Subgroups — C₃×C₁₃×#6875 #23744859

Order 9477.

212 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	C₃×C₁₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#6875	C₃	1	9	yes	maximal, direct product factor
5	C₃²×C₉×C₁₃	—	3	1	no	—
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₁₃×C₂₇⋊C₃	—	3	4	no	—
8	C₁₃×C₂₇⋊C₃	C₉	1	6	yes	complemented
9	C₁₃×C₂₇⋊C₃	C₃²	1	6	yes	—
10	C₁₃×C₂₇⋊C₃	C₃²	1	3	yes	—
11	C₃×C₁₃×C₂₇	—	3	2	no	—
12	C₃×C₁₃×C₂₇	C₉	1	3	yes	complemented
13	C₁₃×C₉⋊C₉	—	3	2	no	—
14	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
15	C₃×#6875	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	3₋¹⁺²	1	1	yes	characteristic
17	C₃×C₉×C₁₃	—	3	3	no	—
18	C₃×C₉×C₁₃	—	9	3	no	—
19	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
20	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
22	C₃×C₉×C₁₃	3₋¹⁺²	1	4	yes	—
23	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
24	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
25	C₁₃×C₂₇	—	3	6	no	—
26	C₁₃×C₂₇	C₃×C₉	1	9	yes	complemented
27	C₃×C₂₇⋊C₃	C₃×C₁₃	1	2	yes	—
28	C₃×C₂₇⋊C₃	C₃×C₁₃	1	1	yes	characteristic
29	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
30	#6875	C₃×C₁₃	1	9	yes	direct product factor
31	C₃²×C₁₃	—	3	3	no	—
32	C₃²×C₁₃	C₉⋊C₉	1	2	yes	—
33	C₃²×C₁₃	C₉⋊C₉	1	1	yes	characteristic
34	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₉×C₁₃	—	9	3	no	—
36	C₉×C₁₃	C₉⋊C₉	1	4	yes	—
37	C₉×C₁₃	C₉⋊C₉	1	2	yes	—
38	C₉×C₁₃	C₃²×C₉	1	1	yes	characteristic
39	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
40	C₃²×C₉	—	3	1	no	—
41	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
42	C₂₇⋊C₃	—	3	4	no	—
43	C₂₇⋊C₃	C₉×C₁₃	1	6	yes	complemented
44	C₂₇⋊C₃	C₃²×C₁₃	1	6	yes	—
45	C₂₇⋊C₃	C₃²×C₁₃	1	3	yes	—
46	C₃×C₂₇	—	3	2	no	—
47	C₃×C₂₇	C₉×C₁₃	1	3	yes	complemented
48	C₉⋊C₉	—	3	2	no	—
49	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
50	C₃×C₁₃	—	3	1	no	—
51	C₃×C₁₃	—	3	2	no	—
52	C₃×C₁₃	#6875	1	3	yes	direct product factor
53	C₃×C₁₃	C₃×C₉⋊C₉	1	1	yes	characteristic
54	C₃³	C₁₃×3₋¹⁺²	1	1	yes	characteristic
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	9	3	no	—
57	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
58	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
59	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
60	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
61	C₃×C₉	C₁₃×3₋¹⁺²	1	4	yes	—
62	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
63	C₂₇	—	3	6	no	—
64	C₂₇	C₃×C₉×C₁₃	1	9	yes	complemented
65	C₁₃	C₃×#6875	1	1	yes	characteristic, direct product factor, Sylow
66	C₃²	—	3	3	no	—
67	C₃²	C₁₃×C₉⋊C₉	1	2	yes	—
68	C₃²	C₁₃×C₉⋊C₉	1	1	yes	characteristic
69	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
70	C₉	—	9	3	no	—
71	C₉	C₁₃×C₉⋊C₉	1	2	yes	—
72	C₉	C₁₃×C₉⋊C₉	1	4	yes	—
73	C₉	C₃²×C₉×C₁₃	1	1	yes	characteristic
74	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
75	C₃	—	3	1	no	—
76	C₃	—	3	2	no	—
77	C₃	C₁₃×#6875	1	3	yes	direct product factor
78	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₁₃	C₉⋊C₉
commutator	C₉	C₃²×C₉×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
prime radical	C₃³×C₁₃	3₋¹⁺²
LCS	G ▷ C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#6875	C₃	direct (N × H)
8. C₁₃×C₂₇⋊C₃	C₉	semidirect
12. C₃×C₁₃×C₂₇	C₉	semidirect
15. C₃×#6875	C₁₃	direct (N × H)
26. C₁₃×C₂₇	C₃×C₉	semidirect
30. #6875	C₃×C₁₃	direct (N × H)
43. C₂₇⋊C₃	C₉×C₁₃	semidirect
47. C₃×C₂₇	C₉×C₁₃	semidirect
52. C₃×C₁₃	#6875	direct (N × H)
64. C₂₇	C₃×C₉×C₁₃	semidirect
65. C₁₃	C₃×#6875	direct (N × H)
77. C₃	C₁₃×#6875	direct (N × H)

Subgroups — C3×C13×#6875 #23744859

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6875 #23744859