Finite Group Databasebeta

← C₅×C₄₃×D₇₃ #44536017

Subgroups — C₅×C₄₃×D₇₃ #44536017

Order 31390.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₇₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₄₃	—	73	1	no	maximal, Hall
6	C₅×C₇₃	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
7	C₅×C₄₃	D₇₃	1	1	yes	characteristic, direct product factor, Hall
8	D₇₃	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₄₃	—	73	1	no	Hall
10	C₇₃	C₂×C₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
11	C₄₃	C₅×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	73	1	no	Hall
13	C₅	C₄₃×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	73	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₄₃	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂×C₅×C₄₃
Frattini	C₁	G
Fitting, socle	C₅×C₄₃×C₇₃	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₅×C₄₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₃×C₇₃	C₂	semidirect
2. C₄₃×D₇₃	C₅	direct (N × H)
3. C₄₃×C₇₃	C₂×C₅	semidirect
4. C₅×D₇₃	C₄₃	direct (N × H)
6. C₅×C₇₃	C₂×C₄₃	semidirect
7. C₅×C₄₃	D₇₃	direct (N × H)
8. D₇₃	C₅×C₄₃	direct (N × H)
10. C₇₃	C₂×C₅×C₄₃	semidirect
11. C₄₃	C₅×D₇₃	direct (N × H)
13. C₅	C₄₃×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₄₃×C₇₃	2
C₄₃×D₇₃	5
C₅×D₇₃	43
C₂×C₅×C₄₃	73