Subgroups — C₁₃⋊C₃×H(5,𝔽₃) #23748614

Order 9477.

6776 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊H(5,𝔽₃)	C₃	1	80	yes	maximal, complemented
2	C₃×H(3,𝔽₃)×C₁₃⋊C₃	C₃	1	40	yes	maximal, complemented
3	C₁₃×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₁₃⋊C₃	C₃²	1	40	yes	complemented
5	C₃×C₃²⋊(C₁₃⋊C₃)	C₃²	1	320	yes	complemented
6	H(3,𝔽₃)×C₁₃⋊C₃	C₃²	1	90	yes	complemented
7	H(3,𝔽₃)×C₁₃⋊C₃	C₃²	1	720	yes	complemented
8	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	40	yes	complemented
9	C₃×H(5,𝔽₃)	—	13	1	no	maximal, Sylow
10	C₃³×C₁₃	C₃³	1	40	yes	complemented
11	C₃²×C₁₃⋊C₃	—	9	120	no	—
12	C₃²×C₁₃⋊C₃	C₃³	1	40	yes	—
13	C₃²×C₁₃⋊C₃	C₃³	1	320	yes	complemented
14	C₁₃×H(3,𝔽₃)	C₃³	1	90	yes	complemented
15	C₃²⋊(C₁₃⋊C₃)	C₃³	1	720	yes	complemented
16	H(5,𝔽₃)	—	13	80	no	—
17	H(5,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₃²×H(3,𝔽₃)	—	13	40	no	—
19	C₃²×C₁₃	—	9	40	no	—
20	C₃²×C₁₃	C₃⁴	1	40	yes	—
21	C₃×C₁₃⋊C₃	—	3	120	no	—
22	C₃×C₁₃⋊C₃	—	9	320	no	—
23	C₃×C₁₃⋊C₃	C₃⁴	1	80	yes	—
24	C₃×C₁₃⋊C₃	C₃⁴	1	1	yes	characteristic
25	C₃⁴	—	13	40	no	—
26	C₃×H(3,𝔽₃)	—	13	320	no	—
27	C₃×H(3,𝔽₃)	—	13	90	no	—
28	C₃×H(3,𝔽₃)	—	13	720	no	—
29	C₃×H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	40	yes	complemented
30	C₃×C₁₃	—	3	40	no	—
31	C₃×C₁₃	C₃⁵	1	1	yes	characteristic
32	C₁₃⋊C₃	—	3	80	no	—
33	C₁₃⋊C₃	H(5,𝔽₃)	1	3	yes	direct product factor
34	C₃³	—	13	40	no	—
35	C₃³	—	13	320	no	—
36	C₃³	—	117	120	no	—
37	C₃³	C₃²×C₁₃⋊C₃	1	40	yes	complemented
38	H(3,𝔽₃)	—	13	720	no	—
39	H(3,𝔽₃)	C₃²×C₁₃⋊C₃	1	90	yes	complemented
40	C₁₃	C₃×H(5,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
41	C₃²	—	9	40	no	—
42	C₃²	—	13	1	no	—
43	C₃²	—	13	80	no	—
44	C₃²	—	39	120	no	—
45	C₃²	—	117	320	no	—
46	C₃²	C₃³×C₁₃⋊C₃	1	40	yes	—
47	C₃	—	3	40	no	—
48	C₃	—	13	3	no	—
49	C₃	—	39	80	no	—
50	C₃	C₃⁴×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃⁴×C₁₃⋊C₃
commutator, socle, cosocle	C₃×C₁₃	C₃⁵
Fitting	C₁₃×H(5,𝔽₃)	C₃
hypercenter	H(5,𝔽₃)	C₁₃⋊C₃
hypocenter	C₁₃	C₃×H(5,𝔽₃)
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃ ◁ H(5,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊H(5,𝔽₃)	C₃	semidirect
2. C₃×H(3,𝔽₃)×C₁₃⋊C₃	C₃	semidirect
3. C₁₃×H(5,𝔽₃)	C₃	semidirect
4. C₃³×C₁₃⋊C₃	C₃²	semidirect
5. C₃×C₃²⋊(C₁₃⋊C₃)	C₃²	semidirect
6. H(3,𝔽₃)×C₁₃⋊C₃	C₃²	semidirect
7. H(3,𝔽₃)×C₁₃⋊C₃	C₃²	semidirect
8. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
10. C₃³×C₁₃	C₃³	semidirect
13. C₃²×C₁₃⋊C₃	C₃³	semidirect
14. C₁₃×H(3,𝔽₃)	C₃³	semidirect
15. C₃²⋊(C₁₃⋊C₃)	C₃³	semidirect
17. H(5,𝔽₃)	C₁₃⋊C₃	direct (N × H)
29. C₃×H(3,𝔽₃)	C₃×C₁₃⋊C₃	semidirect
33. C₁₃⋊C₃	H(5,𝔽₃)	direct (N × H)
37. C₃³	C₃²×C₁₃⋊C₃	semidirect
39. H(3,𝔽₃)	C₃²×C₁₃⋊C₃	semidirect
40. C₁₃	C₃×H(5,𝔽₃)	semidirect

Subgroups — C13⋊C3×H(5,𝔽3) #23748614

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃⋊C₃×H(5,𝔽₃) #23748614