Finite Group Databasebeta

← C₃×D₅₂₉₃ #44540869

Subgroups — C₃×D₅₂₉₃ #44540869

Order 31758.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₇×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₉₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₇×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₉	—	67	1	no	maximal, Hall
5	C₃×D₆₇	—	79	1	no	maximal, Hall
6	C₃×C₇₉	D₆₇	1	1	yes	characteristic, complemented, Hall
7	C₃×C₆₇	D₇₉	1	1	yes	characteristic, complemented, Hall
8	D₇₉	—	67	1	no	Hall
9	D₆₇	—	79	1	no	Hall
10	C₇₉	C₃×D₆₇	1	1	yes	characteristic, complemented, Sylow
11	C₆₇	C₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	5293	1	no	Hall
13	C₃	D₅₂₉₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	5293	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₂₉₃
commutator, cosocle, hypocenter	C₆₇×C₇₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₆₇×C₇₉	C₂
LCS	G ▷ C₆₇×C₇₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₆₇×C₇₉	C₂	semidirect
2. D₅₂₉₃	C₃	direct (N × H)
3. C₆₇×C₇₉	C₂×C₃	semidirect
6. C₃×C₇₉	D₆₇	semidirect
7. C₃×C₆₇	D₇₉	semidirect
10. C₇₉	C₃×D₆₇	semidirect
11. C₆₇	C₃×D₇₉	semidirect
13. C₃	D₅₂₉₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₆₇×C₇₉	2
D₅₂₉₃	3
C₃×D₇₉	67
C₃×D₆₇	79