Subgroups — C₃×C₁₃×C₃²⋊C₂₇ #23744833

Order 9477.

464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₂₇	C₃	1	3	yes	maximal, complemented
3	C₁₃×C₃²⋊C₂₇	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	3	no	—
6	C₃²×C₉×C₁₃	—	3	6	no	—
7	C₃²×C₉×C₁₃	C₉	1	2	yes	—
8	C₃²×C₉×C₁₃	C₉	1	6	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₃×C₁₃×C₂₇	—	3	9	no	—
12	C₃×C₁₃×C₂₇	C₃²	1	9	yes	complemented
13	C₃×C₃²⋊C₂₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	3	3	no	—
15	C₃³×C₁₃	—	3	6	no	—
16	C₃³×C₁₃	C₂₇	1	9	yes	complemented
17	C₃³×C₁₃	C₃×C₉	1	3	yes	—
18	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₁₃	—	3	6	no	—
20	C₃×C₉×C₁₃	—	3	18	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
24	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
25	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
26	C₃×C₉×C₁₃	3₋¹⁺²	1	6	yes	—
27	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
28	C₁₃×C₂₇	—	3	9	no	—
29	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
30	C₃²×C₂₇	C₃×C₁₃	1	3	yes	complemented
31	C₃²⋊C₂₇	C₃×C₁₃	1	9	yes	direct product factor
32	C₃²×C₁₃	—	3	27	no	—
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	3	6	no	—
35	C₃²×C₁₃	C₃²⋊C₉	1	3	yes	—
36	C₃²×C₁₃	C₃×C₂₇	1	3	yes	—
37	C₃²×C₁₃	C₃×C₂₇	1	9	yes	complemented
38	C₃²×C₁₃	C₂₇⋊C₃	1	6	yes	—
39	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
40	C₉×C₁₃	—	3	6	no	—
41	C₉×C₁₃	C₃²⋊C₉	1	6	yes	—
42	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₉×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
44	C₃⁴	C₉×C₁₃	1	1	yes	characteristic
45	C₃²×C₉	—	3	3	no	—
46	C₃²×C₉	—	3	6	no	—
47	C₃²×C₉	C₉×C₁₃	1	2	yes	—
48	C₃²×C₉	C₉×C₁₃	1	6	yes	—
49	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
50	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
51	C₃×C₂₇	—	3	9	no	—
52	C₃×C₂₇	C₃²×C₁₃	1	9	yes	complemented
53	C₃×C₁₃	—	3	9	no	—
54	C₃×C₁₃	C₃²⋊C₂₇	1	9	yes	direct product factor
55	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
56	C₃×C₁₃	C₃²×C₂₇	1	1	yes	characteristic
57	C₃×C₁₃	C₃×C₂₇⋊C₃	1	2	yes	—
58	C₃³	—	3	3	no	—
59	C₃³	—	3	6	no	—
60	C₃³	C₁₃×C₂₇	1	9	yes	complemented
61	C₃³	C₃×C₉×C₁₃	1	3	yes	—
62	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
63	C₃×C₉	—	3	6	no	—
64	C₃×C₉	—	3	18	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	3	6	no	—
67	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
68	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
69	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
70	C₃×C₉	C₁₃×3₋¹⁺²	1	6	yes	—
71	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
72	C₂₇	—	3	9	no	—
73	C₁₃	C₃×C₃²⋊C₂₇	1	1	yes	characteristic, direct product factor, Sylow
74	C₃²	—	3	27	no	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	6	no	—
77	C₃²	C₁₃×C₃²⋊C₉	1	3	yes	—
78	C₃²	C₃×C₁₃×C₂₇	1	3	yes	—
79	C₃²	C₃×C₁₃×C₂₇	1	9	yes	complemented
80	C₃²	C₁₃×C₂₇⋊C₃	1	6	yes	—
81	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
82	C₉	—	3	6	no	—
83	C₉	C₁₃×C₃²⋊C₉	1	6	yes	—
84	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
85	C₉	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
86	C₃	—	3	9	no	—
87	C₃	C₁₃×C₃²⋊C₂₇	1	9	yes	direct product factor
88	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic
89	C₃	C₃²×C₁₃×C₂₇	1	1	yes	characteristic
90	C₃	C₃×C₁₃×C₂₇⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₃²×C₉×C₁₃	C₃²
commutator	C₃	C₃²×C₁₃×C₂₇
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃³×C₁₃	C₃×C₉
prime radical	C₃⁴×C₁₃	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₃×C₂₇	C₃	semidirect
3. C₁₃×C₃²⋊C₂₇	C₃	direct (N × H)
12. C₃×C₁₃×C₂₇	C₃²	semidirect
13. C₃×C₃²⋊C₂₇	C₁₃	direct (N × H)
16. C₃³×C₁₃	C₂₇	semidirect
30. C₃²×C₂₇	C₃×C₁₃	semidirect
31. C₃²⋊C₂₇	C₃×C₁₃	direct (N × H)
37. C₃²×C₁₃	C₃×C₂₇	semidirect
52. C₃×C₂₇	C₃²×C₁₃	semidirect
54. C₃×C₁₃	C₃²⋊C₂₇	direct (N × H)
60. C₃³	C₁₃×C₂₇	semidirect
73. C₁₃	C₃×C₃²⋊C₂₇	direct (N × H)
79. C₃²	C₃×C₁₃×C₂₇	semidirect
87. C₃	C₁₃×C₃²⋊C₂₇	direct (N × H)

Subgroups — C3×C13×C32⋊C27 #23744833

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×C₃²⋊C₂₇ #23744833