Subgroups — C₁₃×#10624707 #23744858

Order 9477.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic
4	C₁₃×C₉⋊C₂₇	C₃	1	9	yes	maximal, complemented
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₁₃×C₂₇⋊C₃	—	3	6	no	—
7	C₃×C₁₃×C₂₇	—	3	3	no	—
8	C₃×C₁₃×C₂₇	C₃²	1	3	yes	—
9	C₃×C₁₃×C₂₇	C₃²	1	6	yes	—
10	C₁₃×C₉⋊C₉	C₉	1	6	yes	—
11	C₁₃×C₃²⋊C₉	C₉	1	3	yes	—
12	C₉²×C₁₃	C₃²	1	3	yes	—
13	#10624707	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
16	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
17	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
18	C₃×C₉×C₁₃	3₋¹⁺²	1	6	yes	—
19	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×C₂₇	—	3	3	no	—
21	C₁₃×C₂₇	—	3	6	no	—
22	C₃×C₂₇⋊C₃	C₃×C₁₃	1	2	yes	—
23	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic
24	#6887	C₃×C₁₃	1	1	yes	characteristic
25	C₉⋊C₂₇	C₃×C₁₃	1	9	yes	complemented
26	C₃²×C₁₃	—	3	3	no	—
27	C₃²×C₁₃	C₉⋊C₉	1	3	yes	—
28	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
29	C₉×C₁₃	—	3	9	no	—
30	C₉×C₁₃	C₉⋊C₉	1	6	yes	—
31	C₉×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
32	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
33	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
34	C₂₇⋊C₃	—	3	6	no	—
35	C₃×C₂₇	—	3	3	no	—
36	C₃×C₂₇	C₃²×C₁₃	1	3	yes	—
37	C₃×C₂₇	C₃²×C₁₃	1	6	yes	—
38	C₉⋊C₉	C₉×C₁₃	1	6	yes	—
39	C₃²⋊C₉	C₉×C₁₃	1	3	yes	—
40	C₉²	C₃²×C₁₃	1	3	yes	—
41	C₃×C₁₃	—	3	3	no	—
42	C₃×C₁₃	C₃×C₉⋊C₉	1	1	yes	characteristic
43	C₃×C₁₃	#6903	1	3	yes	—
44	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
45	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
46	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
47	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
48	C₃×C₉	C₁₃×3₋¹⁺²	1	6	yes	—
49	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
50	C₂₇	—	3	3	no	—
51	C₂₇	—	3	6	no	—
52	C₁₃	#10624707	1	1	yes	characteristic, direct product factor, Sylow
53	C₃²	—	3	3	no	—
54	C₃²	C₁₃×C₉⋊C₉	1	3	yes	—
55	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
56	C₉	—	3	9	no	—
57	C₉	C₁₃×C₉⋊C₉	1	6	yes	—
58	C₉	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
59	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
60	C₃	—	3	3	no	—
61	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic
62	C₃	C₁₃×#6903	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₃×C₉⋊C₂₇	C₃	semidirect
13. #10624707	C₁₃	direct (N × H)
25. C₉⋊C₂₇	C₃×C₁₃	semidirect
52. C₁₃	#10624707	direct (N × H)

Subgroups — C13×#10624707 #23744858

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624707 #23744858