Subgroups — C₁₃×#10624829 #23744980

Order 9477.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6875	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6869	C₃	1	3	yes	maximal
4	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
5	C₁₃×C₂₇⋊C₃	C₃²	1	9	yes	—
6	C₁₃×C₉⋊C₉	—	3	1	no	—
7	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
8	C₁₃×C₃²⋊C₉	—	3	1	no	—
9	C₉²×C₁₃	—	3	1	no	—
10	#10624829	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	3₋¹⁺²	1	1	yes	characteristic
12	C₃×C₉×C₁₃	—	3	3	no	—
13	C₃×C₉×C₁₃	—	3	3	no	—
14	C₃×C₉×C₁₃	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉×C₁₃	3₋¹⁺²	1	1	yes	characteristic
16	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×C₂₇	—	3	9	no	—
18	#6887	C₃×C₁₃	1	1	yes	characteristic
19	#6875	C₃×C₁₃	1	9	yes	complemented
20	#6869	C₃×C₁₃	1	3	yes	—
21	C₃²×C₁₃	—	3	1	no	—
22	C₃²×C₁₃	—	9	1	no	—
23	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
24	C₉×C₁₃	—	3	1	no	—
25	C₉×C₁₃	—	3	1	no	—
26	C₉×C₁₃	—	9	3	no	—
27	C₉×C₁₃	#737	1	3	yes	—
28	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
29	C₂₇⋊C₃	C₃²×C₁₃	1	9	yes	—
30	C₉⋊C₉	—	3	1	no	—
31	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
32	C₃²⋊C₉	—	3	1	no	—
33	C₉²	—	3	1	no	—
34	C₃×C₁₃	—	3	1	no	—
35	C₃×C₁₃	—	9	1	no	—
36	C₃×C₁₃	#6895	1	1	yes	characteristic
37	C₃³	C₁₃×3₋¹⁺²	1	1	yes	characteristic
38	C₃×C₉	—	3	3	no	—
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	C₁₃×3₋¹⁺²	1	1	yes	characteristic
41	C₃×C₉	C₁₃×3₋¹⁺²	1	1	yes	characteristic
42	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
43	C₂₇	—	3	9	no	—
44	C₁₃	#10624829	1	1	yes	characteristic, direct product factor, Sylow
45	C₃²	—	3	1	no	—
46	C₃²	—	9	1	no	—
47	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	C₁₃×#737	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	C₃	C₁₃×#6895	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	#6895
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
prime radical	C₃³×C₁₃	3₋¹⁺²
LCS	G ▷ C₃×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6875	C₃	semidirect
10. #10624829	C₁₃	direct (N × H)
19. #6875	C₃×C₁₃	semidirect
44. C₁₃	#10624829	direct (N × H)

Subgroups — C13×#10624829 #23744980

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624829 #23744980