²	—	39	1	no	—
59	C₃²	—	39	2	no	—
60	C₃²	—	39	4	no	—
61	C₃²	—	39	6	no	—
62	C₃²	—	39	12	no	—
63	C₃²	C₃×C₃³⋊C₁₃	1	1	yes	characteristic
64	C₉	—	13	6	no	—
65	C₉	C₃×C₃³⋊C₁₃	1	3	yes	complemented
66	C₃	—	3	1	no	—
67	C₃	—	13	1	no	—
68	C₃	—	13	2	no	—
69	C₃	—	39	2	no	—
70	C₃	C₃²×C₃³⋊C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃²×C₃³⋊C₁₃
commutator, socle, cosocle	C₃⁴	C₃²×C₁₃
Fitting	C₃³×3₋¹⁺²	C₁₃
prime radical	C₃²×C₃³⋊C₁₃	C₃
hypercenter	3₋¹⁺²	C₃³⋊C₁₃
hypocenter	C₃³	C₁₃×3₋¹⁺²
LCS	G ▷ C₃⁴ ▷ C₃³
UCS	C₁ ◁ C₃ ◁ 3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. C₉×C₃³⋊C₁₃	C₃	semidirect
5. C₃³×3₋¹⁺²	C₁₃	semidirect
6. C₃³⋊C₁₃	3₋¹⁺²	direct (N × H)
12. C₃³×C₉	C₃×C₁₃	semidirect
42. C₃³	C₁₃×3₋¹⁺²	semidirect
47. 3₋¹⁺²	C₃³⋊C₁₃	direct (N × H)
65. C₉	C₃×C₃³⋊C₁₃	semidirect

Subgroups — 3−1+2×C33⋊C13 #23748630

Conjugacy classes of subgroups

Complements

Subgroups — 3₋¹⁺²×C₃³⋊C₁₃ #23748630