Subgroups — C₁₃×C₂₇⋊H(3,𝔽₃) #23744866

Order 9477.

256 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, complemented
2	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	C₁₃×C₃²⋊C₂₇	C₃	1	6	yes	maximal, complemented
5	C₁₃×C₃²⋊C₂₇	C₃	1	2	yes	maximal, complemented
6	C₃×C₁₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₁₃×C₂₇⋊C₃	—	3	9	no	—
10	C₃×C₁₃×C₂₇	—	3	3	no	—
11	C₃×C₁₃×C₂₇	C₃²	1	2	yes	—
12	C₃×C₁₃×C₂₇	C₃²	1	6	yes	—
13	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
14	C₁₃×C₃²⋊C₉	C₉	1	6	yes	—
15	C₁₃×C₃²⋊C₉	C₉	1	2	yes	—
16	C₂₇⋊H(3,𝔽₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	C₃×C₉	1	3	yes	—
18	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
19	C₁₃×H(3,𝔽₃)	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	1	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	2	no	—
23	C₃×C₉×C₁₃	—	3	6	no	—
24	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
25	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
26	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
27	C₁₃×C₂₇	—	3	2	no	—
28	C₁₃×C₂₇	—	3	6	no	—
29	C₁₃×C₂₇	H(3,𝔽₃)	1	3	yes	complemented
30	C₃×C₂₇⋊C₃	C₃×C₁₃	1	3	yes	complemented
31	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic, complemented
32	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
33	C₃²⋊C₂₇	C₃×C₁₃	1	6	yes	complemented
34	C₃²⋊C₂₇	C₃×C₁₃	1	2	yes	complemented
35	C₃²×C₁₃	—	3	1	no	—
36	C₃²×C₁₃	—	3	2	no	—
37	C₃²×C₁₃	—	3	3	no	—
38	C₃²×C₁₃	—	3	3	no	—
39	C₃²×C₁₃	—	3	6	no	—
40	C₃²×C₁₃	C₂₇⋊C₃	1	3	yes	complemented
41	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
42	C₉×C₁₃	—	3	2	no	—
43	C₉×C₁₃	—	3	6	no	—
44	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
45	C₉×C₁₃	#737	1	2	yes	—
46	C₃×H(3,𝔽₃)	C₉×C₁₃	1	1	yes	characteristic
47	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
48	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
49	C₂₇⋊C₃	—	3	9	no	—
50	C₃×C₂₇	—	3	3	no	—
51	C₃×C₂₇	C₃²×C₁₃	1	2	yes	—
52	C₃×C₂₇	C₃²×C₁₃	1	6	yes	—
53	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
54	C₃²⋊C₉	C₉×C₁₃	1	6	yes	—
55	C₃²⋊C₉	C₉×C₁₃	1	2	yes	—
56	C₃×C₁₃	—	3	3	no	—
57	C₃×C₁₃	—	9	3	no	—
58	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
59	C₃×C₁₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic
60	C₃×C₁₃	#6903	1	2	yes	—
61	C₃³	C₃×C₉×C₁₃	1	3	yes	—
62	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
63	H(3,𝔽₃)	—	3	3	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
69	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
70	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
71	C₂₇	—	3	2	no	—
72	C₂₇	—	3	6	no	—
73	C₂₇	C₁₃×H(3,𝔽₃)	1	3	yes	complemented
74	C₁₃	C₂₇⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	3	3	no	—
79	C₃²	—	3	6	no	—
80	C₃²	C₁₃×C₂₇⋊C₃	1	3	yes	complemented
81	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
82	C₉	—	3	2	no	—
83	C₉	—	3	6	no	—
84	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
85	C₉	C₁₃×#737	1	2	yes	—
86	C₃	—	3	3	no	—
87	C₃	—	9	3	no	—
88	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
89	C₃	C₃×C₁₃×C₂₇⋊C₃	1	1	yes	characteristic
90	C₃	C₁₃×#6903	1	2	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	C₃×C₁₃×H(3,𝔽₃)	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
1. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
2. C₃²×C₁₃×C₂₇	C₃	semidirect
4. C₁₃×C₃²⋊C₂₇	C₃	semidirect
5. C₁₃×C₃²⋊C₂₇	C₃	semidirect
16. C₂₇⋊H(3,𝔽₃)	C₁₃	direct (N × H)
29. C₁₃×C₂₇	H(3,𝔽₃)	semidirect
30. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
31. C₃²×C₂₇	C₃×C₁₃	semidirect
33. C₃²⋊C₂₇	C₃×C₁₃	semidirect
34. C₃²⋊C₂₇	C₃×C₁₃	semidirect
40. C₃²×C₁₃	C₂₇⋊C₃	semidirect
73. C₂₇	C₁₃×H(3,𝔽₃)	semidirect
74. C₁₃	C₂₇⋊H(3,𝔽₃)	direct (N × H)
80. C₃²	C₁₃×C₂₇⋊C₃	semidirect

Subgroups — C13×C27⋊H(3,𝔽3) #23744866

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₂₇⋊H(3,𝔽₃) #23744866