Subgroups — C₁₃×C₂₇×3₋¹⁺² #23744877

Order 9477.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₁₃×C₉⋊C₂₇	C₃	1	6	yes	maximal, complemented
4	C₁₃×C₃²⋊C₂₇	C₃	1	2	yes	maximal
5	C₉×C₁₃×C₂₇	C₃	1	3	yes	maximal, complemented
6	C₃×C₁₃×3₋¹⁺²	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×C₂₇	—	3	3	no	—
9	C₃×C₁₃×C₂₇	C₃²	1	6	yes	—
10	C₃×C₁₃×C₂₇	C₃²	1	2	yes	—
11	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
12	C₁₃×C₉⋊C₉	C₉	1	6	yes	—
13	C₁₃×C₃²⋊C₉	C₉	1	2	yes	—
14	C₉²×C₁₃	C₃²	1	3	yes	—
15	C₂₇×3₋¹⁺²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
17	C₁₃×3₋¹⁺²	C₂₇	1	9	yes	direct product factor
18	C₃×C₉×C₁₃	—	3	1	no	—
19	C₃×C₉×C₁₃	—	3	2	no	—
20	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
21	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
22	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
23	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
24	C₁₃×C₂₇	—	3	2	no	—
25	C₁₃×C₂₇	—	3	6	no	—
26	C₁₃×C₂₇	3₋¹⁺²	1	3	yes	direct product factor
27	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic
28	C₉×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
29	C₉⋊C₂₇	C₃×C₁₃	1	6	yes	complemented
30	C₃²⋊C₂₇	C₃×C₁₃	1	2	yes	—
31	C₉×C₂₇	C₃×C₁₃	1	3	yes	complemented
32	C₃²×C₁₃	—	3	1	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	C₃×C₂₇	1	3	yes	—
35	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
36	C₉×C₁₃	—	3	2	no	—
37	C₉×C₁₃	—	3	6	no	—
38	C₉×C₁₃	C₃×C₂₇	1	9	yes	complemented
39	C₉×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
40	C₉×C₁₃	#737	1	2	yes	—
41	C₃×3₋¹⁺²	C₉×C₁₃	1	1	yes	characteristic
42	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
43	C₃×C₂₇	—	3	3	no	—
44	C₃×C₂₇	C₃²×C₁₃	1	6	yes	—
45	C₃×C₂₇	C₃²×C₁₃	1	2	yes	—
46	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
47	C₉⋊C₉	C₉×C₁₃	1	6	yes	—
48	C₃²⋊C₉	C₉×C₁₃	1	2	yes	—
49	C₉²	C₃²×C₁₃	1	3	yes	—
50	C₃×C₁₃	—	3	3	no	—
51	C₃×C₁₃	C₉×3₋¹⁺²	1	1	yes	characteristic
52	C₃×C₁₃	C₃²×C₂₇	1	1	yes	characteristic
53	C₃×C₁₃	#6903	1	2	yes	—
54	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
55	3₋¹⁺²	C₁₃×C₂₇	1	9	yes	direct product factor
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	3	2	no	—
58	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
59	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
60	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
61	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
62	C₂₇	—	3	2	no	—
63	C₂₇	—	3	6	no	—
64	C₂₇	C₁₃×3₋¹⁺²	1	3	yes	direct product factor
65	C₁₃	C₂₇×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₃×C₁₃×C₂₇	1	3	yes	—
69	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
70	C₉	—	3	2	no	—
71	C₉	—	3	6	no	—
72	C₉	C₃×C₁₃×C₂₇	1	9	yes	complemented
73	C₉	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
74	C₉	C₁₃×#737	1	2	yes	—
75	C₃	—	3	3	no	—
76	C₃	C₉×C₁₃×3₋¹⁺²	1	1	yes	characteristic
77	C₃	C₃²×C₁₃×C₂₇	1	1	yes	characteristic
78	C₃	C₁₃×#6903	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×C₉⋊C₂₇	C₃	semidirect
5. C₉×C₁₃×C₂₇	C₃	semidirect
15. C₂₇×3₋¹⁺²	C₁₃	direct (N × H)
17. C₁₃×3₋¹⁺²	C₂₇	direct (N × H)
26. C₁₃×C₂₇	3₋¹⁺²	direct (N × H)
29. C₉⋊C₂₇	C₃×C₁₃	semidirect
31. C₉×C₂₇	C₃×C₁₃	semidirect
38. C₉×C₁₃	C₃×C₂₇	semidirect
55. 3₋¹⁺²	C₁₃×C₂₇	direct (N × H)
64. C₂₇	C₁₃×3₋¹⁺²	direct (N × H)
65. C₁₃	C₂₇×3₋¹⁺²	direct (N × H)
72. C₉	C₃×C₁₃×C₂₇	semidirect

Subgroups — C13×C27×3−1+2 #23744877

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₂₇×3₋¹⁺² #23744877