Subgroups — C₃×C₃⋊#13091733 #27190294

Order 13140.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₃₆₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13091733	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#13091733	—	3	1	no	maximal
4	C₃²×C₅×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₃⋊#64408	—	5	1	no	maximal, Hall
6	C₃×D₃₆₅	—	2	1	no	—
7	C₃×D₃₆₅	D₃	1	1	yes	characteristic
8	C₃×D₃₆₅	C₂×C₃	1	1	yes	characteristic
9	#13091733	—	3	1	no	Hall
10	C₃²×D₇₃	—	5	1	no	—
11	C₃×C₅×C₇₃	—	2	1	no	—
12	C₃×C₅×C₇₃	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃⋊#64408	—	5	1	no	—
15	C₃×#64408	—	15	1	no	—
16	D₃₆₅	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₃×D₇₃	—	5	1	no	—
19	C₃×D₇₃	—	5	1	no	—
20	C₃×D₇₃	—	10	1	no	—
21	C₅×C₇₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	#64408	—	15	1	no	Hall
23	C₃×C₇₃	—	2	1	no	—
24	C₃×C₇₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	C₃×C₇₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
26	C₃×ΓL(1,𝔽₁₆)	—	73	1	no	maximal, Hall
27	D₇₃	—	5	1	no	—
28	C₃²×D₅	—	73	1	no	—
29	C₇₃	C₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₁₆)	—	73	1	no	—
31	C₃×AGL(1,𝔽₅)	—	219	1	no	—
32	C₃²×C₅	#64408	1	1	yes	characteristic, complemented, Hall
33	C₃×Dic₃	—	365	1	no	Hall
34	C₃×D₅	—	73	1	no	—
35	C₃×D₅	—	73	1	no	—
36	C₃×D₅	—	146	1	no	—
37	AGL(1,𝔽₅)	—	219	1	no	Hall
38	C₂×C₃²	—	365	1	no	—
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃×#64408	1	1	yes	characteristic, complemented
41	C₃×C₅	C₃⋊#64408	1	1	yes	characteristic, complemented
42	C₃×C₄	—	1095	1	no	—
43	Dic₃	—	365	1	no	—
44	D₅	—	73	1	no	—
45	C₃²	#13091733	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	365	1	no	—
47	C₂×C₃	—	365	1	no	—
48	C₂×C₃	—	730	1	no	—
49	C₅	C₃×C₃⋊#64408	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	1095	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×#13091733	1	1	yes	characteristic, complemented
53	C₃	C₃⋊#13091733	1	1	yes	characteristic, direct product factor
54	C₂	—	365	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#13091733
commutator, hypocenter	C₃×C₅×C₇₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₃	C₄
prime radical	C₃²×D₃₆₅	C₂
cosocle	C₃×D₃₆₅	C₂×C₃
LCS	G ▷ C₃×C₅×C₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#13091733	C₃	direct (N × H)
4. C₃²×C₅×C₇₃	C₄	semidirect
12. C₃×C₅×C₇₃	Dic₃	semidirect
13. C₃×C₅×C₇₃	C₃×C₄	semidirect
17. C₃²×C₇₃	AGL(1,𝔽₅)	semidirect
21. C₅×C₇₃	C₃×Dic₃	semidirect
24. C₃×C₇₃	C₃×AGL(1,𝔽₅)	semidirect
25. C₃×C₇₃	ΓL(1,𝔽₁₆)	semidirect
29. C₇₃	C₃×ΓL(1,𝔽₁₆)	semidirect
32. C₃²×C₅	#64408	semidirect
40. C₃×C₅	C₃×#64408	semidirect
41. C₃×C₅	C₃⋊#64408	semidirect
45. C₃²	#13091733	semidirect
49. C₅	C₃×C₃⋊#64408	semidirect
52. C₃	C₃×#13091733	semidirect
53. C₃	C₃⋊#13091733	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×D₃₆₅	2
C₃⋊#13091733	3
C₃×#13091733	3
C₃×C₃⋊#64408	5
C₃×ΓL(1,𝔽₁₆)	73

Subgroups — C3×C3⋊#13091733 #27190294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#13091733 #27190294