Subgroups — C₁₃×C₂₇×H(3,𝔽₃) #23744865

Order 9477.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₂₇	C₃	1	4	yes	maximal, complemented
2	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₁₃×C₃²⋊C₂₇	C₃	1	8	yes	maximal, complemented
4	C₃×C₁₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
6	C₃×C₁₃×C₂₇	—	3	12	no	—
7	C₃×C₁₃×C₂₇	C₃²	1	8	yes	—
8	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
9	C₁₃×C₃²⋊C₉	C₉	1	8	yes	—
10	C₂₇×H(3,𝔽₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	C₃×C₉	1	4	yes	—
12	C₁₃×H(3,𝔽₃)	C₂₇	1	9	yes	direct product factor
13	C₃×C₉×C₁₃	—	3	4	no	—
14	C₃×C₉×C₁₃	—	3	8	no	—
15	C₃×C₉×C₁₃	C₃×C₉	1	8	yes	—
16	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×C₂₇	—	3	8	no	—
18	C₁₃×C₂₇	H(3,𝔽₃)	1	3	yes	direct product factor
19	C₃²×C₂₇	C₃×C₁₃	1	4	yes	complemented
20	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
21	C₃²⋊C₂₇	C₃×C₁₃	1	8	yes	complemented
22	C₃²×C₁₃	—	3	4	no	—
23	C₃²×C₁₃	—	3	8	no	—
24	C₃²×C₁₃	C₃×C₂₇	1	12	yes	complemented
25	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
26	C₉×C₁₃	—	3	8	no	—
27	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₉×C₁₃	#737	1	2	yes	—
29	C₃×H(3,𝔽₃)	C₉×C₁₃	1	1	yes	characteristic
30	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
31	C₃×C₂₇	—	3	12	no	—
32	C₃×C₂₇	C₃²×C₁₃	1	8	yes	—
33	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
34	C₃²⋊C₉	C₉×C₁₃	1	8	yes	—
35	C₃×C₁₃	—	3	12	no	—
36	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
37	C₃×C₁₃	C₃²×C₂₇	1	1	yes	characteristic
38	C₃×C₁₃	#6903	1	2	yes	—
39	C₃³	C₃×C₉×C₁₃	1	4	yes	—
40	H(3,𝔽₃)	C₁₃×C₂₇	1	9	yes	direct product factor
41	C₃×C₉	—	3	4	no	—
42	C₃×C₉	—	3	8	no	—
43	C₃×C₉	C₃×C₉×C₁₃	1	8	yes	—
44	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
45	C₂₇	—	3	8	no	—
46	C₂₇	C₁₃×H(3,𝔽₃)	1	3	yes	direct product factor
47	C₁₃	C₂₇×H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
48	C₃²	—	3	4	no	—
49	C₃²	—	3	8	no	—
50	C₃²	C₃×C₁₃×C₂₇	1	12	yes	complemented
51	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
52	C₉	—	3	8	no	—
53	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
54	C₉	C₁₃×#737	1	2	yes	—
55	C₃	—	3	12	no	—
56	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
57	C₃	C₃²×C₁₃×C₂₇	1	1	yes	characteristic
58	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	C₃×C₁₃×H(3,𝔽₃)	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
1. C₃²×C₁₃×C₂₇	C₃	semidirect
3. C₁₃×C₃²⋊C₂₇	C₃	semidirect
10. C₂₇×H(3,𝔽₃)	C₁₃	direct (N × H)
12. C₁₃×H(3,𝔽₃)	C₂₇	direct (N × H)
18. C₁₃×C₂₇	H(3,𝔽₃)	direct (N × H)
19. C₃²×C₂₇	C₃×C₁₃	semidirect
21. C₃²⋊C₂₇	C₃×C₁₃	semidirect
24. C₃²×C₁₃	C₃×C₂₇	semidirect
40. H(3,𝔽₃)	C₁₃×C₂₇	direct (N × H)
46. C₂₇	C₁₃×H(3,𝔽₃)	direct (N × H)
47. C₁₃	C₂₇×H(3,𝔽₃)	direct (N × H)
50. C₃²	C₃×C₁₃×C₂₇	semidirect

Subgroups — C13×C27×H(3,𝔽3) #23744865

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₂₇×H(3,𝔽₃) #23744865