Subgroups — C₁₃×#10624706 #23744857

Order 9477.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₂₇⋊C₃	C₃	1	3	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×C₉⋊C₂₇	C₃	1	9	yes	maximal, complemented
4	C₃²×C₉×C₁₃	C₉	1	3	yes	—
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₁₃×C₂₇⋊C₃	—	3	9	no	—
7	C₃×C₁₃×C₂₇	C₃²	1	9	yes	—
8	C₉²×C₁₃	C₉	1	2	yes	—
9	C₉²×C₁₃	C₉	1	3	yes	—
10	C₉²×C₁₃	C₉	1	1	yes	characteristic
11	C₉²×C₁₃	C₃²	1	3	yes	—
12	#10624706	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₁₃	—	3	9	no	—
15	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
16	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
19	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	—
20	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
21	C₁₃×C₂₇	—	3	9	no	—
22	C₃×C₂₇⋊C₃	C₃×C₁₃	1	3	yes	—
23	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
24	C₉⋊C₂₇	C₃×C₁₃	1	9	yes	complemented
25	C₃²×C₁₃	—	3	3	no	—
26	C₃²×C₁₃	C₉⋊C₉	1	3	yes	—
27	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
28	C₉×C₁₃	—	3	6	no	—
29	C₉×C₁₃	C₉⋊C₉	1	3	yes	—
30	C₉×C₁₃	C₉⋊C₉	1	3	yes	—
31	C₉×C₁₃	C₂₇⋊C₃	1	9	yes	complemented
32	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
33	C₃²×C₉	C₉×C₁₃	1	3	yes	—
34	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
35	C₂₇⋊C₃	—	3	9	no	—
36	C₃×C₂₇	C₃²×C₁₃	1	9	yes	—
37	C₉²	C₉×C₁₃	1	2	yes	—
38	C₉²	C₉×C₁₃	1	3	yes	—
39	C₉²	C₉×C₁₃	1	1	yes	characteristic
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	C₃×C₂₇⋊C₃	1	3	yes	—
44	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
45	C₃×C₉	—	3	9	no	—
46	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
47	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
48	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
49	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
50	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	—
51	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
52	C₂₇	—	3	9	no	—
53	C₁₃	#10624706	1	1	yes	characteristic, direct product factor, Sylow
54	C₃²	—	3	3	no	—
55	C₃²	C₁₃×C₉⋊C₉	1	3	yes	—
56	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
57	C₉	—	3	6	no	—
58	C₉	C₁₃×C₉⋊C₉	1	3	yes	—
59	C₉	C₁₃×C₉⋊C₉	1	3	yes	—
60	C₉	C₁₃×C₂₇⋊C₃	1	9	yes	complemented
61	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
62	C₃	—	3	3	no	—
63	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic
64	C₃	C₃×C₁₃×C₂₇⋊C₃	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
3. C₁₃×C₉⋊C₂₇	C₃	semidirect
12. #10624706	C₁₃	direct (N × H)
24. C₉⋊C₂₇	C₃×C₁₃	semidirect
31. C₉×C₁₃	C₂₇⋊C₃	semidirect
53. C₁₃	#10624706	direct (N × H)
60. C₉	C₁₃×C₂₇⋊C₃	semidirect

Subgroups — C13×#10624706 #23744857

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624706 #23744857