Subgroups — C₇₃×C₃⋊ΓL(1,𝔽₁₆) #27190304

Order 13140.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₇₃	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₁₆)×C₇₃	—	3	4	no	maximal
3	C₃²×C₅×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₃×C₇₃	—	5	1	no	maximal, Hall
5	C₃×D₅×C₇₃	D₃	1	4	yes	—
6	AGL(1,𝔽₅)×C₇₃	—	9	1	no	Hall
7	C₂×C₃²×C₇₃	—	5	1	no	—
8	C₃×C₅×C₇₃	Dic₃	1	4	yes	complemented
9	Dic₃×C₇₃	—	15	4	no	—
10	D₅×C₇₃	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇₃	—	5	4	no	—
13	C₅×C₇₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
14	C₄×C₇₃	—	45	1	no	Hall
15	C₃×C₇₃	ΓL(1,𝔽₁₆)	1	4	yes	complemented
16	C₃⋊ΓL(1,𝔽₁₆)	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₇₃	—	5	1	no	—
18	C₃²×D₅	C₂×C₇₃	1	1	yes	characteristic
19	C₇₃	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
20	ΓL(1,𝔽₁₆)	—	3	4	no	—
21	C₃²×C₅	C₄×C₇₃	1	1	yes	characteristic, complemented, Hall
22	C₃⋊Dic₃	—	5	1	no	Hall
23	C₃×D₅	D₃×C₇₃	1	4	yes	—
24	AGL(1,𝔽₅)	—	9	1	no	Hall
25	C₂×C₃²	—	5	1	no	—
26	C₃×C₅	Dic₃×C₇₃	1	4	yes	complemented
27	Dic₃	—	15	4	no	—
28	D₅	C₃⋊D₃×C₇₃	1	1	yes	characteristic
29	C₃²	AGL(1,𝔽₅)×C₇₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	4	no	—
31	C₅	C₃⋊Dic₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	45	1	no	Sylow
33	C₃	ΓL(1,𝔽₁₆)×C₇₃	1	4	yes	complemented
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₇₃	C₃⋊ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃²×C₅	C₄×C₇₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₃	C₄
prime radical	C₃²×D₅×C₇₃	C₂
cosocle	C₃²×D₅	C₂×C₇₃
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇₃

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅×C₇₃	C₄	semidirect
8. C₃×C₅×C₇₃	Dic₃	semidirect
11. C₃²×C₇₃	AGL(1,𝔽₅)	semidirect
13. C₅×C₇₃	C₃⋊Dic₃	semidirect
15. C₃×C₇₃	ΓL(1,𝔽₁₆)	semidirect
16. C₃⋊ΓL(1,𝔽₁₆)	C₇₃	direct (N × H)
19. C₇₃	C₃⋊ΓL(1,𝔽₁₆)	direct (N × H)
21. C₃²×C₅	C₄×C₇₃	semidirect
26. C₃×C₅	Dic₃×C₇₃	semidirect
29. C₃²	AGL(1,𝔽₅)×C₇₃	semidirect
31. C₅	C₃⋊Dic₃×C₇₃	semidirect
33. C₃	ΓL(1,𝔽₁₆)×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₅×C₇₃	2
ΓL(1,𝔽₁₆)×C₇₃	3
C₃⋊Dic₃×C₇₃	5
C₃⋊ΓL(1,𝔽₁₆)	73

Subgroups — C73×C3⋊ΓL(1,𝔽16) #27190304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×C₃⋊ΓL(1,𝔽₁₆) #27190304